TSTP Solution File: ITP248^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP248^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 03:25:36 EDT 2023
% Result : Timeout 299.59s 300.11s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.83/2.88 % Problem : ITP248^1 : TPTP v8.1.2. Released v8.1.0.
% 2.83/2.89 % Command : do_cvc5 %s %d
% 2.89/3.09 % Computer : n024.cluster.edu
% 2.89/3.09 % Model : x86_64 x86_64
% 2.89/3.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.89/3.09 % Memory : 8042.1875MB
% 2.89/3.09 % OS : Linux 3.10.0-693.el7.x86_64
% 2.89/3.09 % CPULimit : 300
% 2.89/3.09 % WCLimit : 300
% 2.89/3.09 % DateTime : Sun Aug 27 12:32:11 EDT 2023
% 2.89/3.09 % CPUTime :
% 5.55/5.80 %----Proving TH0
% 5.55/5.80 %------------------------------------------------------------------------------
% 5.55/5.80 % File : ITP248^1 : TPTP v8.1.2. Released v8.1.0.
% 5.55/5.80 % Domain : Interactive Theorem Proving
% 5.55/5.80 % Problem : Sledgehammer problem VEBT_Bounds 00370_016817
% 5.55/5.80 % Version : [Des22] axioms.
% 5.55/5.80 % English :
% 5.55/5.80
% 5.55/5.80 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.55/5.80 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.55/5.80 % Source : [Des22]
% 5.55/5.80 % Names : 0071_VEBT_Bounds_00370_016817 [Des22]
% 5.55/5.80
% 5.55/5.80 % Status : Theorem
% 5.55/5.80 % Rating : 1.00 v8.1.0
% 5.55/5.80 % Syntax : Number of formulae : 11266 (5746 unt;1015 typ; 0 def)
% 5.55/5.80 % Number of atoms : 28291 (12254 equ; 0 cnn)
% 5.55/5.80 % Maximal formula atoms : 71 ( 2 avg)
% 5.55/5.80 % Number of connectives : 115455 (2850 ~; 521 |;1800 &;99627 @)
% 5.55/5.80 % ( 0 <=>;10657 =>; 0 <=; 0 <~>)
% 5.55/5.80 % Maximal formula depth : 39 ( 6 avg)
% 5.55/5.80 % Number of types : 86 ( 85 usr)
% 5.55/5.80 % Number of type conns : 4218 (4218 >; 0 *; 0 +; 0 <<)
% 5.55/5.80 % Number of symbols : 933 ( 930 usr; 61 con; 0-8 aty)
% 5.55/5.80 % Number of variables : 26000 (2131 ^;23118 !; 751 ?;26000 :)
% 5.55/5.80 % SPC : TH0_THM_EQU_NAR
% 5.55/5.80
% 5.55/5.80 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.55/5.80 % from the van Emde Boas Trees session in the Archive of Formal
% 5.55/5.80 % proofs -
% 5.55/5.80 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.55/5.80 % 2022-02-18 02:07:51.605
% 5.55/5.80 %------------------------------------------------------------------------------
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% 5.55/5.80 thf(ty_n_t__Complex__Ocomplex,type,
% 5.55/5.80 complex: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 5.55/5.80 set_o: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__String__Ochar,type,
% 5.55/5.80 char: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__Real__Oreal,type,
% 5.55/5.80 real: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__Rat__Orat,type,
% 5.55/5.80 rat: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__Num__Onum,type,
% 5.55/5.80 num: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__Nat__Onat,type,
% 5.55/5.80 nat: $tType ).
% 5.55/5.80
% 5.55/5.80 thf(ty_n_t__Int__Oint,type,
% 5.55/5.80 int: $tType ).
% 5.55/5.80
% 5.55/5.80 % Explicit typings (930)
% 5.55/5.80 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 5.55/5.80 archim2889992004027027881ng_rat: rat > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Archimedean__Field_Oceiling_001t__Real__Oreal,type,
% 5.55/5.80 archim7802044766580827645g_real: real > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 5.55/5.80 archim3151403230148437115or_rat: rat > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Real__Oreal,type,
% 5.55/5.80 archim6058952711729229775r_real: real > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 5.55/5.80 archim7778729529865785530nd_rat: rat > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Archimedean__Field_Oround_001t__Real__Oreal,type,
% 5.55/5.80 archim8280529875227126926d_real: real > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 5.55/5.80 bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 5.55/5.80 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.55/5.80 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.55/5.80 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.55/5.80 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.55/5.80 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.55/5.80 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 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,
% 5.55/5.80 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 ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Binomial_Obinomial,type,
% 5.55/5.80 binomial: nat > nat > nat ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 5.55/5.80 gbinomial_complex: complex > nat > complex ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 5.55/5.80 gbinomial_int: int > nat > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 5.55/5.80 gbinomial_nat: nat > nat > nat ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 5.55/5.80 gbinomial_rat: rat > nat > rat ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 5.55/5.80 gbinomial_real: real > nat > real ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 5.55/5.80 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oand__not__num,type,
% 5.55/5.80 bit_and_not_num: num > num > option_num ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oand__not__num__rel,type,
% 5.55/5.80 bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 5.55/5.80 bit_concat_bit: nat > int > int > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oor__not__num__neg,type,
% 5.55/5.80 bit_or_not_num_neg: num > num > num ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oor__not__num__neg__rel,type,
% 5.55/5.80 bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 5.55/5.80 bit_ri7919022796975470100ot_int: int > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 5.55/5.80 bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 5.55/5.80 bit_ri631733984087533419it_int: nat > int > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 5.55/5.80 bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 5.55/5.80 bit_se725231765392027082nd_int: int > int > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 5.55/5.80 bit_se727722235901077358nd_nat: nat > nat > nat ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 5.55/5.80 bit_se8568078237143864401it_int: nat > int > int ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 5.55/5.80 bit_se8570568707652914677it_nat: nat > nat > nat ).
% 5.55/5.80
% 5.55/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 5.55/5.80 bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Int__Oint,type,
% 5.64/5.80 bit_se2159334234014336723it_int: nat > int > int ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Nat__Onat,type,
% 5.64/5.80 bit_se2161824704523386999it_nat: nat > nat > nat ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Code____Numeral__Ointeger,type,
% 5.64/5.80 bit_se2119862282449309892nteger: nat > code_integer ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Int__Oint,type,
% 5.64/5.80 bit_se2000444600071755411sk_int: nat > int ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Omask_001t__Nat__Onat,type,
% 5.64/5.80 bit_se2002935070580805687sk_nat: nat > nat ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Code____Numeral__Ointeger,type,
% 5.64/5.80 bit_se1080825931792720795nteger: code_integer > code_integer > code_integer ).
% 5.64/5.80
% 5.64/5.80 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Int__Oint,type,
% 5.64/5.80 bit_se1409905431419307370or_int: int > int > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oor_001t__Nat__Onat,type,
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% 5.64/5.81 nil_int: list_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.64/5.81 nil_nat: list_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.64/5.81 hd_nat: list_nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.64/5.81 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.64/5.81 set_o2: list_o > set_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.64/5.81 set_complex2: list_complex > set_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.64/5.81 set_int2: list_int > set_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.64/5.81 set_nat2: list_nat > set_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.64/5.81 set_real2: list_real > set_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.64/5.81 tl_nat: list_nat > list_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.64/5.81 list_update_o: list_o > nat > $o > list_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.64/5.81 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.64/5.81 list_update_int: list_int > nat > int > list_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.64/5.81 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.64/5.81 list_update_real: list_real > nat > real > list_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001_Eo,type,
% 5.64/5.81 nth_o: list_o > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.64/5.81 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.64/5.81 nth_complex: list_complex > nat > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.64/5.81 nth_int: list_int > nat > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.64/5.81 nth_nat: list_nat > nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.64/5.81 nth_num: list_num > nat > num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
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% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__Real__Oreal,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.64/5.81 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 5.64/5.81 remdups_nat: list_nat > list_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.64/5.81 replicate_o: nat > $o > list_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.64/5.81 replicate_complex: nat > complex > list_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.64/5.81 replicate_int: nat > int > list_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.64/5.81 replicate_nat: nat > nat > list_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.64/5.81 replicate_real: nat > real > list_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.64/5.81 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.64/5.81 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Otake_001t__Nat__Onat,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oupt,type,
% 5.64/5.81 upt: nat > nat > list_nat ).
% 5.64/5.81
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oupto__aux,type,
% 5.64/5.81 upto_aux: int > int > list_int > list_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_List_Oupto__rel,type,
% 5.64/5.81 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_OSuc,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.64/5.81 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.64/5.81
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% 5.64/5.81
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
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% 5.64/5.81
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
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% 5.64/5.81
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.64/5.81
% 5.64/5.81 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
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% 5.64/5.81 produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.64/5.81 produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 5.64/5.81 product_Pair_o_o: $o > $o > product_prod_o_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 5.64/5.81 product_Pair_o_int: $o > int > product_prod_o_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 5.64/5.81 product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.64/5.81 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.64/5.81 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 5.64/5.81 product_Pair_int_int: int > int > product_prod_int_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.64/5.81 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.64/5.81 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.64/5.81 produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 5.64/5.81 product_Pair_num_num: num > num > product_prod_num_num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.64/5.81 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.64/5.81 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.64/5.81 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.64/5.81 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.64/5.81 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.64/5.81 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.64/5.81 produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.64/5.81 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 5.64/5.81 produc7828578312038201481er_o_o: ( code_integer > $o > $o ) > produc6271795597528267376eger_o > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.64/5.81 produc1043322548047392435omplex: ( code_integer > $o > set_complex ) > produc6271795597528267376eger_o > set_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 5.64/5.81 produc1253318751659547953et_int: ( code_integer > $o > set_int ) > produc6271795597528267376eger_o > set_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.64/5.81 produc5431169771168744661et_nat: ( code_integer > $o > set_nat ) > produc6271795597528267376eger_o > set_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.64/5.81 produc242741666403216561t_real: ( code_integer > $o > set_real ) > produc6271795597528267376eger_o > set_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.64/5.81 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.64/5.81 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.64/5.81 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.64/5.81
% 5.64/5.81 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,
% 5.64/5.81 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.64/5.81
% 5.64/5.81 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,
% 5.64/5.81 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.64/5.81 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.64/5.81 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.64/5.81
% 5.64/5.81 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,
% 5.64/5.81 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.64/5.81
% 5.64/5.81 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,
% 5.64/5.81 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.64/5.81
% 5.64/5.81 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,
% 5.64/5.81 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.64/5.81 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.64/5.81 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.64/5.81 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.64/5.81 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.64/5.81
% 5.64/5.81 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,
% 5.64/5.81 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.64/5.81 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.64/5.81 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 5.64/5.81 produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.64/5.81 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.64/5.81 produc6231982587499038204omplex: ( nat > num > set_complex ) > product_prod_nat_num > set_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.64/5.81 produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 5.64/5.81 produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.64/5.81 produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J,type,
% 5.64/5.81 produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.64/5.81 produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.64/5.81 produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ofst_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.64/5.81 produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.64/5.81 product_fst_int_int: product_prod_int_int > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.64/5.81 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.64/5.81 product_snd_int_int: product_prod_int_int > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.64/5.81 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_OAbs__Rat,type,
% 5.64/5.81 abs_Rat: product_prod_int_int > rat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_OFract,type,
% 5.64/5.81 fract: int > int > rat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_OFrct,type,
% 5.64/5.81 frct: product_prod_int_int > rat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_ORep__Rat,type,
% 5.64/5.81 rep_Rat: rat > product_prod_int_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 5.64/5.81 field_5140801741446780682s_real: set_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Ofield__char__0__class_Oof__rat_001t__Real__Oreal,type,
% 5.64/5.81 field_7254667332652039916t_real: rat > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Onormalize,type,
% 5.64/5.81 normalize: product_prod_int_int > product_prod_int_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Opcr__rat,type,
% 5.64/5.81 pcr_rat: product_prod_int_int > rat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Opositive,type,
% 5.64/5.81 positive: rat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Oquotient__of,type,
% 5.64/5.81 quotient_of: rat > product_prod_int_int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Rat_Oratrel,type,
% 5.64/5.81 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real_Ocauchy,type,
% 5.64/5.81 cauchy: ( nat > rat ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real_Ovanishes,type,
% 5.64/5.81 vanishes: ( nat > rat ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.64/5.81 real_V2521375963428798218omplex: set_complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.64/5.81 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.64/5.81 real_V1022390504157884413omplex: complex > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.64/5.81 real_V7735802525324610683m_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.64/5.81 real_V4546457046886955230omplex: real > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Real__Oreal,type,
% 5.64/5.81 real_V1803761363581548252l_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
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% 5.64/5.81
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% 5.64/5.81
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% 5.64/5.81
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% 5.64/5.81 integer_of_char: char > code_integer ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.64/5.81 unique3096191561947761185of_nat: nat > char ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.64/5.81 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.64/5.81 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.64/5.81 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.64/5.81 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.64/5.81 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.64/5.81 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.64/5.81 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.64/5.81 topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.64/5.81 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.64/5.81 topolo2815343760600316023s_real: real > filter_real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.64/5.81 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oarccos,type,
% 5.64/5.81 arccos: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.64/5.81 arcosh_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oarcsin,type,
% 5.64/5.81 arcsin: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oarctan,type,
% 5.64/5.81 arctan: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.64/5.81 arsinh_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.64/5.81 artanh_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.64/5.81 cos_complex: complex > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.64/5.81 cos_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.64/5.81 cos_coeff: nat > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.64/5.81 cosh_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.64/5.81 cot_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.64/5.81 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.64/5.81 diffs_int: ( nat > int ) > nat > int ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 5.64/5.81 diffs_rat: ( nat > rat ) > nat > rat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.64/5.81 diffs_real: ( nat > real ) > nat > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.64/5.81 exp_complex: complex > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.64/5.81 exp_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.64/5.81 ln_ln_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Olog,type,
% 5.64/5.81 log: real > real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Opi,type,
% 5.64/5.81 pi: real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.64/5.81 powr_real: real > real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.64/5.81 sin_complex: complex > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.64/5.81 sin_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.64/5.81 sin_coeff: nat > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.64/5.81 sinh_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.64/5.81 tan_complex: complex > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.64/5.81 tan_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.64/5.81 tanh_complex: complex > complex ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.64/5.81 tanh_real: real > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.64/5.81 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.64/5.81 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r,type,
% 5.64/5.81 vEBT_T_m_e_m_b_e_r: vEBT_VEBT > nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H,type,
% 5.64/5.81 vEBT_T_m_e_m_b_e_r2: vEBT_VEBT > nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H__rel,type,
% 5.64/5.81 vEBT_T8099345112685741742_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Bounds_OT_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r__rel,type,
% 5.64/5.81 vEBT_T5837161174952499735_r_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.64/5.81 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.64/5.81 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.64/5.81 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.64/5.81 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.64/5.81 vEBT_VEBT_high: nat > nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.64/5.81 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.64/5.81 vEBT_VEBT_low: nat > nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.64/5.81 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.64/5.81 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.64/5.81 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.64/5.81 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.64/5.81 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.64/5.81 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.64/5.81 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.64/5.81 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.64/5.81 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.64/5.81 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight,type,
% 5.64/5.81 vEBT_VEBT_height: vEBT_VEBT > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Height_OVEBT__internal_Oheight__rel,type,
% 5.64/5.81 vEBT_VEBT_height_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.64/5.81 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.64/5.81 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.64/5.81 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.64/5.81 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.64/5.81 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.64/5.81 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.64/5.81 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.64/5.81 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.64/5.81 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.64/5.81 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.64/5.81 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.64/5.81 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.64/5.81 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.64/5.81 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.64/5.81 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.64/5.81 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.64/5.81 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.64/5.81 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.64/5.81 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.64/5.81 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.64/5.81 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.64/5.81 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.64/5.81 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.64/5.81 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.64/5.81 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.64/5.81 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.64/5.81 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.64/5.81 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.64/5.81 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.64/5.81 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.64/5.81 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.64/5.81 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.64/5.81 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.64/5.81 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 5.64/5.81 wf_nat: set_Pr1261947904930325089at_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.64/5.81 fChoice_real: ( real > $o ) > real ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001_Eo,type,
% 5.64/5.81 member_o: $o > set_o > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.64/5.81 member_complex: complex > set_complex > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Int__Oint,type,
% 5.64/5.81 member_int: int > set_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.64/5.81 member_list_o: list_o > set_list_o > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.64/5.81 member_list_int: list_int > set_list_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.64/5.81 member_list_nat: list_nat > set_list_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.64/5.81 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Nat__Onat,type,
% 5.64/5.81 member_nat: nat > set_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Num__Onum,type,
% 5.64/5.81 member_num: num > set_num > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.64/5.81 member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.64/5.81 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.64/5.81 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 5.64/5.81 member9148766508732265716at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.64/5.81 member7279096912039735102um_num: product_prod_num_num > set_Pr8218934625190621173um_num > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Rat__Orat,type,
% 5.64/5.81 member_rat: rat > set_rat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Real__Oreal,type,
% 5.64/5.81 member_real: real > set_real > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.64/5.81 member_set_nat: set_nat > set_set_nat > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.64/5.81 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_deg____,type,
% 5.64/5.81 deg: nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_m____,type,
% 5.64/5.81 m: nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_ma____,type,
% 5.64/5.81 ma: nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_mi____,type,
% 5.64/5.81 mi: nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_na____,type,
% 5.64/5.81 na: nat ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_summary____,type,
% 5.64/5.81 summary: vEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_treeList____,type,
% 5.64/5.81 treeList: list_VEBT_VEBT ).
% 5.64/5.81
% 5.64/5.81 thf(sy_v_xa____,type,
% 5.64/5.81 xa: nat ).
% 5.64/5.81
% 5.64/5.81 % Relevant facts (10208)
% 5.64/5.81 thf(fact_0__092_060open_0622_A_092_060le_062_Adeg_092_060close_062,axiom,
% 5.64/5.81 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.64/5.81
% 5.64/5.81 % \<open>2 \<le> deg\<close>
% 5.64/5.81 thf(fact_1__C5_Ohyps_C_I7_J,axiom,
% 5.64/5.81 ord_less_eq_nat @ mi @ ma ).
% 5.64/5.81
% 5.64/5.81 % "5.hyps"(7)
% 5.64/5.81 thf(fact_2_max__in__set__def,axiom,
% 5.64/5.81 ( vEBT_VEBT_max_in_set
% 5.64/5.81 = ( ^ [Xs: set_nat,X: nat] :
% 5.64/5.81 ( ( member_nat @ X @ Xs )
% 5.64/5.81 & ! [Y: nat] :
% 5.64/5.81 ( ( member_nat @ Y @ Xs )
% 5.64/5.81 => ( ord_less_eq_nat @ Y @ X ) ) ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % max_in_set_def
% 5.64/5.81 thf(fact_3_min__in__set__def,axiom,
% 5.64/5.81 ( vEBT_VEBT_min_in_set
% 5.64/5.81 = ( ^ [Xs: set_nat,X: nat] :
% 5.64/5.81 ( ( member_nat @ X @ Xs )
% 5.64/5.81 & ! [Y: nat] :
% 5.64/5.81 ( ( member_nat @ Y @ Xs )
% 5.64/5.81 => ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % min_in_set_def
% 5.64/5.81 thf(fact_4_height__compose__summary,axiom,
% 5.64/5.81 ! [Summary: vEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ Summary ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % height_compose_summary
% 5.64/5.81 thf(fact_5__C5_OIH_C_I2_J,axiom,
% 5.64/5.81 ! [X2: nat] : ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ summary @ X2 ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ summary ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % "5.IH"(2)
% 5.64/5.81 thf(fact_6_nat__add__left__cancel__le,axiom,
% 5.64/5.81 ! [K: nat,M: nat,N: nat] :
% 5.64/5.81 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.64/5.81 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.81
% 5.64/5.81 % nat_add_left_cancel_le
% 5.64/5.81 thf(fact_7_add__le__cancel__left,axiom,
% 5.64/5.81 ! [C: real,A: real,B: real] :
% 5.64/5.81 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.64/5.81 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_left
% 5.64/5.81 thf(fact_8_add__le__cancel__left,axiom,
% 5.64/5.81 ! [C: rat,A: rat,B: rat] :
% 5.64/5.81 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.64/5.81 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_left
% 5.64/5.81 thf(fact_9_add__le__cancel__left,axiom,
% 5.64/5.81 ! [C: nat,A: nat,B: nat] :
% 5.64/5.81 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.64/5.81 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_left
% 5.64/5.81 thf(fact_10_add__le__cancel__left,axiom,
% 5.64/5.81 ! [C: int,A: int,B: int] :
% 5.64/5.81 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.64/5.81 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_left
% 5.64/5.81 thf(fact_11_add__le__cancel__right,axiom,
% 5.64/5.81 ! [A: real,C: real,B: real] :
% 5.64/5.81 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.64/5.81 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_right
% 5.64/5.81 thf(fact_12_add__le__cancel__right,axiom,
% 5.64/5.81 ! [A: rat,C: rat,B: rat] :
% 5.64/5.81 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.81 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_right
% 5.64/5.81 thf(fact_13_add__le__cancel__right,axiom,
% 5.64/5.81 ! [A: nat,C: nat,B: nat] :
% 5.64/5.81 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.81 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_right
% 5.64/5.81 thf(fact_14_add__le__cancel__right,axiom,
% 5.64/5.81 ! [A: int,C: int,B: int] :
% 5.64/5.81 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.64/5.81 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_le_cancel_right
% 5.64/5.81 thf(fact_15_height__compose__child,axiom,
% 5.64/5.81 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Info: option4927543243414619207at_nat,Deg: nat,Summary: vEBT_VEBT] :
% 5.64/5.81 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.81 => ( ord_less_eq_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( vEBT_VEBT_height @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % height_compose_child
% 5.64/5.81 thf(fact_16__C5_Ohyps_C_I4_J,axiom,
% 5.64/5.81 ( deg
% 5.64/5.81 = ( plus_plus_nat @ na @ m ) ) ).
% 5.64/5.81
% 5.64/5.81 % "5.hyps"(4)
% 5.64/5.81 thf(fact_17_VEBT_Oinject_I1_J,axiom,
% 5.64/5.81 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.64/5.81 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.64/5.81 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.64/5.81 = ( ( X11 = Y11 )
% 5.64/5.81 & ( X12 = Y12 )
% 5.64/5.81 & ( X13 = Y13 )
% 5.64/5.81 & ( X14 = Y14 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % VEBT.inject(1)
% 5.64/5.81 thf(fact_18_option_Oinject,axiom,
% 5.64/5.81 ! [X22: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 5.64/5.81 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.64/5.81 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 5.64/5.81 = ( X22 = Y2 ) ) ).
% 5.64/5.81
% 5.64/5.81 % option.inject
% 5.64/5.81 thf(fact_19_option_Oinject,axiom,
% 5.64/5.81 ! [X22: nat,Y2: nat] :
% 5.64/5.81 ( ( ( some_nat @ X22 )
% 5.64/5.81 = ( some_nat @ Y2 ) )
% 5.64/5.81 = ( X22 = Y2 ) ) ).
% 5.64/5.81
% 5.64/5.81 % option.inject
% 5.64/5.81 thf(fact_20_option_Oinject,axiom,
% 5.64/5.81 ! [X22: num,Y2: num] :
% 5.64/5.81 ( ( ( some_num @ X22 )
% 5.64/5.81 = ( some_num @ Y2 ) )
% 5.64/5.81 = ( X22 = Y2 ) ) ).
% 5.64/5.81
% 5.64/5.81 % option.inject
% 5.64/5.81 thf(fact_21_prod_Oinject,axiom,
% 5.64/5.81 ! [X1: code_integer,X22: $o,Y1: code_integer,Y2: $o] :
% 5.64/5.81 ( ( ( produc6677183202524767010eger_o @ X1 @ X22 )
% 5.64/5.81 = ( produc6677183202524767010eger_o @ Y1 @ Y2 ) )
% 5.64/5.81 = ( ( X1 = Y1 )
% 5.64/5.81 & ( X22 = Y2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % prod.inject
% 5.64/5.81 thf(fact_22_prod_Oinject,axiom,
% 5.64/5.81 ! [X1: num,X22: num,Y1: num,Y2: num] :
% 5.64/5.81 ( ( ( product_Pair_num_num @ X1 @ X22 )
% 5.64/5.81 = ( product_Pair_num_num @ Y1 @ Y2 ) )
% 5.64/5.81 = ( ( X1 = Y1 )
% 5.64/5.81 & ( X22 = Y2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % prod.inject
% 5.64/5.81 thf(fact_23_prod_Oinject,axiom,
% 5.64/5.81 ! [X1: nat,X22: num,Y1: nat,Y2: num] :
% 5.64/5.81 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 5.64/5.81 = ( product_Pair_nat_num @ Y1 @ Y2 ) )
% 5.64/5.81 = ( ( X1 = Y1 )
% 5.64/5.81 & ( X22 = Y2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % prod.inject
% 5.64/5.81 thf(fact_24_prod_Oinject,axiom,
% 5.64/5.81 ! [X1: nat,X22: nat,Y1: nat,Y2: nat] :
% 5.64/5.81 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 5.64/5.81 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 5.64/5.81 = ( ( X1 = Y1 )
% 5.64/5.81 & ( X22 = Y2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % prod.inject
% 5.64/5.81 thf(fact_25_prod_Oinject,axiom,
% 5.64/5.81 ! [X1: int,X22: int,Y1: int,Y2: int] :
% 5.64/5.81 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.64/5.81 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 5.64/5.81 = ( ( X1 = Y1 )
% 5.64/5.81 & ( X22 = Y2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % prod.inject
% 5.64/5.81 thf(fact_26_old_Oprod_Oinject,axiom,
% 5.64/5.81 ! [A: code_integer,B: $o,A2: code_integer,B2: $o] :
% 5.64/5.81 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.64/5.81 = ( produc6677183202524767010eger_o @ A2 @ B2 ) )
% 5.64/5.81 = ( ( A = A2 )
% 5.64/5.81 & ( B = B2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % old.prod.inject
% 5.64/5.81 thf(fact_27_old_Oprod_Oinject,axiom,
% 5.64/5.81 ! [A: num,B: num,A2: num,B2: num] :
% 5.64/5.81 ( ( ( product_Pair_num_num @ A @ B )
% 5.64/5.81 = ( product_Pair_num_num @ A2 @ B2 ) )
% 5.64/5.81 = ( ( A = A2 )
% 5.64/5.81 & ( B = B2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % old.prod.inject
% 5.64/5.81 thf(fact_28_old_Oprod_Oinject,axiom,
% 5.64/5.81 ! [A: nat,B: num,A2: nat,B2: num] :
% 5.64/5.81 ( ( ( product_Pair_nat_num @ A @ B )
% 5.64/5.81 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 5.64/5.81 = ( ( A = A2 )
% 5.64/5.81 & ( B = B2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % old.prod.inject
% 5.64/5.81 thf(fact_29_old_Oprod_Oinject,axiom,
% 5.64/5.81 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 5.64/5.81 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.64/5.81 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 5.64/5.81 = ( ( A = A2 )
% 5.64/5.81 & ( B = B2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % old.prod.inject
% 5.64/5.81 thf(fact_30_old_Oprod_Oinject,axiom,
% 5.64/5.81 ! [A: int,B: int,A2: int,B2: int] :
% 5.64/5.81 ( ( ( product_Pair_int_int @ A @ B )
% 5.64/5.81 = ( product_Pair_int_int @ A2 @ B2 ) )
% 5.64/5.81 = ( ( A = A2 )
% 5.64/5.81 & ( B = B2 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % old.prod.inject
% 5.64/5.81 thf(fact_31_add__left__cancel,axiom,
% 5.64/5.81 ! [A: real,B: real,C: real] :
% 5.64/5.81 ( ( ( plus_plus_real @ A @ B )
% 5.64/5.81 = ( plus_plus_real @ A @ C ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_cancel
% 5.64/5.81 thf(fact_32_add__left__cancel,axiom,
% 5.64/5.81 ! [A: rat,B: rat,C: rat] :
% 5.64/5.81 ( ( ( plus_plus_rat @ A @ B )
% 5.64/5.81 = ( plus_plus_rat @ A @ C ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_cancel
% 5.64/5.81 thf(fact_33_add__left__cancel,axiom,
% 5.64/5.81 ! [A: nat,B: nat,C: nat] :
% 5.64/5.81 ( ( ( plus_plus_nat @ A @ B )
% 5.64/5.81 = ( plus_plus_nat @ A @ C ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_cancel
% 5.64/5.81 thf(fact_34_add__left__cancel,axiom,
% 5.64/5.81 ! [A: int,B: int,C: int] :
% 5.64/5.81 ( ( ( plus_plus_int @ A @ B )
% 5.64/5.81 = ( plus_plus_int @ A @ C ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_cancel
% 5.64/5.81 thf(fact_35_add__right__cancel,axiom,
% 5.64/5.81 ! [B: real,A: real,C: real] :
% 5.64/5.81 ( ( ( plus_plus_real @ B @ A )
% 5.64/5.81 = ( plus_plus_real @ C @ A ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_cancel
% 5.64/5.81 thf(fact_36_add__right__cancel,axiom,
% 5.64/5.81 ! [B: rat,A: rat,C: rat] :
% 5.64/5.81 ( ( ( plus_plus_rat @ B @ A )
% 5.64/5.81 = ( plus_plus_rat @ C @ A ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_cancel
% 5.64/5.81 thf(fact_37_add__right__cancel,axiom,
% 5.64/5.81 ! [B: nat,A: nat,C: nat] :
% 5.64/5.81 ( ( ( plus_plus_nat @ B @ A )
% 5.64/5.81 = ( plus_plus_nat @ C @ A ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_cancel
% 5.64/5.81 thf(fact_38_add__right__cancel,axiom,
% 5.64/5.81 ! [B: int,A: int,C: int] :
% 5.64/5.81 ( ( ( plus_plus_int @ B @ A )
% 5.64/5.81 = ( plus_plus_int @ C @ A ) )
% 5.64/5.81 = ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_cancel
% 5.64/5.81 thf(fact_39__092_060open_0621_A_092_060le_062_An_A_092_060and_062_A1_A_092_060le_062_Am_092_060close_062,axiom,
% 5.64/5.81 ( ( ord_less_eq_nat @ one_one_nat @ na )
% 5.64/5.81 & ( ord_less_eq_nat @ one_one_nat @ m ) ) ).
% 5.64/5.81
% 5.64/5.81 % \<open>1 \<le> n \<and> 1 \<le> m\<close>
% 5.64/5.81 thf(fact_40_lesseq__shift,axiom,
% 5.64/5.81 ( ord_less_eq_nat
% 5.64/5.81 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % lesseq_shift
% 5.64/5.81 thf(fact_41__C5_Ohyps_C_I3_J,axiom,
% 5.64/5.81 ( m
% 5.64/5.81 = ( suc @ na ) ) ).
% 5.64/5.81
% 5.64/5.81 % "5.hyps"(3)
% 5.64/5.81 thf(fact_42__C5_Ohyps_C_I1_J,axiom,
% 5.64/5.81 vEBT_invar_vebt @ summary @ m ).
% 5.64/5.81
% 5.64/5.81 % "5.hyps"(1)
% 5.64/5.81 thf(fact_43__C5_Ohyps_C_I6_J,axiom,
% 5.64/5.81 ( ( mi = ma )
% 5.64/5.81 => ! [X3: vEBT_VEBT] :
% 5.64/5.81 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.64/5.81 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % "5.hyps"(6)
% 5.64/5.81 thf(fact_44__C5_OIH_C_I1_J,axiom,
% 5.64/5.81 ! [X3: vEBT_VEBT] :
% 5.64/5.81 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.64/5.81 => ( ( vEBT_invar_vebt @ X3 @ na )
% 5.64/5.81 & ! [Xa: nat] : ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ X3 @ Xa ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ X3 ) ) ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % "5.IH"(1)
% 5.64/5.81 thf(fact_45_one__reorient,axiom,
% 5.64/5.81 ! [X2: complex] :
% 5.64/5.81 ( ( one_one_complex = X2 )
% 5.64/5.81 = ( X2 = one_one_complex ) ) ).
% 5.64/5.81
% 5.64/5.81 % one_reorient
% 5.64/5.81 thf(fact_46_one__reorient,axiom,
% 5.64/5.81 ! [X2: real] :
% 5.64/5.81 ( ( one_one_real = X2 )
% 5.64/5.81 = ( X2 = one_one_real ) ) ).
% 5.64/5.81
% 5.64/5.81 % one_reorient
% 5.64/5.81 thf(fact_47_one__reorient,axiom,
% 5.64/5.81 ! [X2: rat] :
% 5.64/5.81 ( ( one_one_rat = X2 )
% 5.64/5.81 = ( X2 = one_one_rat ) ) ).
% 5.64/5.81
% 5.64/5.81 % one_reorient
% 5.64/5.81 thf(fact_48_one__reorient,axiom,
% 5.64/5.81 ! [X2: nat] :
% 5.64/5.81 ( ( one_one_nat = X2 )
% 5.64/5.81 = ( X2 = one_one_nat ) ) ).
% 5.64/5.81
% 5.64/5.81 % one_reorient
% 5.64/5.81 thf(fact_49_one__reorient,axiom,
% 5.64/5.81 ! [X2: int] :
% 5.64/5.81 ( ( one_one_int = X2 )
% 5.64/5.81 = ( X2 = one_one_int ) ) ).
% 5.64/5.81
% 5.64/5.81 % one_reorient
% 5.64/5.81 thf(fact_50_add__right__imp__eq,axiom,
% 5.64/5.81 ! [B: real,A: real,C: real] :
% 5.64/5.81 ( ( ( plus_plus_real @ B @ A )
% 5.64/5.81 = ( plus_plus_real @ C @ A ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_imp_eq
% 5.64/5.81 thf(fact_51_add__right__imp__eq,axiom,
% 5.64/5.81 ! [B: rat,A: rat,C: rat] :
% 5.64/5.81 ( ( ( plus_plus_rat @ B @ A )
% 5.64/5.81 = ( plus_plus_rat @ C @ A ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_imp_eq
% 5.64/5.81 thf(fact_52_add__right__imp__eq,axiom,
% 5.64/5.81 ! [B: nat,A: nat,C: nat] :
% 5.64/5.81 ( ( ( plus_plus_nat @ B @ A )
% 5.64/5.81 = ( plus_plus_nat @ C @ A ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_imp_eq
% 5.64/5.81 thf(fact_53_add__right__imp__eq,axiom,
% 5.64/5.81 ! [B: int,A: int,C: int] :
% 5.64/5.81 ( ( ( plus_plus_int @ B @ A )
% 5.64/5.81 = ( plus_plus_int @ C @ A ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_right_imp_eq
% 5.64/5.81 thf(fact_54_add__left__imp__eq,axiom,
% 5.64/5.81 ! [A: real,B: real,C: real] :
% 5.64/5.81 ( ( ( plus_plus_real @ A @ B )
% 5.64/5.81 = ( plus_plus_real @ A @ C ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_imp_eq
% 5.64/5.81 thf(fact_55_add__left__imp__eq,axiom,
% 5.64/5.81 ! [A: rat,B: rat,C: rat] :
% 5.64/5.81 ( ( ( plus_plus_rat @ A @ B )
% 5.64/5.81 = ( plus_plus_rat @ A @ C ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_imp_eq
% 5.64/5.81 thf(fact_56_add__left__imp__eq,axiom,
% 5.64/5.81 ! [A: nat,B: nat,C: nat] :
% 5.64/5.81 ( ( ( plus_plus_nat @ A @ B )
% 5.64/5.81 = ( plus_plus_nat @ A @ C ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_imp_eq
% 5.64/5.81 thf(fact_57_add__left__imp__eq,axiom,
% 5.64/5.81 ! [A: int,B: int,C: int] :
% 5.64/5.81 ( ( ( plus_plus_int @ A @ B )
% 5.64/5.81 = ( plus_plus_int @ A @ C ) )
% 5.64/5.81 => ( B = C ) ) ).
% 5.64/5.81
% 5.64/5.81 % add_left_imp_eq
% 5.64/5.81 thf(fact_58_add_Oleft__commute,axiom,
% 5.64/5.81 ! [B: real,A: real,C: real] :
% 5.64/5.81 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.64/5.81 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % add.left_commute
% 5.64/5.81 thf(fact_59_add_Oleft__commute,axiom,
% 5.64/5.81 ! [B: rat,A: rat,C: rat] :
% 5.64/5.81 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.64/5.81 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % add.left_commute
% 5.64/5.81 thf(fact_60_add_Oleft__commute,axiom,
% 5.64/5.81 ! [B: nat,A: nat,C: nat] :
% 5.64/5.81 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.64/5.81 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.64/5.81
% 5.64/5.81 % add.left_commute
% 5.64/5.81 thf(fact_61_add_Oleft__commute,axiom,
% 5.64/5.81 ! [B: int,A: int,C: int] :
% 5.64/5.81 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.64/5.81 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.left_commute
% 5.64/5.82 thf(fact_62_add_Ocommute,axiom,
% 5.64/5.82 ( plus_plus_real
% 5.64/5.82 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ B3 @ A3 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.commute
% 5.64/5.82 thf(fact_63_add_Ocommute,axiom,
% 5.64/5.82 ( plus_plus_rat
% 5.64/5.82 = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ B3 @ A3 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.commute
% 5.64/5.82 thf(fact_64_add_Ocommute,axiom,
% 5.64/5.82 ( plus_plus_nat
% 5.64/5.82 = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.commute
% 5.64/5.82 thf(fact_65_add_Ocommute,axiom,
% 5.64/5.82 ( plus_plus_int
% 5.64/5.82 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.commute
% 5.64/5.82 thf(fact_66_add_Oright__cancel,axiom,
% 5.64/5.82 ! [B: real,A: real,C: real] :
% 5.64/5.82 ( ( ( plus_plus_real @ B @ A )
% 5.64/5.82 = ( plus_plus_real @ C @ A ) )
% 5.64/5.82 = ( B = C ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.right_cancel
% 5.64/5.82 thf(fact_67_add_Oright__cancel,axiom,
% 5.64/5.82 ! [B: rat,A: rat,C: rat] :
% 5.64/5.82 ( ( ( plus_plus_rat @ B @ A )
% 5.64/5.82 = ( plus_plus_rat @ C @ A ) )
% 5.64/5.82 = ( B = C ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.right_cancel
% 5.64/5.82 thf(fact_68_add_Oright__cancel,axiom,
% 5.64/5.82 ! [B: int,A: int,C: int] :
% 5.64/5.82 ( ( ( plus_plus_int @ B @ A )
% 5.64/5.82 = ( plus_plus_int @ C @ A ) )
% 5.64/5.82 = ( B = C ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.right_cancel
% 5.64/5.82 thf(fact_69_add_Oleft__cancel,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( ( plus_plus_real @ A @ B )
% 5.64/5.82 = ( plus_plus_real @ A @ C ) )
% 5.64/5.82 = ( B = C ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.left_cancel
% 5.64/5.82 thf(fact_70_add_Oleft__cancel,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( ( plus_plus_rat @ A @ B )
% 5.64/5.82 = ( plus_plus_rat @ A @ C ) )
% 5.64/5.82 = ( B = C ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.left_cancel
% 5.64/5.82 thf(fact_71_add_Oleft__cancel,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( ( plus_plus_int @ A @ B )
% 5.64/5.82 = ( plus_plus_int @ A @ C ) )
% 5.64/5.82 = ( B = C ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.left_cancel
% 5.64/5.82 thf(fact_72_add_Oassoc,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.assoc
% 5.64/5.82 thf(fact_73_add_Oassoc,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.assoc
% 5.64/5.82 thf(fact_74_add_Oassoc,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.assoc
% 5.64/5.82 thf(fact_75_add_Oassoc,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add.assoc
% 5.64/5.82 thf(fact_76_group__cancel_Oadd2,axiom,
% 5.64/5.82 ! [B4: real,K: real,B: real,A: real] :
% 5.64/5.82 ( ( B4
% 5.64/5.82 = ( plus_plus_real @ K @ B ) )
% 5.64/5.82 => ( ( plus_plus_real @ A @ B4 )
% 5.64/5.82 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add2
% 5.64/5.82 thf(fact_77_group__cancel_Oadd2,axiom,
% 5.64/5.82 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.64/5.82 ( ( B4
% 5.64/5.82 = ( plus_plus_rat @ K @ B ) )
% 5.64/5.82 => ( ( plus_plus_rat @ A @ B4 )
% 5.64/5.82 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add2
% 5.64/5.82 thf(fact_78_group__cancel_Oadd2,axiom,
% 5.64/5.82 ! [B4: nat,K: nat,B: nat,A: nat] :
% 5.64/5.82 ( ( B4
% 5.64/5.82 = ( plus_plus_nat @ K @ B ) )
% 5.64/5.82 => ( ( plus_plus_nat @ A @ B4 )
% 5.64/5.82 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add2
% 5.64/5.82 thf(fact_79_group__cancel_Oadd2,axiom,
% 5.64/5.82 ! [B4: int,K: int,B: int,A: int] :
% 5.64/5.82 ( ( B4
% 5.64/5.82 = ( plus_plus_int @ K @ B ) )
% 5.64/5.82 => ( ( plus_plus_int @ A @ B4 )
% 5.64/5.82 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add2
% 5.64/5.82 thf(fact_80_group__cancel_Oadd1,axiom,
% 5.64/5.82 ! [A4: real,K: real,A: real,B: real] :
% 5.64/5.82 ( ( A4
% 5.64/5.82 = ( plus_plus_real @ K @ A ) )
% 5.64/5.82 => ( ( plus_plus_real @ A4 @ B )
% 5.64/5.82 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add1
% 5.64/5.82 thf(fact_81_group__cancel_Oadd1,axiom,
% 5.64/5.82 ! [A4: rat,K: rat,A: rat,B: rat] :
% 5.64/5.82 ( ( A4
% 5.64/5.82 = ( plus_plus_rat @ K @ A ) )
% 5.64/5.82 => ( ( plus_plus_rat @ A4 @ B )
% 5.64/5.82 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add1
% 5.64/5.82 thf(fact_82_group__cancel_Oadd1,axiom,
% 5.64/5.82 ! [A4: nat,K: nat,A: nat,B: nat] :
% 5.64/5.82 ( ( A4
% 5.64/5.82 = ( plus_plus_nat @ K @ A ) )
% 5.64/5.82 => ( ( plus_plus_nat @ A4 @ B )
% 5.64/5.82 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add1
% 5.64/5.82 thf(fact_83_group__cancel_Oadd1,axiom,
% 5.64/5.82 ! [A4: int,K: int,A: int,B: int] :
% 5.64/5.82 ( ( A4
% 5.64/5.82 = ( plus_plus_int @ K @ A ) )
% 5.64/5.82 => ( ( plus_plus_int @ A4 @ B )
% 5.64/5.82 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % group_cancel.add1
% 5.64/5.82 thf(fact_84_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.64/5.82 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ( plus_plus_real @ I @ K )
% 5.64/5.82 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(4)
% 5.64/5.82 thf(fact_85_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.64/5.82 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ( plus_plus_rat @ I @ K )
% 5.64/5.82 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(4)
% 5.64/5.82 thf(fact_86_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ( plus_plus_nat @ I @ K )
% 5.64/5.82 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(4)
% 5.64/5.82 thf(fact_87_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.64/5.82 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ( plus_plus_int @ I @ K )
% 5.64/5.82 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(4)
% 5.64/5.82 thf(fact_88_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ab_semigroup_add_class.add_ac(1)
% 5.64/5.82 thf(fact_89_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ab_semigroup_add_class.add_ac(1)
% 5.64/5.82 thf(fact_90_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ab_semigroup_add_class.add_ac(1)
% 5.64/5.82 thf(fact_91_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ab_semigroup_add_class.add_ac(1)
% 5.64/5.82 thf(fact_92_mem__Collect__eq,axiom,
% 5.64/5.82 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.64/5.82 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.64/5.82 = ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % mem_Collect_eq
% 5.64/5.82 thf(fact_93_mem__Collect__eq,axiom,
% 5.64/5.82 ! [A: complex,P: complex > $o] :
% 5.64/5.82 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.64/5.82 = ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % mem_Collect_eq
% 5.64/5.82 thf(fact_94_mem__Collect__eq,axiom,
% 5.64/5.82 ! [A: real,P: real > $o] :
% 5.64/5.82 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.64/5.82 = ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % mem_Collect_eq
% 5.64/5.82 thf(fact_95_mem__Collect__eq,axiom,
% 5.64/5.82 ! [A: list_nat,P: list_nat > $o] :
% 5.64/5.82 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.64/5.82 = ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % mem_Collect_eq
% 5.64/5.82 thf(fact_96_mem__Collect__eq,axiom,
% 5.64/5.82 ! [A: nat,P: nat > $o] :
% 5.64/5.82 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.64/5.82 = ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % mem_Collect_eq
% 5.64/5.82 thf(fact_97_mem__Collect__eq,axiom,
% 5.64/5.82 ! [A: int,P: int > $o] :
% 5.64/5.82 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.64/5.82 = ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % mem_Collect_eq
% 5.64/5.82 thf(fact_98_Collect__mem__eq,axiom,
% 5.64/5.82 ! [A4: set_Pr1261947904930325089at_nat] :
% 5.64/5.82 ( ( collec3392354462482085612at_nat
% 5.64/5.82 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A4 ) )
% 5.64/5.82 = A4 ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_mem_eq
% 5.64/5.82 thf(fact_99_Collect__mem__eq,axiom,
% 5.64/5.82 ! [A4: set_complex] :
% 5.64/5.82 ( ( collect_complex
% 5.64/5.82 @ ^ [X: complex] : ( member_complex @ X @ A4 ) )
% 5.64/5.82 = A4 ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_mem_eq
% 5.64/5.82 thf(fact_100_Collect__mem__eq,axiom,
% 5.64/5.82 ! [A4: set_real] :
% 5.64/5.82 ( ( collect_real
% 5.64/5.82 @ ^ [X: real] : ( member_real @ X @ A4 ) )
% 5.64/5.82 = A4 ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_mem_eq
% 5.64/5.82 thf(fact_101_Collect__mem__eq,axiom,
% 5.64/5.82 ! [A4: set_list_nat] :
% 5.64/5.82 ( ( collect_list_nat
% 5.64/5.82 @ ^ [X: list_nat] : ( member_list_nat @ X @ A4 ) )
% 5.64/5.82 = A4 ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_mem_eq
% 5.64/5.82 thf(fact_102_Collect__mem__eq,axiom,
% 5.64/5.82 ! [A4: set_nat] :
% 5.64/5.82 ( ( collect_nat
% 5.64/5.82 @ ^ [X: nat] : ( member_nat @ X @ A4 ) )
% 5.64/5.82 = A4 ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_mem_eq
% 5.64/5.82 thf(fact_103_Collect__mem__eq,axiom,
% 5.64/5.82 ! [A4: set_int] :
% 5.64/5.82 ( ( collect_int
% 5.64/5.82 @ ^ [X: int] : ( member_int @ X @ A4 ) )
% 5.64/5.82 = A4 ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_mem_eq
% 5.64/5.82 thf(fact_104_Collect__cong,axiom,
% 5.64/5.82 ! [P: complex > $o,Q: complex > $o] :
% 5.64/5.82 ( ! [X4: complex] :
% 5.64/5.82 ( ( P @ X4 )
% 5.64/5.82 = ( Q @ X4 ) )
% 5.64/5.82 => ( ( collect_complex @ P )
% 5.64/5.82 = ( collect_complex @ Q ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_cong
% 5.64/5.82 thf(fact_105_Collect__cong,axiom,
% 5.64/5.82 ! [P: real > $o,Q: real > $o] :
% 5.64/5.82 ( ! [X4: real] :
% 5.64/5.82 ( ( P @ X4 )
% 5.64/5.82 = ( Q @ X4 ) )
% 5.64/5.82 => ( ( collect_real @ P )
% 5.64/5.82 = ( collect_real @ Q ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_cong
% 5.64/5.82 thf(fact_106_Collect__cong,axiom,
% 5.64/5.82 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.64/5.82 ( ! [X4: list_nat] :
% 5.64/5.82 ( ( P @ X4 )
% 5.64/5.82 = ( Q @ X4 ) )
% 5.64/5.82 => ( ( collect_list_nat @ P )
% 5.64/5.82 = ( collect_list_nat @ Q ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_cong
% 5.64/5.82 thf(fact_107_Collect__cong,axiom,
% 5.64/5.82 ! [P: nat > $o,Q: nat > $o] :
% 5.64/5.82 ( ! [X4: nat] :
% 5.64/5.82 ( ( P @ X4 )
% 5.64/5.82 = ( Q @ X4 ) )
% 5.64/5.82 => ( ( collect_nat @ P )
% 5.64/5.82 = ( collect_nat @ Q ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_cong
% 5.64/5.82 thf(fact_108_Collect__cong,axiom,
% 5.64/5.82 ! [P: int > $o,Q: int > $o] :
% 5.64/5.82 ( ! [X4: int] :
% 5.64/5.82 ( ( P @ X4 )
% 5.64/5.82 = ( Q @ X4 ) )
% 5.64/5.82 => ( ( collect_int @ P )
% 5.64/5.82 = ( collect_int @ Q ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Collect_cong
% 5.64/5.82 thf(fact_109_Pair__inject,axiom,
% 5.64/5.82 ! [A: code_integer,B: $o,A2: code_integer,B2: $o] :
% 5.64/5.82 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 5.64/5.82 = ( produc6677183202524767010eger_o @ A2 @ B2 ) )
% 5.64/5.82 => ~ ( ( A = A2 )
% 5.64/5.82 => ( B = ~ B2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Pair_inject
% 5.64/5.82 thf(fact_110_Pair__inject,axiom,
% 5.64/5.82 ! [A: num,B: num,A2: num,B2: num] :
% 5.64/5.82 ( ( ( product_Pair_num_num @ A @ B )
% 5.64/5.82 = ( product_Pair_num_num @ A2 @ B2 ) )
% 5.64/5.82 => ~ ( ( A = A2 )
% 5.64/5.82 => ( B != B2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Pair_inject
% 5.64/5.82 thf(fact_111_Pair__inject,axiom,
% 5.64/5.82 ! [A: nat,B: num,A2: nat,B2: num] :
% 5.64/5.82 ( ( ( product_Pair_nat_num @ A @ B )
% 5.64/5.82 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 5.64/5.82 => ~ ( ( A = A2 )
% 5.64/5.82 => ( B != B2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Pair_inject
% 5.64/5.82 thf(fact_112_Pair__inject,axiom,
% 5.64/5.82 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 5.64/5.82 ( ( ( product_Pair_nat_nat @ A @ B )
% 5.64/5.82 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 5.64/5.82 => ~ ( ( A = A2 )
% 5.64/5.82 => ( B != B2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Pair_inject
% 5.64/5.82 thf(fact_113_Pair__inject,axiom,
% 5.64/5.82 ! [A: int,B: int,A2: int,B2: int] :
% 5.64/5.82 ( ( ( product_Pair_int_int @ A @ B )
% 5.64/5.82 = ( product_Pair_int_int @ A2 @ B2 ) )
% 5.64/5.82 => ~ ( ( A = A2 )
% 5.64/5.82 => ( B != B2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Pair_inject
% 5.64/5.82 thf(fact_114_prod__cases,axiom,
% 5.64/5.82 ! [P: produc6271795597528267376eger_o > $o,P2: produc6271795597528267376eger_o] :
% 5.64/5.82 ( ! [A5: code_integer,B5: $o] : ( P @ ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ P2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % prod_cases
% 5.64/5.82 thf(fact_115_prod__cases,axiom,
% 5.64/5.82 ! [P: product_prod_num_num > $o,P2: product_prod_num_num] :
% 5.64/5.82 ( ! [A5: num,B5: num] : ( P @ ( product_Pair_num_num @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ P2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % prod_cases
% 5.64/5.82 thf(fact_116_prod__cases,axiom,
% 5.64/5.82 ! [P: product_prod_nat_num > $o,P2: product_prod_nat_num] :
% 5.64/5.82 ( ! [A5: nat,B5: num] : ( P @ ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ P2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % prod_cases
% 5.64/5.82 thf(fact_117_prod__cases,axiom,
% 5.64/5.82 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 5.64/5.82 ( ! [A5: nat,B5: nat] : ( P @ ( product_Pair_nat_nat @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ P2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % prod_cases
% 5.64/5.82 thf(fact_118_prod__cases,axiom,
% 5.64/5.82 ! [P: product_prod_int_int > $o,P2: product_prod_int_int] :
% 5.64/5.82 ( ! [A5: int,B5: int] : ( P @ ( product_Pair_int_int @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ P2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % prod_cases
% 5.64/5.82 thf(fact_119_surj__pair,axiom,
% 5.64/5.82 ! [P2: produc6271795597528267376eger_o] :
% 5.64/5.82 ? [X4: code_integer,Y3: $o] :
% 5.64/5.82 ( P2
% 5.64/5.82 = ( produc6677183202524767010eger_o @ X4 @ Y3 ) ) ).
% 5.64/5.82
% 5.64/5.82 % surj_pair
% 5.64/5.82 thf(fact_120_surj__pair,axiom,
% 5.64/5.82 ! [P2: product_prod_num_num] :
% 5.64/5.82 ? [X4: num,Y3: num] :
% 5.64/5.82 ( P2
% 5.64/5.82 = ( product_Pair_num_num @ X4 @ Y3 ) ) ).
% 5.64/5.82
% 5.64/5.82 % surj_pair
% 5.64/5.82 thf(fact_121_surj__pair,axiom,
% 5.64/5.82 ! [P2: product_prod_nat_num] :
% 5.64/5.82 ? [X4: nat,Y3: num] :
% 5.64/5.82 ( P2
% 5.64/5.82 = ( product_Pair_nat_num @ X4 @ Y3 ) ) ).
% 5.64/5.82
% 5.64/5.82 % surj_pair
% 5.64/5.82 thf(fact_122_surj__pair,axiom,
% 5.64/5.82 ! [P2: product_prod_nat_nat] :
% 5.64/5.82 ? [X4: nat,Y3: nat] :
% 5.64/5.82 ( P2
% 5.64/5.82 = ( product_Pair_nat_nat @ X4 @ Y3 ) ) ).
% 5.64/5.82
% 5.64/5.82 % surj_pair
% 5.64/5.82 thf(fact_123_surj__pair,axiom,
% 5.64/5.82 ! [P2: product_prod_int_int] :
% 5.64/5.82 ? [X4: int,Y3: int] :
% 5.64/5.82 ( P2
% 5.64/5.82 = ( product_Pair_int_int @ X4 @ Y3 ) ) ).
% 5.64/5.82
% 5.64/5.82 % surj_pair
% 5.64/5.82 thf(fact_124_old_Oprod_Oexhaust,axiom,
% 5.64/5.82 ! [Y4: produc6271795597528267376eger_o] :
% 5.64/5.82 ~ ! [A5: code_integer,B5: $o] :
% 5.64/5.82 ( Y4
% 5.64/5.82 != ( produc6677183202524767010eger_o @ A5 @ B5 ) ) ).
% 5.64/5.82
% 5.64/5.82 % old.prod.exhaust
% 5.64/5.82 thf(fact_125_old_Oprod_Oexhaust,axiom,
% 5.64/5.82 ! [Y4: product_prod_num_num] :
% 5.64/5.82 ~ ! [A5: num,B5: num] :
% 5.64/5.82 ( Y4
% 5.64/5.82 != ( product_Pair_num_num @ A5 @ B5 ) ) ).
% 5.64/5.82
% 5.64/5.82 % old.prod.exhaust
% 5.64/5.82 thf(fact_126_old_Oprod_Oexhaust,axiom,
% 5.64/5.82 ! [Y4: product_prod_nat_num] :
% 5.64/5.82 ~ ! [A5: nat,B5: num] :
% 5.64/5.82 ( Y4
% 5.64/5.82 != ( product_Pair_nat_num @ A5 @ B5 ) ) ).
% 5.64/5.82
% 5.64/5.82 % old.prod.exhaust
% 5.64/5.82 thf(fact_127_old_Oprod_Oexhaust,axiom,
% 5.64/5.82 ! [Y4: product_prod_nat_nat] :
% 5.64/5.82 ~ ! [A5: nat,B5: nat] :
% 5.64/5.82 ( Y4
% 5.64/5.82 != ( product_Pair_nat_nat @ A5 @ B5 ) ) ).
% 5.64/5.82
% 5.64/5.82 % old.prod.exhaust
% 5.64/5.82 thf(fact_128_old_Oprod_Oexhaust,axiom,
% 5.64/5.82 ! [Y4: product_prod_int_int] :
% 5.64/5.82 ~ ! [A5: int,B5: int] :
% 5.64/5.82 ( Y4
% 5.64/5.82 != ( product_Pair_int_int @ A5 @ B5 ) ) ).
% 5.64/5.82
% 5.64/5.82 % old.prod.exhaust
% 5.64/5.82 thf(fact_129_Nat_Oex__has__greatest__nat,axiom,
% 5.64/5.82 ! [P: nat > $o,K: nat,B: nat] :
% 5.64/5.82 ( ( P @ K )
% 5.64/5.82 => ( ! [Y3: nat] :
% 5.64/5.82 ( ( P @ Y3 )
% 5.64/5.82 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.64/5.82 => ? [X4: nat] :
% 5.64/5.82 ( ( P @ X4 )
% 5.64/5.82 & ! [Y5: nat] :
% 5.64/5.82 ( ( P @ Y5 )
% 5.64/5.82 => ( ord_less_eq_nat @ Y5 @ X4 ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Nat.ex_has_greatest_nat
% 5.64/5.82 thf(fact_130_nat__le__linear,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat_le_linear
% 5.64/5.82 thf(fact_131_le__antisym,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.82 => ( M = N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_antisym
% 5.64/5.82 thf(fact_132_eq__imp__le,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( M = N )
% 5.64/5.82 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % eq_imp_le
% 5.64/5.82 thf(fact_133_le__trans,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 => ( ( ord_less_eq_nat @ J @ K )
% 5.64/5.82 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_trans
% 5.64/5.82 thf(fact_134_le__refl,axiom,
% 5.64/5.82 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.64/5.82
% 5.64/5.82 % le_refl
% 5.64/5.82 thf(fact_135_add__le__imp__le__right,axiom,
% 5.64/5.82 ! [A: rat,C: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.82 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_right
% 5.64/5.82 thf(fact_136_add__le__imp__le__right,axiom,
% 5.64/5.82 ! [A: nat,C: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.82 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_right
% 5.64/5.82 thf(fact_137_add__le__imp__le__right,axiom,
% 5.64/5.82 ! [A: int,C: int,B: int] :
% 5.64/5.82 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.64/5.82 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_right
% 5.64/5.82 thf(fact_138_add__le__imp__le__right,axiom,
% 5.64/5.82 ! [A: real,C: real,B: real] :
% 5.64/5.82 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.64/5.82 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_right
% 5.64/5.82 thf(fact_139_add__le__imp__le__left,axiom,
% 5.64/5.82 ! [C: rat,A: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.64/5.82 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_left
% 5.64/5.82 thf(fact_140_add__le__imp__le__left,axiom,
% 5.64/5.82 ! [C: nat,A: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.64/5.82 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_left
% 5.64/5.82 thf(fact_141_add__le__imp__le__left,axiom,
% 5.64/5.82 ! [C: int,A: int,B: int] :
% 5.64/5.82 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.64/5.82 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_left
% 5.64/5.82 thf(fact_142_add__le__imp__le__left,axiom,
% 5.64/5.82 ! [C: real,A: real,B: real] :
% 5.64/5.82 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.64/5.82 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_imp_le_left
% 5.64/5.82 thf(fact_143_le__iff__add,axiom,
% 5.64/5.82 ( ord_less_eq_nat
% 5.64/5.82 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.82 ? [C2: nat] :
% 5.64/5.82 ( B3
% 5.64/5.82 = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_iff_add
% 5.64/5.82 thf(fact_144_add__right__mono,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_right_mono
% 5.64/5.82 thf(fact_145_add__right__mono,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_right_mono
% 5.64/5.82 thf(fact_146_add__right__mono,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.82 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_right_mono
% 5.64/5.82 thf(fact_147_add__right__mono,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.82 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_right_mono
% 5.64/5.82 thf(fact_148_less__eqE,axiom,
% 5.64/5.82 ! [A: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.82 => ~ ! [C3: nat] :
% 5.64/5.82 ( B
% 5.64/5.82 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_eqE
% 5.64/5.82 thf(fact_149_add__left__mono,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_left_mono
% 5.64/5.82 thf(fact_150_add__left__mono,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_left_mono
% 5.64/5.82 thf(fact_151_add__left__mono,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.82 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_left_mono
% 5.64/5.82 thf(fact_152_add__left__mono,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.82 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_left_mono
% 5.64/5.82 thf(fact_153_add__mono,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.82 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.82 => ( ( ord_less_eq_rat @ C @ D )
% 5.64/5.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono
% 5.64/5.82 thf(fact_154_add__mono,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.82 => ( ( ord_less_eq_nat @ C @ D )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono
% 5.64/5.82 thf(fact_155_add__mono,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.82 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.82 => ( ( ord_less_eq_int @ C @ D )
% 5.64/5.82 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono
% 5.64/5.82 thf(fact_156_add__mono,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.82 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.82 => ( ( ord_less_eq_real @ C @ D )
% 5.64/5.82 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono
% 5.64/5.82 thf(fact_157_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.64/5.82 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.82 ( ( ( ord_less_eq_rat @ I @ J )
% 5.64/5.82 & ( ord_less_eq_rat @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(1)
% 5.64/5.82 thf(fact_158_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.82 ( ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 & ( ord_less_eq_nat @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(1)
% 5.64/5.82 thf(fact_159_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.64/5.82 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.82 ( ( ( ord_less_eq_int @ I @ J )
% 5.64/5.82 & ( ord_less_eq_int @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(1)
% 5.64/5.82 thf(fact_160_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.64/5.82 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.82 ( ( ( ord_less_eq_real @ I @ J )
% 5.64/5.82 & ( ord_less_eq_real @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(1)
% 5.64/5.82 thf(fact_161_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.64/5.82 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( ord_less_eq_rat @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(2)
% 5.64/5.82 thf(fact_162_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( ord_less_eq_nat @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(2)
% 5.64/5.82 thf(fact_163_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.64/5.82 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( ord_less_eq_int @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(2)
% 5.64/5.82 thf(fact_164_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.64/5.82 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.82 ( ( ( I = J )
% 5.64/5.82 & ( ord_less_eq_real @ K @ L ) )
% 5.64/5.82 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(2)
% 5.64/5.82 thf(fact_165_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.64/5.82 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.82 ( ( ( ord_less_eq_rat @ I @ J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(3)
% 5.64/5.82 thf(fact_166_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.82 ( ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(3)
% 5.64/5.82 thf(fact_167_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.64/5.82 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.82 ( ( ( ord_less_eq_int @ I @ J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(3)
% 5.64/5.82 thf(fact_168_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.64/5.82 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.82 ( ( ( ord_less_eq_real @ I @ J )
% 5.64/5.82 & ( K = L ) )
% 5.64/5.82 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_mono_thms_linordered_semiring(3)
% 5.64/5.82 thf(fact_169_nat__le__iff__add,axiom,
% 5.64/5.82 ( ord_less_eq_nat
% 5.64/5.82 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.82 ? [K2: nat] :
% 5.64/5.82 ( N2
% 5.64/5.82 = ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat_le_iff_add
% 5.64/5.82 thf(fact_170_trans__le__add2,axiom,
% 5.64/5.82 ! [I: nat,J: nat,M: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % trans_le_add2
% 5.64/5.82 thf(fact_171_trans__le__add1,axiom,
% 5.64/5.82 ! [I: nat,J: nat,M: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % trans_le_add1
% 5.64/5.82 thf(fact_172_add__le__mono1,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_mono1
% 5.64/5.82 thf(fact_173_add__le__mono,axiom,
% 5.64/5.82 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.82 => ( ( ord_less_eq_nat @ K @ L )
% 5.64/5.82 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_le_mono
% 5.64/5.82 thf(fact_174_le__Suc__ex,axiom,
% 5.64/5.82 ! [K: nat,L: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ K @ L )
% 5.64/5.82 => ? [N3: nat] :
% 5.64/5.82 ( L
% 5.64/5.82 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_Suc_ex
% 5.64/5.82 thf(fact_175_add__leD2,axiom,
% 5.64/5.82 ! [M: nat,K: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.64/5.82 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_leD2
% 5.64/5.82 thf(fact_176_add__leD1,axiom,
% 5.64/5.82 ! [M: nat,K: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.64/5.82 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_leD1
% 5.64/5.82 thf(fact_177_le__add2,axiom,
% 5.64/5.82 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_add2
% 5.64/5.82 thf(fact_178_le__add1,axiom,
% 5.64/5.82 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_add1
% 5.64/5.82 thf(fact_179_add__leE,axiom,
% 5.64/5.82 ! [M: nat,K: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.64/5.82 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_leE
% 5.64/5.82 thf(fact_180_insert__simp__mima,axiom,
% 5.64/5.82 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.82 ( ( ( X2 = Mi )
% 5.64/5.82 | ( X2 = Ma ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.82 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % insert_simp_mima
% 5.64/5.82 thf(fact_181_one__add__one,axiom,
% 5.64/5.82 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.64/5.82 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_add_one
% 5.64/5.82 thf(fact_182_one__add__one,axiom,
% 5.64/5.82 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.64/5.82 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_add_one
% 5.64/5.82 thf(fact_183_one__add__one,axiom,
% 5.64/5.82 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.64/5.82 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_add_one
% 5.64/5.82 thf(fact_184_one__add__one,axiom,
% 5.64/5.82 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.64/5.82 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_add_one
% 5.64/5.82 thf(fact_185_one__add__one,axiom,
% 5.64/5.82 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.64/5.82 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_add_one
% 5.64/5.82 thf(fact_186_one__plus__numeral,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.82 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral
% 5.64/5.82 thf(fact_187_one__plus__numeral,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral
% 5.64/5.82 thf(fact_188_one__plus__numeral,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral
% 5.64/5.82 thf(fact_189_one__plus__numeral,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral
% 5.64/5.82 thf(fact_190_one__plus__numeral,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral
% 5.64/5.82 thf(fact_191_numeral__plus__one,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.64/5.82 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_one
% 5.64/5.82 thf(fact_192_numeral__plus__one,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.64/5.82 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_one
% 5.64/5.82 thf(fact_193_numeral__plus__one,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.64/5.82 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_one
% 5.64/5.82 thf(fact_194_numeral__plus__one,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.64/5.82 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_one
% 5.64/5.82 thf(fact_195_numeral__plus__one,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.64/5.82 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_one
% 5.64/5.82 thf(fact_196_numeral__le__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.64/5.82 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_one_iff
% 5.64/5.82 thf(fact_197_numeral__le__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.64/5.82 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_one_iff
% 5.64/5.82 thf(fact_198_numeral__le__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.64/5.82 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_one_iff
% 5.64/5.82 thf(fact_199_numeral__le__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.64/5.82 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_one_iff
% 5.64/5.82 thf(fact_200_one__eq__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( one_one_complex
% 5.64/5.82 = ( numera6690914467698888265omplex @ N ) )
% 5.64/5.82 = ( one = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_eq_numeral_iff
% 5.64/5.82 thf(fact_201_one__eq__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( one_one_real
% 5.64/5.82 = ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( one = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_eq_numeral_iff
% 5.64/5.82 thf(fact_202_one__eq__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( one_one_rat
% 5.64/5.82 = ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( one = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_eq_numeral_iff
% 5.64/5.82 thf(fact_203_one__eq__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( one_one_nat
% 5.64/5.82 = ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( one = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_eq_numeral_iff
% 5.64/5.82 thf(fact_204_one__eq__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( one_one_int
% 5.64/5.82 = ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( one = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_eq_numeral_iff
% 5.64/5.82 thf(fact_205_numeral__eq__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ( numera6690914467698888265omplex @ N )
% 5.64/5.82 = one_one_complex )
% 5.64/5.82 = ( N = one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_one_iff
% 5.64/5.82 thf(fact_206_numeral__eq__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_real @ N )
% 5.64/5.82 = one_one_real )
% 5.64/5.82 = ( N = one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_one_iff
% 5.64/5.82 thf(fact_207_numeral__eq__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_rat @ N )
% 5.64/5.82 = one_one_rat )
% 5.64/5.82 = ( N = one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_one_iff
% 5.64/5.82 thf(fact_208_numeral__eq__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_nat @ N )
% 5.64/5.82 = one_one_nat )
% 5.64/5.82 = ( N = one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_one_iff
% 5.64/5.82 thf(fact_209_numeral__eq__one__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_int @ N )
% 5.64/5.82 = one_one_int )
% 5.64/5.82 = ( N = one ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_one_iff
% 5.64/5.82 thf(fact_210_nat__1__add__1,axiom,
% 5.64/5.82 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.64/5.82 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat_1_add_1
% 5.64/5.82 thf(fact_211_semiring__norm_I85_J,axiom,
% 5.64/5.82 ! [M: num] :
% 5.64/5.82 ( ( bit0 @ M )
% 5.64/5.82 != one ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(85)
% 5.64/5.82 thf(fact_212_semiring__norm_I83_J,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( one
% 5.64/5.82 != ( bit0 @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(83)
% 5.64/5.82 thf(fact_213_semiring__norm_I69_J,axiom,
% 5.64/5.82 ! [M: num] :
% 5.64/5.82 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(69)
% 5.64/5.82 thf(fact_214_semiring__norm_I2_J,axiom,
% 5.64/5.82 ( ( plus_plus_num @ one @ one )
% 5.64/5.82 = ( bit0 @ one ) ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(2)
% 5.64/5.82 thf(fact_215_even__odd__cases,axiom,
% 5.64/5.82 ! [X2: nat] :
% 5.64/5.82 ( ! [N3: nat] :
% 5.64/5.82 ( X2
% 5.64/5.82 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.64/5.82 => ~ ! [N3: nat] :
% 5.64/5.82 ( X2
% 5.64/5.82 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % even_odd_cases
% 5.64/5.82 thf(fact_216_deg__deg__n,axiom,
% 5.64/5.82 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.82 => ( Deg = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % deg_deg_n
% 5.64/5.82 thf(fact_217_deg__SUcn__Node,axiom,
% 5.64/5.82 ! [Tree: vEBT_VEBT,N: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.64/5.82 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.82 ( Tree
% 5.64/5.82 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList2 @ S ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % deg_SUcn_Node
% 5.64/5.82 thf(fact_218_numeral__eq__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ( numera6690914467698888265omplex @ M )
% 5.64/5.82 = ( numera6690914467698888265omplex @ N ) )
% 5.64/5.82 = ( M = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_iff
% 5.64/5.82 thf(fact_219_numeral__eq__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_real @ M )
% 5.64/5.82 = ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( M = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_iff
% 5.64/5.82 thf(fact_220_numeral__eq__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_rat @ M )
% 5.64/5.82 = ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( M = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_iff
% 5.64/5.82 thf(fact_221_numeral__eq__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_nat @ M )
% 5.64/5.82 = ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( M = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_iff
% 5.64/5.82 thf(fact_222_numeral__eq__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ( numeral_numeral_int @ M )
% 5.64/5.82 = ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( M = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_eq_iff
% 5.64/5.82 thf(fact_223_semiring__norm_I87_J,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ( bit0 @ M )
% 5.64/5.82 = ( bit0 @ N ) )
% 5.64/5.82 = ( M = N ) ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(87)
% 5.64/5.82 thf(fact_224_nat_Oinject,axiom,
% 5.64/5.82 ! [X22: nat,Y2: nat] :
% 5.64/5.82 ( ( ( suc @ X22 )
% 5.64/5.82 = ( suc @ Y2 ) )
% 5.64/5.82 = ( X22 = Y2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat.inject
% 5.64/5.82 thf(fact_225_old_Onat_Oinject,axiom,
% 5.64/5.82 ! [Nat: nat,Nat2: nat] :
% 5.64/5.82 ( ( ( suc @ Nat )
% 5.64/5.82 = ( suc @ Nat2 ) )
% 5.64/5.82 = ( Nat = Nat2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % old.nat.inject
% 5.64/5.82 thf(fact_226_mi__eq__ma__no__ch,axiom,
% 5.64/5.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.64/5.82 => ( ( Mi = Ma )
% 5.64/5.82 => ( ! [X3: vEBT_VEBT] :
% 5.64/5.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 5.64/5.82 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % mi_eq_ma_no_ch
% 5.64/5.82 thf(fact_227_Suc__le__mono,axiom,
% 5.64/5.82 ! [N: nat,M: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.64/5.82 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_le_mono
% 5.64/5.82 thf(fact_228_add__Suc__right,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.64/5.82 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_Suc_right
% 5.64/5.82 thf(fact_229_semiring__norm_I6_J,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.82 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(6)
% 5.64/5.82 thf(fact_230_semiring__norm_I71_J,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(71)
% 5.64/5.82 thf(fact_231_semiring__norm_I68_J,axiom,
% 5.64/5.82 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.64/5.82
% 5.64/5.82 % semiring_norm(68)
% 5.64/5.82 thf(fact_232_numeral__plus__numeral,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.82 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_numeral
% 5.64/5.82 thf(fact_233_numeral__plus__numeral,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_numeral
% 5.64/5.82 thf(fact_234_numeral__plus__numeral,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_numeral
% 5.64/5.82 thf(fact_235_numeral__plus__numeral,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_numeral
% 5.64/5.82 thf(fact_236_numeral__plus__numeral,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_plus_numeral
% 5.64/5.82 thf(fact_237_add__numeral__left,axiom,
% 5.64/5.82 ! [V: num,W: num,Z: complex] :
% 5.64/5.82 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.64/5.82 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_numeral_left
% 5.64/5.82 thf(fact_238_add__numeral__left,axiom,
% 5.64/5.82 ! [V: num,W: num,Z: real] :
% 5.64/5.82 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.64/5.82 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_numeral_left
% 5.64/5.82 thf(fact_239_add__numeral__left,axiom,
% 5.64/5.82 ! [V: num,W: num,Z: rat] :
% 5.64/5.82 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.64/5.82 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_numeral_left
% 5.64/5.82 thf(fact_240_add__numeral__left,axiom,
% 5.64/5.82 ! [V: num,W: num,Z: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.64/5.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_numeral_left
% 5.64/5.82 thf(fact_241_add__numeral__left,axiom,
% 5.64/5.82 ! [V: num,W: num,Z: int] :
% 5.64/5.82 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.64/5.82 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_numeral_left
% 5.64/5.82 thf(fact_242_numeral__le__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_iff
% 5.64/5.82 thf(fact_243_numeral__le__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_iff
% 5.64/5.82 thf(fact_244_numeral__le__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_iff
% 5.64/5.82 thf(fact_245_numeral__le__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_le_iff
% 5.64/5.82 thf(fact_246_Suc__numeral,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_numeral
% 5.64/5.82 thf(fact_247_add__2__eq__Suc_H,axiom,
% 5.64/5.82 ! [N: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.82 = ( suc @ ( suc @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_2_eq_Suc'
% 5.64/5.82 thf(fact_248_add__2__eq__Suc,axiom,
% 5.64/5.82 ! [N: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.82 = ( suc @ ( suc @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_2_eq_Suc
% 5.64/5.82 thf(fact_249_Suc__1,axiom,
% 5.64/5.82 ( ( suc @ one_one_nat )
% 5.64/5.82 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_1
% 5.64/5.82 thf(fact_250_Suc__inject,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ( ( suc @ X2 )
% 5.64/5.82 = ( suc @ Y4 ) )
% 5.64/5.82 => ( X2 = Y4 ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_inject
% 5.64/5.82 thf(fact_251_n__not__Suc__n,axiom,
% 5.64/5.82 ! [N: nat] :
% 5.64/5.82 ( N
% 5.64/5.82 != ( suc @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % n_not_Suc_n
% 5.64/5.82 thf(fact_252_Suc__leD,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.64/5.82 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_leD
% 5.64/5.82 thf(fact_253_le__SucE,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.82 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 => ( M
% 5.64/5.82 = ( suc @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_SucE
% 5.64/5.82 thf(fact_254_le__SucI,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_SucI
% 5.64/5.82 thf(fact_255_Suc__le__D,axiom,
% 5.64/5.82 ! [N: nat,M3: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( suc @ N ) @ M3 )
% 5.64/5.82 => ? [M4: nat] :
% 5.64/5.82 ( M3
% 5.64/5.82 = ( suc @ M4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_le_D
% 5.64/5.82 thf(fact_256_le__Suc__eq,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.82 = ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 | ( M
% 5.64/5.82 = ( suc @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_Suc_eq
% 5.64/5.82 thf(fact_257_Suc__n__not__le__n,axiom,
% 5.64/5.82 ! [N: nat] :
% 5.64/5.82 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_n_not_le_n
% 5.64/5.82 thf(fact_258_not__less__eq__eq,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.64/5.82 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_less_eq_eq
% 5.64/5.82 thf(fact_259_full__nat__induct,axiom,
% 5.64/5.82 ! [P: nat > $o,N: nat] :
% 5.64/5.82 ( ! [N3: nat] :
% 5.64/5.82 ( ! [M5: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ ( suc @ M5 ) @ N3 )
% 5.64/5.82 => ( P @ M5 ) )
% 5.64/5.82 => ( P @ N3 ) )
% 5.64/5.82 => ( P @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % full_nat_induct
% 5.64/5.82 thf(fact_260_nat__induct__at__least,axiom,
% 5.64/5.82 ! [M: nat,N: nat,P: nat > $o] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 => ( ( P @ M )
% 5.64/5.82 => ( ! [N3: nat] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ N3 )
% 5.64/5.82 => ( ( P @ N3 )
% 5.64/5.82 => ( P @ ( suc @ N3 ) ) ) )
% 5.64/5.82 => ( P @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat_induct_at_least
% 5.64/5.82 thf(fact_261_transitive__stepwise__le,axiom,
% 5.64/5.82 ! [M: nat,N: nat,R: nat > nat > $o] :
% 5.64/5.82 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.82 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 5.64/5.82 => ( ! [X4: nat,Y3: nat,Z2: nat] :
% 5.64/5.82 ( ( R @ X4 @ Y3 )
% 5.64/5.82 => ( ( R @ Y3 @ Z2 )
% 5.64/5.82 => ( R @ X4 @ Z2 ) ) )
% 5.64/5.82 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.64/5.82 => ( R @ M @ N ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % transitive_stepwise_le
% 5.64/5.82 thf(fact_262_nat__arith_Osuc1,axiom,
% 5.64/5.82 ! [A4: nat,K: nat,A: nat] :
% 5.64/5.82 ( ( A4
% 5.64/5.82 = ( plus_plus_nat @ K @ A ) )
% 5.64/5.82 => ( ( suc @ A4 )
% 5.64/5.82 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat_arith.suc1
% 5.64/5.82 thf(fact_263_add__Suc,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.64/5.82 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_Suc
% 5.64/5.82 thf(fact_264_add__Suc__shift,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.64/5.82 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_Suc_shift
% 5.64/5.82 thf(fact_265_Suc__nat__number__of__add,axiom,
% 5.64/5.82 ! [V: num,N: nat] :
% 5.64/5.82 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.64/5.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_nat_number_of_add
% 5.64/5.82 thf(fact_266_lift__Suc__mono__le,axiom,
% 5.64/5.82 ! [F: nat > set_nat,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_mono_le
% 5.64/5.82 thf(fact_267_lift__Suc__mono__le,axiom,
% 5.64/5.82 ! [F: nat > rat,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_mono_le
% 5.64/5.82 thf(fact_268_lift__Suc__mono__le,axiom,
% 5.64/5.82 ! [F: nat > num,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_mono_le
% 5.64/5.82 thf(fact_269_lift__Suc__mono__le,axiom,
% 5.64/5.82 ! [F: nat > nat,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_mono_le
% 5.64/5.82 thf(fact_270_lift__Suc__mono__le,axiom,
% 5.64/5.82 ! [F: nat > int,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_mono_le
% 5.64/5.82 thf(fact_271_lift__Suc__mono__le,axiom,
% 5.64/5.82 ! [F: nat > real,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_real @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_mono_le
% 5.64/5.82 thf(fact_272_lift__Suc__antimono__le,axiom,
% 5.64/5.82 ! [F: nat > set_nat,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_set_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_antimono_le
% 5.64/5.82 thf(fact_273_lift__Suc__antimono__le,axiom,
% 5.64/5.82 ! [F: nat > rat,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_rat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_antimono_le
% 5.64/5.82 thf(fact_274_lift__Suc__antimono__le,axiom,
% 5.64/5.82 ! [F: nat > num,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_num @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_antimono_le
% 5.64/5.82 thf(fact_275_lift__Suc__antimono__le,axiom,
% 5.64/5.82 ! [F: nat > nat,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_antimono_le
% 5.64/5.82 thf(fact_276_lift__Suc__antimono__le,axiom,
% 5.64/5.82 ! [F: nat > int,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_int @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_antimono_le
% 5.64/5.82 thf(fact_277_lift__Suc__antimono__le,axiom,
% 5.64/5.82 ! [F: nat > real,N: nat,N4: nat] :
% 5.64/5.82 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.64/5.82 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.64/5.82 => ( ord_less_eq_real @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % lift_Suc_antimono_le
% 5.64/5.82 thf(fact_278_Suc__eq__plus1,axiom,
% 5.64/5.82 ( suc
% 5.64/5.82 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_eq_plus1
% 5.64/5.82 thf(fact_279_plus__1__eq__Suc,axiom,
% 5.64/5.82 ( ( plus_plus_nat @ one_one_nat )
% 5.64/5.82 = suc ) ).
% 5.64/5.82
% 5.64/5.82 % plus_1_eq_Suc
% 5.64/5.82 thf(fact_280_Suc__eq__plus1__left,axiom,
% 5.64/5.82 ( suc
% 5.64/5.82 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_eq_plus1_left
% 5.64/5.82 thf(fact_281_is__num__normalize_I1_J,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % is_num_normalize(1)
% 5.64/5.82 thf(fact_282_is__num__normalize_I1_J,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % is_num_normalize(1)
% 5.64/5.82 thf(fact_283_is__num__normalize_I1_J,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.82 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % is_num_normalize(1)
% 5.64/5.82 thf(fact_284_add__One__commute,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( plus_plus_num @ one @ N )
% 5.64/5.82 = ( plus_plus_num @ N @ one ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_One_commute
% 5.64/5.82 thf(fact_285_le__num__One__iff,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ( ( ord_less_eq_num @ X2 @ one )
% 5.64/5.82 = ( X2 = one ) ) ).
% 5.64/5.82
% 5.64/5.82 % le_num_One_iff
% 5.64/5.82 thf(fact_286_height__node,axiom,
% 5.64/5.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.82 => ( ord_less_eq_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % height_node
% 5.64/5.82 thf(fact_287_le__numeral__extra_I4_J,axiom,
% 5.64/5.82 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.64/5.82
% 5.64/5.82 % le_numeral_extra(4)
% 5.64/5.82 thf(fact_288_le__numeral__extra_I4_J,axiom,
% 5.64/5.82 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.64/5.82
% 5.64/5.82 % le_numeral_extra(4)
% 5.64/5.82 thf(fact_289_le__numeral__extra_I4_J,axiom,
% 5.64/5.82 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.64/5.82
% 5.64/5.82 % le_numeral_extra(4)
% 5.64/5.82 thf(fact_290_le__numeral__extra_I4_J,axiom,
% 5.64/5.82 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.64/5.82
% 5.64/5.82 % le_numeral_extra(4)
% 5.64/5.82 thf(fact_291_one__le__numeral,axiom,
% 5.64/5.82 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_le_numeral
% 5.64/5.82 thf(fact_292_one__le__numeral,axiom,
% 5.64/5.82 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_le_numeral
% 5.64/5.82 thf(fact_293_one__le__numeral,axiom,
% 5.64/5.82 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_le_numeral
% 5.64/5.82 thf(fact_294_one__le__numeral,axiom,
% 5.64/5.82 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_le_numeral
% 5.64/5.82 thf(fact_295_numeral__Bit0,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.64/5.82 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_Bit0
% 5.64/5.82 thf(fact_296_numeral__Bit0,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.64/5.82 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_Bit0
% 5.64/5.82 thf(fact_297_numeral__Bit0,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.64/5.82 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_Bit0
% 5.64/5.82 thf(fact_298_numeral__Bit0,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.64/5.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_Bit0
% 5.64/5.82 thf(fact_299_numeral__Bit0,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.64/5.82 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_Bit0
% 5.64/5.82 thf(fact_300_one__plus__numeral__commute,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X2 ) )
% 5.64/5.82 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral_commute
% 5.64/5.82 thf(fact_301_one__plus__numeral__commute,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.64/5.82 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral_commute
% 5.64/5.82 thf(fact_302_one__plus__numeral__commute,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.64/5.82 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral_commute
% 5.64/5.82 thf(fact_303_one__plus__numeral__commute,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.64/5.82 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral_commute
% 5.64/5.82 thf(fact_304_one__plus__numeral__commute,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.64/5.82 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_plus_numeral_commute
% 5.64/5.82 thf(fact_305_numeral__One,axiom,
% 5.64/5.82 ( ( numera6690914467698888265omplex @ one )
% 5.64/5.82 = one_one_complex ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_One
% 5.64/5.82 thf(fact_306_numeral__One,axiom,
% 5.64/5.82 ( ( numeral_numeral_real @ one )
% 5.64/5.82 = one_one_real ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_One
% 5.64/5.82 thf(fact_307_numeral__One,axiom,
% 5.64/5.82 ( ( numeral_numeral_rat @ one )
% 5.64/5.82 = one_one_rat ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_One
% 5.64/5.82 thf(fact_308_numeral__One,axiom,
% 5.64/5.82 ( ( numeral_numeral_nat @ one )
% 5.64/5.82 = one_one_nat ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_One
% 5.64/5.82 thf(fact_309_numeral__One,axiom,
% 5.64/5.82 ( ( numeral_numeral_int @ one )
% 5.64/5.82 = one_one_int ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_One
% 5.64/5.82 thf(fact_310_numerals_I1_J,axiom,
% 5.64/5.82 ( ( numeral_numeral_nat @ one )
% 5.64/5.82 = one_one_nat ) ).
% 5.64/5.82
% 5.64/5.82 % numerals(1)
% 5.64/5.82 thf(fact_311_enat__ord__number_I1_J,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.64/5.82 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % enat_ord_number(1)
% 5.64/5.82 thf(fact_312_add__shift,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.82 ( ( ( plus_plus_nat @ X2 @ Y4 )
% 5.64/5.82 = Z )
% 5.64/5.82 = ( ( vEBT_VEBT_add @ ( some_nat @ X2 ) @ ( some_nat @ Y4 ) )
% 5.64/5.82 = ( some_nat @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_shift
% 5.64/5.82 thf(fact_313_maxbmo,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,X2: nat] :
% 5.64/5.82 ( ( ( vEBT_vebt_maxt @ T )
% 5.64/5.82 = ( some_nat @ X2 ) )
% 5.64/5.82 => ( vEBT_V8194947554948674370ptions @ T @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % maxbmo
% 5.64/5.82 thf(fact_314_not__min__Null__member,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT] :
% 5.64/5.82 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.64/5.82 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_min_Null_member
% 5.64/5.82 thf(fact_315_dbl__simps_I3_J,axiom,
% 5.64/5.82 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.64/5.82 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(3)
% 5.64/5.82 thf(fact_316_dbl__simps_I3_J,axiom,
% 5.64/5.82 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.64/5.82 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(3)
% 5.64/5.82 thf(fact_317_dbl__simps_I3_J,axiom,
% 5.64/5.82 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.64/5.82 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(3)
% 5.64/5.82 thf(fact_318_dbl__simps_I3_J,axiom,
% 5.64/5.82 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.64/5.82 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(3)
% 5.64/5.82 thf(fact_319__C5_Ohyps_C_I8_J,axiom,
% 5.64/5.82 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.64/5.82
% 5.64/5.82 % "5.hyps"(8)
% 5.64/5.82 thf(fact_320__C5_Ohyps_C_I2_J,axiom,
% 5.64/5.82 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.64/5.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.64/5.82
% 5.64/5.82 % "5.hyps"(2)
% 5.64/5.82 thf(fact_321_valid__member__both__member__options,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.64/5.82 => ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % valid_member_both_member_options
% 5.64/5.82 thf(fact_322_both__member__options__equiv__member,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.64/5.82 = ( vEBT_vebt_member @ T @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % both_member_options_equiv_member
% 5.64/5.82 thf(fact_323_verit__eq__simplify_I8_J,axiom,
% 5.64/5.82 ! [X22: num,Y2: num] :
% 5.64/5.82 ( ( ( bit0 @ X22 )
% 5.64/5.82 = ( bit0 @ Y2 ) )
% 5.64/5.82 = ( X22 = Y2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % verit_eq_simplify(8)
% 5.64/5.82 thf(fact_324_order__refl,axiom,
% 5.64/5.82 ! [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_refl
% 5.64/5.82 thf(fact_325_order__refl,axiom,
% 5.64/5.82 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_refl
% 5.64/5.82 thf(fact_326_order__refl,axiom,
% 5.64/5.82 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_refl
% 5.64/5.82 thf(fact_327_order__refl,axiom,
% 5.64/5.82 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_refl
% 5.64/5.82 thf(fact_328_order__refl,axiom,
% 5.64/5.82 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_refl
% 5.64/5.82 thf(fact_329_order__refl,axiom,
% 5.64/5.82 ! [X2: real] : ( ord_less_eq_real @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_refl
% 5.64/5.82 thf(fact_330_min__Null__member,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,X2: nat] :
% 5.64/5.82 ( ( vEBT_VEBT_minNull @ T )
% 5.64/5.82 => ~ ( vEBT_vebt_member @ T @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % min_Null_member
% 5.64/5.82 thf(fact_331_power__shift,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.82 ( ( ( power_power_nat @ X2 @ Y4 )
% 5.64/5.82 = Z )
% 5.64/5.82 = ( ( vEBT_VEBT_power @ ( some_nat @ X2 ) @ ( some_nat @ Y4 ) )
% 5.64/5.82 = ( some_nat @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % power_shift
% 5.64/5.82 thf(fact_332_dual__order_Orefl,axiom,
% 5.64/5.82 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.refl
% 5.64/5.82 thf(fact_333_dual__order_Orefl,axiom,
% 5.64/5.82 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.refl
% 5.64/5.82 thf(fact_334_dual__order_Orefl,axiom,
% 5.64/5.82 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.refl
% 5.64/5.82 thf(fact_335_dual__order_Orefl,axiom,
% 5.64/5.82 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.refl
% 5.64/5.82 thf(fact_336_dual__order_Orefl,axiom,
% 5.64/5.82 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.refl
% 5.64/5.82 thf(fact_337_dual__order_Orefl,axiom,
% 5.64/5.82 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.refl
% 5.64/5.82 thf(fact_338_maxt__member,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( ( vEBT_vebt_maxt @ T )
% 5.64/5.82 = ( some_nat @ Maxi ) )
% 5.64/5.82 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % maxt_member
% 5.64/5.82 thf(fact_339_maxt__corr__help,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X2: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( ( vEBT_vebt_maxt @ T )
% 5.64/5.82 = ( some_nat @ Maxi ) )
% 5.64/5.82 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.64/5.82 => ( ord_less_eq_nat @ X2 @ Maxi ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % maxt_corr_help
% 5.64/5.82 thf(fact_340_member__bound,axiom,
% 5.64/5.82 ! [Tree: vEBT_VEBT,X2: nat,N: nat] :
% 5.64/5.82 ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.64/5.82 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.64/5.82 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % member_bound
% 5.64/5.82 thf(fact_341_numeral__less__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_less_iff
% 5.64/5.82 thf(fact_342_numeral__less__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_less_iff
% 5.64/5.82 thf(fact_343_numeral__less__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_less_iff
% 5.64/5.82 thf(fact_344_numeral__less__iff,axiom,
% 5.64/5.82 ! [M: num,N: num] :
% 5.64/5.82 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % numeral_less_iff
% 5.64/5.82 thf(fact_345_add__less__cancel__right,axiom,
% 5.64/5.82 ! [A: real,C: real,B: real] :
% 5.64/5.82 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.64/5.82 = ( ord_less_real @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_right
% 5.64/5.82 thf(fact_346_add__less__cancel__right,axiom,
% 5.64/5.82 ! [A: rat,C: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.82 = ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_right
% 5.64/5.82 thf(fact_347_add__less__cancel__right,axiom,
% 5.64/5.82 ! [A: nat,C: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.82 = ( ord_less_nat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_right
% 5.64/5.82 thf(fact_348_add__less__cancel__right,axiom,
% 5.64/5.82 ! [A: int,C: int,B: int] :
% 5.64/5.82 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.64/5.82 = ( ord_less_int @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_right
% 5.64/5.82 thf(fact_349_add__less__cancel__left,axiom,
% 5.64/5.82 ! [C: real,A: real,B: real] :
% 5.64/5.82 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.64/5.82 = ( ord_less_real @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_left
% 5.64/5.82 thf(fact_350_add__less__cancel__left,axiom,
% 5.64/5.82 ! [C: rat,A: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.64/5.82 = ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_left
% 5.64/5.82 thf(fact_351_add__less__cancel__left,axiom,
% 5.64/5.82 ! [C: nat,A: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.64/5.82 = ( ord_less_nat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_left
% 5.64/5.82 thf(fact_352_add__less__cancel__left,axiom,
% 5.64/5.82 ! [C: int,A: int,B: int] :
% 5.64/5.82 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.64/5.82 = ( ord_less_int @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_less_cancel_left
% 5.64/5.82 thf(fact_353_Suc__less__eq,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.64/5.82 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_less_eq
% 5.64/5.82 thf(fact_354_Suc__mono,axiom,
% 5.64/5.82 ! [M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_nat @ M @ N )
% 5.64/5.82 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % Suc_mono
% 5.64/5.82 thf(fact_355_lessI,axiom,
% 5.64/5.82 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % lessI
% 5.64/5.82 thf(fact_356_nat__add__left__cancel__less,axiom,
% 5.64/5.82 ! [K: nat,M: nat,N: nat] :
% 5.64/5.82 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.64/5.82 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % nat_add_left_cancel_less
% 5.64/5.82 thf(fact_357_valid__insert__both__member__options__add,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X2 ) @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % valid_insert_both_member_options_add
% 5.64/5.82 thf(fact_358_valid__insert__both__member__options__pres,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,X2: nat,Y4: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.82 => ( ( ord_less_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.82 => ( ( vEBT_V8194947554948674370ptions @ T @ X2 )
% 5.64/5.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y4 ) @ X2 ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % valid_insert_both_member_options_pres
% 5.64/5.82 thf(fact_359_post__member__pre__member,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,X2: nat,Y4: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.82 => ( ( ord_less_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.82 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X2 ) @ Y4 )
% 5.64/5.82 => ( ( vEBT_vebt_member @ T @ Y4 )
% 5.64/5.82 | ( X2 = Y4 ) ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % post_member_pre_member
% 5.64/5.82 thf(fact_360_member__correct,axiom,
% 5.64/5.82 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.82 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.64/5.82 = ( member_nat @ X2 @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % member_correct
% 5.64/5.82 thf(fact_361_set__n__deg__not__0,axiom,
% 5.64/5.82 ! [TreeList: list_VEBT_VEBT,N: nat,M: nat] :
% 5.64/5.82 ( ! [X4: vEBT_VEBT] :
% 5.64/5.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.82 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.64/5.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.64/5.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.82 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % set_n_deg_not_0
% 5.64/5.82 thf(fact_362_mi__ma__2__deg,axiom,
% 5.64/5.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.64/5.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.82 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.64/5.82 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % mi_ma_2_deg
% 5.64/5.82 thf(fact_363_dbl__simps_I5_J,axiom,
% 5.64/5.82 ! [K: num] :
% 5.64/5.82 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.64/5.82 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(5)
% 5.64/5.82 thf(fact_364_dbl__simps_I5_J,axiom,
% 5.64/5.82 ! [K: num] :
% 5.64/5.82 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.64/5.82 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(5)
% 5.64/5.82 thf(fact_365_dbl__simps_I5_J,axiom,
% 5.64/5.82 ! [K: num] :
% 5.64/5.82 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.64/5.82 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(5)
% 5.64/5.82 thf(fact_366_dbl__simps_I5_J,axiom,
% 5.64/5.82 ! [K: num] :
% 5.64/5.82 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.64/5.82 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dbl_simps(5)
% 5.64/5.82 thf(fact_367_one__less__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.64/5.82 = ( ord_less_num @ one @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_less_numeral_iff
% 5.64/5.82 thf(fact_368_one__less__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.64/5.82 = ( ord_less_num @ one @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_less_numeral_iff
% 5.64/5.82 thf(fact_369_one__less__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.64/5.82 = ( ord_less_num @ one @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_less_numeral_iff
% 5.64/5.82 thf(fact_370_one__less__numeral__iff,axiom,
% 5.64/5.82 ! [N: num] :
% 5.64/5.82 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.64/5.82 = ( ord_less_num @ one @ N ) ) ).
% 5.64/5.82
% 5.64/5.82 % one_less_numeral_iff
% 5.64/5.82 thf(fact_371_add__def,axiom,
% 5.64/5.82 ( vEBT_VEBT_add
% 5.64/5.82 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.64/5.82
% 5.64/5.82 % add_def
% 5.64/5.82 thf(fact_372__C5_Ohyps_C_I5_J,axiom,
% 5.64/5.82 ! [I2: nat] :
% 5.64/5.82 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.64/5.82 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X5 ) )
% 5.64/5.82 = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % "5.hyps"(5)
% 5.64/5.82 thf(fact_373_verit__comp__simplify1_I1_J,axiom,
% 5.64/5.82 ! [A: real] :
% 5.64/5.82 ~ ( ord_less_real @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % verit_comp_simplify1(1)
% 5.64/5.82 thf(fact_374_verit__comp__simplify1_I1_J,axiom,
% 5.64/5.82 ! [A: rat] :
% 5.64/5.82 ~ ( ord_less_rat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % verit_comp_simplify1(1)
% 5.64/5.82 thf(fact_375_verit__comp__simplify1_I1_J,axiom,
% 5.64/5.82 ! [A: num] :
% 5.64/5.82 ~ ( ord_less_num @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % verit_comp_simplify1(1)
% 5.64/5.82 thf(fact_376_verit__comp__simplify1_I1_J,axiom,
% 5.64/5.82 ! [A: nat] :
% 5.64/5.82 ~ ( ord_less_nat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % verit_comp_simplify1(1)
% 5.64/5.82 thf(fact_377_verit__comp__simplify1_I1_J,axiom,
% 5.64/5.82 ! [A: int] :
% 5.64/5.82 ~ ( ord_less_int @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % verit_comp_simplify1(1)
% 5.64/5.82 thf(fact_378_lt__ex,axiom,
% 5.64/5.82 ! [X2: real] :
% 5.64/5.82 ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % lt_ex
% 5.64/5.82 thf(fact_379_lt__ex,axiom,
% 5.64/5.82 ! [X2: rat] :
% 5.64/5.82 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % lt_ex
% 5.64/5.82 thf(fact_380_lt__ex,axiom,
% 5.64/5.82 ! [X2: int] :
% 5.64/5.82 ? [Y3: int] : ( ord_less_int @ Y3 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % lt_ex
% 5.64/5.82 thf(fact_381_gt__ex,axiom,
% 5.64/5.82 ! [X2: real] :
% 5.64/5.82 ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 5.64/5.82
% 5.64/5.82 % gt_ex
% 5.64/5.82 thf(fact_382_gt__ex,axiom,
% 5.64/5.82 ! [X2: rat] :
% 5.64/5.82 ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 5.64/5.82
% 5.64/5.82 % gt_ex
% 5.64/5.82 thf(fact_383_gt__ex,axiom,
% 5.64/5.82 ! [X2: nat] :
% 5.64/5.82 ? [X_12: nat] : ( ord_less_nat @ X2 @ X_12 ) ).
% 5.64/5.82
% 5.64/5.82 % gt_ex
% 5.64/5.82 thf(fact_384_gt__ex,axiom,
% 5.64/5.82 ! [X2: int] :
% 5.64/5.82 ? [X_12: int] : ( ord_less_int @ X2 @ X_12 ) ).
% 5.64/5.82
% 5.64/5.82 % gt_ex
% 5.64/5.82 thf(fact_385_dense,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 => ? [Z2: real] :
% 5.64/5.82 ( ( ord_less_real @ X2 @ Z2 )
% 5.64/5.82 & ( ord_less_real @ Z2 @ Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dense
% 5.64/5.82 thf(fact_386_dense,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 => ? [Z2: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X2 @ Z2 )
% 5.64/5.82 & ( ord_less_rat @ Z2 @ Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dense
% 5.64/5.82 thf(fact_387_less__imp__neq,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 => ( X2 != Y4 ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_imp_neq
% 5.64/5.82 thf(fact_388_less__imp__neq,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 => ( X2 != Y4 ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_imp_neq
% 5.64/5.82 thf(fact_389_less__imp__neq,axiom,
% 5.64/5.82 ! [X2: num,Y4: num] :
% 5.64/5.82 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.82 => ( X2 != Y4 ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_imp_neq
% 5.64/5.82 thf(fact_390_less__imp__neq,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.82 => ( X2 != Y4 ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_imp_neq
% 5.64/5.82 thf(fact_391_less__imp__neq,axiom,
% 5.64/5.82 ! [X2: int,Y4: int] :
% 5.64/5.82 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.82 => ( X2 != Y4 ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_imp_neq
% 5.64/5.82 thf(fact_392_order_Oasym,axiom,
% 5.64/5.82 ! [A: real,B: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.asym
% 5.64/5.82 thf(fact_393_order_Oasym,axiom,
% 5.64/5.82 ! [A: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.asym
% 5.64/5.82 thf(fact_394_order_Oasym,axiom,
% 5.64/5.82 ! [A: num,B: num] :
% 5.64/5.82 ( ( ord_less_num @ A @ B )
% 5.64/5.82 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.asym
% 5.64/5.82 thf(fact_395_order_Oasym,axiom,
% 5.64/5.82 ! [A: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_nat @ A @ B )
% 5.64/5.82 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.asym
% 5.64/5.82 thf(fact_396_order_Oasym,axiom,
% 5.64/5.82 ! [A: int,B: int] :
% 5.64/5.82 ( ( ord_less_int @ A @ B )
% 5.64/5.82 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.asym
% 5.64/5.82 thf(fact_397_ord__eq__less__trans,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( A = B )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ord_less_real @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_trans
% 5.64/5.82 thf(fact_398_ord__eq__less__trans,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( A = B )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_trans
% 5.64/5.82 thf(fact_399_ord__eq__less__trans,axiom,
% 5.64/5.82 ! [A: num,B: num,C: num] :
% 5.64/5.82 ( ( A = B )
% 5.64/5.82 => ( ( ord_less_num @ B @ C )
% 5.64/5.82 => ( ord_less_num @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_trans
% 5.64/5.82 thf(fact_400_ord__eq__less__trans,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( A = B )
% 5.64/5.82 => ( ( ord_less_nat @ B @ C )
% 5.64/5.82 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_trans
% 5.64/5.82 thf(fact_401_ord__eq__less__trans,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( A = B )
% 5.64/5.82 => ( ( ord_less_int @ B @ C )
% 5.64/5.82 => ( ord_less_int @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_trans
% 5.64/5.82 thf(fact_402_ord__less__eq__trans,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( B = C )
% 5.64/5.82 => ( ord_less_real @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_trans
% 5.64/5.82 thf(fact_403_ord__less__eq__trans,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( B = C )
% 5.64/5.82 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_trans
% 5.64/5.82 thf(fact_404_ord__less__eq__trans,axiom,
% 5.64/5.82 ! [A: num,B: num,C: num] :
% 5.64/5.82 ( ( ord_less_num @ A @ B )
% 5.64/5.82 => ( ( B = C )
% 5.64/5.82 => ( ord_less_num @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_trans
% 5.64/5.82 thf(fact_405_ord__less__eq__trans,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_nat @ A @ B )
% 5.64/5.82 => ( ( B = C )
% 5.64/5.82 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_trans
% 5.64/5.82 thf(fact_406_ord__less__eq__trans,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( ord_less_int @ A @ B )
% 5.64/5.82 => ( ( B = C )
% 5.64/5.82 => ( ord_less_int @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_trans
% 5.64/5.82 thf(fact_407_less__induct,axiom,
% 5.64/5.82 ! [P: nat > $o,A: nat] :
% 5.64/5.82 ( ! [X4: nat] :
% 5.64/5.82 ( ! [Y5: nat] :
% 5.64/5.82 ( ( ord_less_nat @ Y5 @ X4 )
% 5.64/5.82 => ( P @ Y5 ) )
% 5.64/5.82 => ( P @ X4 ) )
% 5.64/5.82 => ( P @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % less_induct
% 5.64/5.82 thf(fact_408_antisym__conv3,axiom,
% 5.64/5.82 ! [Y4: real,X2: real] :
% 5.64/5.82 ( ~ ( ord_less_real @ Y4 @ X2 )
% 5.64/5.82 => ( ( ~ ( ord_less_real @ X2 @ Y4 ) )
% 5.64/5.82 = ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % antisym_conv3
% 5.64/5.82 thf(fact_409_antisym__conv3,axiom,
% 5.64/5.82 ! [Y4: rat,X2: rat] :
% 5.64/5.82 ( ~ ( ord_less_rat @ Y4 @ X2 )
% 5.64/5.82 => ( ( ~ ( ord_less_rat @ X2 @ Y4 ) )
% 5.64/5.82 = ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % antisym_conv3
% 5.64/5.82 thf(fact_410_antisym__conv3,axiom,
% 5.64/5.82 ! [Y4: num,X2: num] :
% 5.64/5.82 ( ~ ( ord_less_num @ Y4 @ X2 )
% 5.64/5.82 => ( ( ~ ( ord_less_num @ X2 @ Y4 ) )
% 5.64/5.82 = ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % antisym_conv3
% 5.64/5.82 thf(fact_411_antisym__conv3,axiom,
% 5.64/5.82 ! [Y4: nat,X2: nat] :
% 5.64/5.82 ( ~ ( ord_less_nat @ Y4 @ X2 )
% 5.64/5.82 => ( ( ~ ( ord_less_nat @ X2 @ Y4 ) )
% 5.64/5.82 = ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % antisym_conv3
% 5.64/5.82 thf(fact_412_antisym__conv3,axiom,
% 5.64/5.82 ! [Y4: int,X2: int] :
% 5.64/5.82 ( ~ ( ord_less_int @ Y4 @ X2 )
% 5.64/5.82 => ( ( ~ ( ord_less_int @ X2 @ Y4 ) )
% 5.64/5.82 = ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % antisym_conv3
% 5.64/5.82 thf(fact_413_linorder__cases,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ~ ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 => ( ( X2 != Y4 )
% 5.64/5.82 => ( ord_less_real @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_cases
% 5.64/5.82 thf(fact_414_linorder__cases,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ~ ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 => ( ( X2 != Y4 )
% 5.64/5.82 => ( ord_less_rat @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_cases
% 5.64/5.82 thf(fact_415_linorder__cases,axiom,
% 5.64/5.82 ! [X2: num,Y4: num] :
% 5.64/5.82 ( ~ ( ord_less_num @ X2 @ Y4 )
% 5.64/5.82 => ( ( X2 != Y4 )
% 5.64/5.82 => ( ord_less_num @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_cases
% 5.64/5.82 thf(fact_416_linorder__cases,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ~ ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.82 => ( ( X2 != Y4 )
% 5.64/5.82 => ( ord_less_nat @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_cases
% 5.64/5.82 thf(fact_417_linorder__cases,axiom,
% 5.64/5.82 ! [X2: int,Y4: int] :
% 5.64/5.82 ( ~ ( ord_less_int @ X2 @ Y4 )
% 5.64/5.82 => ( ( X2 != Y4 )
% 5.64/5.82 => ( ord_less_int @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_cases
% 5.64/5.82 thf(fact_418_dual__order_Oasym,axiom,
% 5.64/5.82 ! [B: real,A: real] :
% 5.64/5.82 ( ( ord_less_real @ B @ A )
% 5.64/5.82 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.asym
% 5.64/5.82 thf(fact_419_dual__order_Oasym,axiom,
% 5.64/5.82 ! [B: rat,A: rat] :
% 5.64/5.82 ( ( ord_less_rat @ B @ A )
% 5.64/5.82 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.asym
% 5.64/5.82 thf(fact_420_dual__order_Oasym,axiom,
% 5.64/5.82 ! [B: num,A: num] :
% 5.64/5.82 ( ( ord_less_num @ B @ A )
% 5.64/5.82 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.asym
% 5.64/5.82 thf(fact_421_dual__order_Oasym,axiom,
% 5.64/5.82 ! [B: nat,A: nat] :
% 5.64/5.82 ( ( ord_less_nat @ B @ A )
% 5.64/5.82 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.asym
% 5.64/5.82 thf(fact_422_dual__order_Oasym,axiom,
% 5.64/5.82 ! [B: int,A: int] :
% 5.64/5.82 ( ( ord_less_int @ B @ A )
% 5.64/5.82 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.asym
% 5.64/5.82 thf(fact_423_dual__order_Oirrefl,axiom,
% 5.64/5.82 ! [A: real] :
% 5.64/5.82 ~ ( ord_less_real @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.irrefl
% 5.64/5.82 thf(fact_424_dual__order_Oirrefl,axiom,
% 5.64/5.82 ! [A: rat] :
% 5.64/5.82 ~ ( ord_less_rat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.irrefl
% 5.64/5.82 thf(fact_425_dual__order_Oirrefl,axiom,
% 5.64/5.82 ! [A: num] :
% 5.64/5.82 ~ ( ord_less_num @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.irrefl
% 5.64/5.82 thf(fact_426_dual__order_Oirrefl,axiom,
% 5.64/5.82 ! [A: nat] :
% 5.64/5.82 ~ ( ord_less_nat @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.irrefl
% 5.64/5.82 thf(fact_427_dual__order_Oirrefl,axiom,
% 5.64/5.82 ! [A: int] :
% 5.64/5.82 ~ ( ord_less_int @ A @ A ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.irrefl
% 5.64/5.82 thf(fact_428_exists__least__iff,axiom,
% 5.64/5.82 ( ( ^ [P3: nat > $o] :
% 5.64/5.82 ? [X6: nat] : ( P3 @ X6 ) )
% 5.64/5.82 = ( ^ [P4: nat > $o] :
% 5.64/5.82 ? [N2: nat] :
% 5.64/5.82 ( ( P4 @ N2 )
% 5.64/5.82 & ! [M2: nat] :
% 5.64/5.82 ( ( ord_less_nat @ M2 @ N2 )
% 5.64/5.82 => ~ ( P4 @ M2 ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % exists_least_iff
% 5.64/5.82 thf(fact_429_linorder__less__wlog,axiom,
% 5.64/5.82 ! [P: real > real > $o,A: real,B: real] :
% 5.64/5.82 ( ! [A5: real,B5: real] :
% 5.64/5.82 ( ( ord_less_real @ A5 @ B5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 5.64/5.82 => ( ! [A5: real,B5: real] :
% 5.64/5.82 ( ( P @ B5 @ A5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_less_wlog
% 5.64/5.82 thf(fact_430_linorder__less__wlog,axiom,
% 5.64/5.82 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.64/5.82 ( ! [A5: rat,B5: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A5 @ B5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 5.64/5.82 => ( ! [A5: rat,B5: rat] :
% 5.64/5.82 ( ( P @ B5 @ A5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_less_wlog
% 5.64/5.82 thf(fact_431_linorder__less__wlog,axiom,
% 5.64/5.82 ! [P: num > num > $o,A: num,B: num] :
% 5.64/5.82 ( ! [A5: num,B5: num] :
% 5.64/5.82 ( ( ord_less_num @ A5 @ B5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( ! [A5: num] : ( P @ A5 @ A5 )
% 5.64/5.82 => ( ! [A5: num,B5: num] :
% 5.64/5.82 ( ( P @ B5 @ A5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_less_wlog
% 5.64/5.82 thf(fact_432_linorder__less__wlog,axiom,
% 5.64/5.82 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.64/5.82 ( ! [A5: nat,B5: nat] :
% 5.64/5.82 ( ( ord_less_nat @ A5 @ B5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 5.64/5.82 => ( ! [A5: nat,B5: nat] :
% 5.64/5.82 ( ( P @ B5 @ A5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_less_wlog
% 5.64/5.82 thf(fact_433_linorder__less__wlog,axiom,
% 5.64/5.82 ! [P: int > int > $o,A: int,B: int] :
% 5.64/5.82 ( ! [A5: int,B5: int] :
% 5.64/5.82 ( ( ord_less_int @ A5 @ B5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 5.64/5.82 => ( ! [A5: int,B5: int] :
% 5.64/5.82 ( ( P @ B5 @ A5 )
% 5.64/5.82 => ( P @ A5 @ B5 ) )
% 5.64/5.82 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_less_wlog
% 5.64/5.82 thf(fact_434_order_Ostrict__trans,axiom,
% 5.64/5.82 ! [A: real,B: real,C: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ord_less_real @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_trans
% 5.64/5.82 thf(fact_435_order_Ostrict__trans,axiom,
% 5.64/5.82 ! [A: rat,B: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_trans
% 5.64/5.82 thf(fact_436_order_Ostrict__trans,axiom,
% 5.64/5.82 ! [A: num,B: num,C: num] :
% 5.64/5.82 ( ( ord_less_num @ A @ B )
% 5.64/5.82 => ( ( ord_less_num @ B @ C )
% 5.64/5.82 => ( ord_less_num @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_trans
% 5.64/5.82 thf(fact_437_order_Ostrict__trans,axiom,
% 5.64/5.82 ! [A: nat,B: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_nat @ A @ B )
% 5.64/5.82 => ( ( ord_less_nat @ B @ C )
% 5.64/5.82 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_trans
% 5.64/5.82 thf(fact_438_order_Ostrict__trans,axiom,
% 5.64/5.82 ! [A: int,B: int,C: int] :
% 5.64/5.82 ( ( ord_less_int @ A @ B )
% 5.64/5.82 => ( ( ord_less_int @ B @ C )
% 5.64/5.82 => ( ord_less_int @ A @ C ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_trans
% 5.64/5.82 thf(fact_439_not__less__iff__gr__or__eq,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ( ~ ( ord_less_real @ X2 @ Y4 ) )
% 5.64/5.82 = ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.82 | ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_less_iff_gr_or_eq
% 5.64/5.82 thf(fact_440_not__less__iff__gr__or__eq,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ( ~ ( ord_less_rat @ X2 @ Y4 ) )
% 5.64/5.82 = ( ( ord_less_rat @ Y4 @ X2 )
% 5.64/5.82 | ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_less_iff_gr_or_eq
% 5.64/5.82 thf(fact_441_not__less__iff__gr__or__eq,axiom,
% 5.64/5.82 ! [X2: num,Y4: num] :
% 5.64/5.82 ( ( ~ ( ord_less_num @ X2 @ Y4 ) )
% 5.64/5.82 = ( ( ord_less_num @ Y4 @ X2 )
% 5.64/5.82 | ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_less_iff_gr_or_eq
% 5.64/5.82 thf(fact_442_not__less__iff__gr__or__eq,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ( ~ ( ord_less_nat @ X2 @ Y4 ) )
% 5.64/5.82 = ( ( ord_less_nat @ Y4 @ X2 )
% 5.64/5.82 | ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_less_iff_gr_or_eq
% 5.64/5.82 thf(fact_443_not__less__iff__gr__or__eq,axiom,
% 5.64/5.82 ! [X2: int,Y4: int] :
% 5.64/5.82 ( ( ~ ( ord_less_int @ X2 @ Y4 ) )
% 5.64/5.82 = ( ( ord_less_int @ Y4 @ X2 )
% 5.64/5.82 | ( X2 = Y4 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % not_less_iff_gr_or_eq
% 5.64/5.82 thf(fact_444_dual__order_Ostrict__trans,axiom,
% 5.64/5.82 ! [B: real,A: real,C: real] :
% 5.64/5.82 ( ( ord_less_real @ B @ A )
% 5.64/5.82 => ( ( ord_less_real @ C @ B )
% 5.64/5.82 => ( ord_less_real @ C @ A ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_trans
% 5.64/5.82 thf(fact_445_dual__order_Ostrict__trans,axiom,
% 5.64/5.82 ! [B: rat,A: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_rat @ B @ A )
% 5.64/5.82 => ( ( ord_less_rat @ C @ B )
% 5.64/5.82 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_trans
% 5.64/5.82 thf(fact_446_dual__order_Ostrict__trans,axiom,
% 5.64/5.82 ! [B: num,A: num,C: num] :
% 5.64/5.82 ( ( ord_less_num @ B @ A )
% 5.64/5.82 => ( ( ord_less_num @ C @ B )
% 5.64/5.82 => ( ord_less_num @ C @ A ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_trans
% 5.64/5.82 thf(fact_447_dual__order_Ostrict__trans,axiom,
% 5.64/5.82 ! [B: nat,A: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_nat @ B @ A )
% 5.64/5.82 => ( ( ord_less_nat @ C @ B )
% 5.64/5.82 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_trans
% 5.64/5.82 thf(fact_448_dual__order_Ostrict__trans,axiom,
% 5.64/5.82 ! [B: int,A: int,C: int] :
% 5.64/5.82 ( ( ord_less_int @ B @ A )
% 5.64/5.82 => ( ( ord_less_int @ C @ B )
% 5.64/5.82 => ( ord_less_int @ C @ A ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_trans
% 5.64/5.82 thf(fact_449_order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [A: real,B: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_implies_not_eq
% 5.64/5.82 thf(fact_450_order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [A: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_implies_not_eq
% 5.64/5.82 thf(fact_451_order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [A: num,B: num] :
% 5.64/5.82 ( ( ord_less_num @ A @ B )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_implies_not_eq
% 5.64/5.82 thf(fact_452_order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [A: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_nat @ A @ B )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_implies_not_eq
% 5.64/5.82 thf(fact_453_order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [A: int,B: int] :
% 5.64/5.82 ( ( ord_less_int @ A @ B )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % order.strict_implies_not_eq
% 5.64/5.82 thf(fact_454_dual__order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [B: real,A: real] :
% 5.64/5.82 ( ( ord_less_real @ B @ A )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_implies_not_eq
% 5.64/5.82 thf(fact_455_dual__order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [B: rat,A: rat] :
% 5.64/5.82 ( ( ord_less_rat @ B @ A )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_implies_not_eq
% 5.64/5.82 thf(fact_456_dual__order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [B: num,A: num] :
% 5.64/5.82 ( ( ord_less_num @ B @ A )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_implies_not_eq
% 5.64/5.82 thf(fact_457_dual__order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [B: nat,A: nat] :
% 5.64/5.82 ( ( ord_less_nat @ B @ A )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_implies_not_eq
% 5.64/5.82 thf(fact_458_dual__order_Ostrict__implies__not__eq,axiom,
% 5.64/5.82 ! [B: int,A: int] :
% 5.64/5.82 ( ( ord_less_int @ B @ A )
% 5.64/5.82 => ( A != B ) ) ).
% 5.64/5.82
% 5.64/5.82 % dual_order.strict_implies_not_eq
% 5.64/5.82 thf(fact_459_linorder__neqE,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 => ( ~ ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 => ( ord_less_real @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neqE
% 5.64/5.82 thf(fact_460_linorder__neqE,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 => ( ~ ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 => ( ord_less_rat @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neqE
% 5.64/5.82 thf(fact_461_linorder__neqE,axiom,
% 5.64/5.82 ! [X2: num,Y4: num] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 => ( ~ ( ord_less_num @ X2 @ Y4 )
% 5.64/5.82 => ( ord_less_num @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neqE
% 5.64/5.82 thf(fact_462_linorder__neqE,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 => ( ~ ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.82 => ( ord_less_nat @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neqE
% 5.64/5.82 thf(fact_463_linorder__neqE,axiom,
% 5.64/5.82 ! [X2: int,Y4: int] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 => ( ~ ( ord_less_int @ X2 @ Y4 )
% 5.64/5.82 => ( ord_less_int @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neqE
% 5.64/5.82 thf(fact_464_order__less__asym,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 => ~ ( ord_less_real @ Y4 @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym
% 5.64/5.82 thf(fact_465_order__less__asym,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 => ~ ( ord_less_rat @ Y4 @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym
% 5.64/5.82 thf(fact_466_order__less__asym,axiom,
% 5.64/5.82 ! [X2: num,Y4: num] :
% 5.64/5.82 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.82 => ~ ( ord_less_num @ Y4 @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym
% 5.64/5.82 thf(fact_467_order__less__asym,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.82 => ~ ( ord_less_nat @ Y4 @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym
% 5.64/5.82 thf(fact_468_order__less__asym,axiom,
% 5.64/5.82 ! [X2: int,Y4: int] :
% 5.64/5.82 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.82 => ~ ( ord_less_int @ Y4 @ X2 ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym
% 5.64/5.82 thf(fact_469_linorder__neq__iff,axiom,
% 5.64/5.82 ! [X2: real,Y4: real] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 = ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 | ( ord_less_real @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neq_iff
% 5.64/5.82 thf(fact_470_linorder__neq__iff,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 = ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 | ( ord_less_rat @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neq_iff
% 5.64/5.82 thf(fact_471_linorder__neq__iff,axiom,
% 5.64/5.82 ! [X2: num,Y4: num] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 = ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.82 | ( ord_less_num @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neq_iff
% 5.64/5.82 thf(fact_472_linorder__neq__iff,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 = ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.82 | ( ord_less_nat @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neq_iff
% 5.64/5.82 thf(fact_473_linorder__neq__iff,axiom,
% 5.64/5.82 ! [X2: int,Y4: int] :
% 5.64/5.82 ( ( X2 != Y4 )
% 5.64/5.82 = ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.82 | ( ord_less_int @ Y4 @ X2 ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % linorder_neq_iff
% 5.64/5.82 thf(fact_474_order__less__asym_H,axiom,
% 5.64/5.82 ! [A: real,B: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym'
% 5.64/5.82 thf(fact_475_order__less__asym_H,axiom,
% 5.64/5.82 ! [A: rat,B: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym'
% 5.64/5.82 thf(fact_476_order__less__asym_H,axiom,
% 5.64/5.82 ! [A: num,B: num] :
% 5.64/5.82 ( ( ord_less_num @ A @ B )
% 5.64/5.82 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym'
% 5.64/5.82 thf(fact_477_order__less__asym_H,axiom,
% 5.64/5.82 ! [A: nat,B: nat] :
% 5.64/5.82 ( ( ord_less_nat @ A @ B )
% 5.64/5.82 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym'
% 5.64/5.82 thf(fact_478_order__less__asym_H,axiom,
% 5.64/5.82 ! [A: int,B: int] :
% 5.64/5.82 ( ( ord_less_int @ A @ B )
% 5.64/5.82 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_asym'
% 5.64/5.82 thf(fact_479_order__less__trans,axiom,
% 5.64/5.82 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.82 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.82 => ( ( ord_less_real @ Y4 @ Z )
% 5.64/5.82 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_trans
% 5.64/5.82 thf(fact_480_order__less__trans,axiom,
% 5.64/5.82 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.82 => ( ( ord_less_rat @ Y4 @ Z )
% 5.64/5.82 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_trans
% 5.64/5.82 thf(fact_481_order__less__trans,axiom,
% 5.64/5.82 ! [X2: num,Y4: num,Z: num] :
% 5.64/5.82 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.82 => ( ( ord_less_num @ Y4 @ Z )
% 5.64/5.82 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_trans
% 5.64/5.82 thf(fact_482_order__less__trans,axiom,
% 5.64/5.82 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.82 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.82 => ( ( ord_less_nat @ Y4 @ Z )
% 5.64/5.82 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_trans
% 5.64/5.82 thf(fact_483_order__less__trans,axiom,
% 5.64/5.82 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.82 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.82 => ( ( ord_less_int @ Y4 @ Z )
% 5.64/5.82 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_trans
% 5.64/5.82 thf(fact_484_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: real,F: real > real,B: real,C: real] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_485_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_486_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: num,F: real > num,B: real,C: real] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_487_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_488_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: int,F: real > int,B: real,C: real] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_489_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_490_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_491_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_492_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_493_ord__eq__less__subst,axiom,
% 5.64/5.82 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.64/5.82 ( ( A
% 5.64/5.82 = ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_eq_less_subst
% 5.64/5.82 thf(fact_494_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: real,B: real,F: real > real,C: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_495_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_496_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: real,B: real,F: real > num,C: num] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_497_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_498_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: real,B: real,F: real > int,C: int] :
% 5.64/5.82 ( ( ord_less_real @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_499_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_500_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_501_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_502_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_503_ord__less__eq__subst,axiom,
% 5.64/5.82 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.64/5.82 ( ( ord_less_rat @ A @ B )
% 5.64/5.82 => ( ( ( F @ B )
% 5.64/5.82 = C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % ord_less_eq_subst
% 5.64/5.82 thf(fact_504_order__less__irrefl,axiom,
% 5.64/5.82 ! [X2: real] :
% 5.64/5.82 ~ ( ord_less_real @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_irrefl
% 5.64/5.82 thf(fact_505_order__less__irrefl,axiom,
% 5.64/5.82 ! [X2: rat] :
% 5.64/5.82 ~ ( ord_less_rat @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_irrefl
% 5.64/5.82 thf(fact_506_order__less__irrefl,axiom,
% 5.64/5.82 ! [X2: num] :
% 5.64/5.82 ~ ( ord_less_num @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_irrefl
% 5.64/5.82 thf(fact_507_order__less__irrefl,axiom,
% 5.64/5.82 ! [X2: nat] :
% 5.64/5.82 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_irrefl
% 5.64/5.82 thf(fact_508_order__less__irrefl,axiom,
% 5.64/5.82 ! [X2: int] :
% 5.64/5.82 ~ ( ord_less_int @ X2 @ X2 ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_irrefl
% 5.64/5.82 thf(fact_509_order__less__subst1,axiom,
% 5.64/5.82 ! [A: real,F: real > real,B: real,C: real] :
% 5.64/5.82 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_510_order__less__subst1,axiom,
% 5.64/5.82 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_511_order__less__subst1,axiom,
% 5.64/5.82 ! [A: real,F: num > real,B: num,C: num] :
% 5.64/5.82 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_num @ B @ C )
% 5.64/5.82 => ( ! [X4: num,Y3: num] :
% 5.64/5.82 ( ( ord_less_num @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_512_order__less__subst1,axiom,
% 5.64/5.82 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_nat @ B @ C )
% 5.64/5.82 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.82 ( ( ord_less_nat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_513_order__less__subst1,axiom,
% 5.64/5.82 ! [A: real,F: int > real,B: int,C: int] :
% 5.64/5.82 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_int @ B @ C )
% 5.64/5.82 => ( ! [X4: int,Y3: int] :
% 5.64/5.82 ( ( ord_less_int @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_514_order__less__subst1,axiom,
% 5.64/5.82 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.64/5.82 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_real @ B @ C )
% 5.64/5.82 => ( ! [X4: real,Y3: real] :
% 5.64/5.82 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_515_order__less__subst1,axiom,
% 5.64/5.82 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_rat @ B @ C )
% 5.64/5.82 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.82 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_516_order__less__subst1,axiom,
% 5.64/5.82 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.64/5.82 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_num @ B @ C )
% 5.64/5.82 => ( ! [X4: num,Y3: num] :
% 5.64/5.82 ( ( ord_less_num @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_517_order__less__subst1,axiom,
% 5.64/5.82 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.64/5.82 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_nat @ B @ C )
% 5.64/5.82 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.82 ( ( ord_less_nat @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.82
% 5.64/5.82 % order_less_subst1
% 5.64/5.82 thf(fact_518_order__less__subst1,axiom,
% 5.64/5.82 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.64/5.82 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.82 => ( ( ord_less_int @ B @ C )
% 5.64/5.82 => ( ! [X4: int,Y3: int] :
% 5.64/5.82 ( ( ord_less_int @ X4 @ Y3 )
% 5.64/5.82 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.82 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst1
% 5.64/5.83 thf(fact_519_order__less__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > real,C: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_520_order__less__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_521_order__less__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > num,C: num] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_522_order__less__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_523_order__less__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > int,C: int] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_524_order__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_525_order__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_526_order__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_527_order__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_528_order__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_subst2
% 5.64/5.83 thf(fact_529_order__less__not__sym,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_not_sym
% 5.64/5.83 thf(fact_530_order__less__not__sym,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_not_sym
% 5.64/5.83 thf(fact_531_order__less__not__sym,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_not_sym
% 5.64/5.83 thf(fact_532_order__less__not__sym,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_not_sym
% 5.64/5.83 thf(fact_533_order__less__not__sym,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_not_sym
% 5.64/5.83 thf(fact_534_order__less__imp__triv,axiom,
% 5.64/5.83 ! [X2: real,Y4: real,P: $o] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.83 => P ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_triv
% 5.64/5.83 thf(fact_535_order__less__imp__triv,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat,P: $o] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_rat @ Y4 @ X2 )
% 5.64/5.83 => P ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_triv
% 5.64/5.83 thf(fact_536_order__less__imp__triv,axiom,
% 5.64/5.83 ! [X2: num,Y4: num,P: $o] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_num @ Y4 @ X2 )
% 5.64/5.83 => P ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_triv
% 5.64/5.83 thf(fact_537_order__less__imp__triv,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat,P: $o] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_nat @ Y4 @ X2 )
% 5.64/5.83 => P ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_triv
% 5.64/5.83 thf(fact_538_order__less__imp__triv,axiom,
% 5.64/5.83 ! [X2: int,Y4: int,P: $o] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_int @ Y4 @ X2 )
% 5.64/5.83 => P ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_triv
% 5.64/5.83 thf(fact_539_linorder__less__linear,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 )
% 5.64/5.83 | ( ord_less_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_less_linear
% 5.64/5.83 thf(fact_540_linorder__less__linear,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 )
% 5.64/5.83 | ( ord_less_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_less_linear
% 5.64/5.83 thf(fact_541_linorder__less__linear,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 )
% 5.64/5.83 | ( ord_less_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_less_linear
% 5.64/5.83 thf(fact_542_linorder__less__linear,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 )
% 5.64/5.83 | ( ord_less_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_less_linear
% 5.64/5.83 thf(fact_543_linorder__less__linear,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 )
% 5.64/5.83 | ( ord_less_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_less_linear
% 5.64/5.83 thf(fact_544_order__less__imp__not__eq,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq
% 5.64/5.83 thf(fact_545_order__less__imp__not__eq,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq
% 5.64/5.83 thf(fact_546_order__less__imp__not__eq,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq
% 5.64/5.83 thf(fact_547_order__less__imp__not__eq,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq
% 5.64/5.83 thf(fact_548_order__less__imp__not__eq,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq
% 5.64/5.83 thf(fact_549_order__less__imp__not__eq2,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( Y4 != X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq2
% 5.64/5.83 thf(fact_550_order__less__imp__not__eq2,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( Y4 != X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq2
% 5.64/5.83 thf(fact_551_order__less__imp__not__eq2,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( Y4 != X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq2
% 5.64/5.83 thf(fact_552_order__less__imp__not__eq2,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( Y4 != X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq2
% 5.64/5.83 thf(fact_553_order__less__imp__not__eq2,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( Y4 != X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_eq2
% 5.64/5.83 thf(fact_554_order__less__imp__not__less,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_less
% 5.64/5.83 thf(fact_555_order__less__imp__not__less,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_less
% 5.64/5.83 thf(fact_556_order__less__imp__not__less,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_less
% 5.64/5.83 thf(fact_557_order__less__imp__not__less,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_less
% 5.64/5.83 thf(fact_558_order__less__imp__not__less,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ~ ( ord_less_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_not_less
% 5.64/5.83 thf(fact_559_linorder__neqE__nat,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( X2 != Y4 )
% 5.64/5.83 => ( ~ ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_nat @ Y4 @ X2 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_neqE_nat
% 5.64/5.83 thf(fact_560_infinite__descent,axiom,
% 5.64/5.83 ! [P: nat > $o,N: nat] :
% 5.64/5.83 ( ! [N3: nat] :
% 5.64/5.83 ( ~ ( P @ N3 )
% 5.64/5.83 => ? [M5: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M5 @ N3 )
% 5.64/5.83 & ~ ( P @ M5 ) ) )
% 5.64/5.83 => ( P @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % infinite_descent
% 5.64/5.83 thf(fact_561_nat__less__induct,axiom,
% 5.64/5.83 ! [P: nat > $o,N: nat] :
% 5.64/5.83 ( ! [N3: nat] :
% 5.64/5.83 ( ! [M5: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M5 @ N3 )
% 5.64/5.83 => ( P @ M5 ) )
% 5.64/5.83 => ( P @ N3 ) )
% 5.64/5.83 => ( P @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % nat_less_induct
% 5.64/5.83 thf(fact_562_less__irrefl__nat,axiom,
% 5.64/5.83 ! [N: nat] :
% 5.64/5.83 ~ ( ord_less_nat @ N @ N ) ).
% 5.64/5.83
% 5.64/5.83 % less_irrefl_nat
% 5.64/5.83 thf(fact_563_less__not__refl3,axiom,
% 5.64/5.83 ! [S2: nat,T: nat] :
% 5.64/5.83 ( ( ord_less_nat @ S2 @ T )
% 5.64/5.83 => ( S2 != T ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_not_refl3
% 5.64/5.83 thf(fact_564_less__not__refl2,axiom,
% 5.64/5.83 ! [N: nat,M: nat] :
% 5.64/5.83 ( ( ord_less_nat @ N @ M )
% 5.64/5.83 => ( M != N ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_not_refl2
% 5.64/5.83 thf(fact_565_less__not__refl,axiom,
% 5.64/5.83 ! [N: nat] :
% 5.64/5.83 ~ ( ord_less_nat @ N @ N ) ).
% 5.64/5.83
% 5.64/5.83 % less_not_refl
% 5.64/5.83 thf(fact_566_nat__neq__iff,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( M != N )
% 5.64/5.83 = ( ( ord_less_nat @ M @ N )
% 5.64/5.83 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nat_neq_iff
% 5.64/5.83 thf(fact_567_lift__Suc__mono__less__iff,axiom,
% 5.64/5.83 ! [F: nat > real,N: nat,M: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.64/5.83 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less_iff
% 5.64/5.83 thf(fact_568_lift__Suc__mono__less__iff,axiom,
% 5.64/5.83 ! [F: nat > rat,N: nat,M: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.64/5.83 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less_iff
% 5.64/5.83 thf(fact_569_lift__Suc__mono__less__iff,axiom,
% 5.64/5.83 ! [F: nat > num,N: nat,M: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.64/5.83 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less_iff
% 5.64/5.83 thf(fact_570_lift__Suc__mono__less__iff,axiom,
% 5.64/5.83 ! [F: nat > nat,N: nat,M: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.64/5.83 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less_iff
% 5.64/5.83 thf(fact_571_lift__Suc__mono__less__iff,axiom,
% 5.64/5.83 ! [F: nat > int,N: nat,M: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.64/5.83 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less_iff
% 5.64/5.83 thf(fact_572_lift__Suc__mono__less,axiom,
% 5.64/5.83 ! [F: nat > real,N: nat,N4: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_nat @ N @ N4 )
% 5.64/5.83 => ( ord_less_real @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less
% 5.64/5.83 thf(fact_573_lift__Suc__mono__less,axiom,
% 5.64/5.83 ! [F: nat > rat,N: nat,N4: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_nat @ N @ N4 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less
% 5.64/5.83 thf(fact_574_lift__Suc__mono__less,axiom,
% 5.64/5.83 ! [F: nat > num,N: nat,N4: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_nat @ N @ N4 )
% 5.64/5.83 => ( ord_less_num @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less
% 5.64/5.83 thf(fact_575_lift__Suc__mono__less,axiom,
% 5.64/5.83 ! [F: nat > nat,N: nat,N4: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_nat @ N @ N4 )
% 5.64/5.83 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less
% 5.64/5.83 thf(fact_576_lift__Suc__mono__less,axiom,
% 5.64/5.83 ! [F: nat > int,N: nat,N4: nat] :
% 5.64/5.83 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/5.83 => ( ( ord_less_nat @ N @ N4 )
% 5.64/5.83 => ( ord_less_int @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % lift_Suc_mono_less
% 5.64/5.83 thf(fact_577_order__le__imp__less__or__eq,axiom,
% 5.64/5.83 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_set_nat @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_imp_less_or_eq
% 5.64/5.83 thf(fact_578_order__le__imp__less__or__eq,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_imp_less_or_eq
% 5.64/5.83 thf(fact_579_order__le__imp__less__or__eq,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_imp_less_or_eq
% 5.64/5.83 thf(fact_580_order__le__imp__less__or__eq,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_imp_less_or_eq
% 5.64/5.83 thf(fact_581_order__le__imp__less__or__eq,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_imp_less_or_eq
% 5.64/5.83 thf(fact_582_order__le__imp__less__or__eq,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 | ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_imp_less_or_eq
% 5.64/5.83 thf(fact_583_linorder__le__less__linear,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 | ( ord_less_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_less_linear
% 5.64/5.83 thf(fact_584_linorder__le__less__linear,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 | ( ord_less_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_less_linear
% 5.64/5.83 thf(fact_585_linorder__le__less__linear,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 | ( ord_less_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_less_linear
% 5.64/5.83 thf(fact_586_linorder__le__less__linear,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 | ( ord_less_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_less_linear
% 5.64/5.83 thf(fact_587_linorder__le__less__linear,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 | ( ord_less_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_less_linear
% 5.64/5.83 thf(fact_588_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_589_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_590_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_591_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_592_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: int,Y3: int] :
% 5.64/5.83 ( ( ord_less_int @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_593_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: real,B: real,F: real > num,C: num] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_594_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_595_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > num,C: num] :
% 5.64/5.83 ( ( ord_less_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_596_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_597_order__less__le__subst2,axiom,
% 5.64/5.83 ! [A: int,B: int,F: int > num,C: num] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: int,Y3: int] :
% 5.64/5.83 ( ( ord_less_int @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst2
% 5.64/5.83 thf(fact_598_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_599_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_600_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_601_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_602_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_603_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_604_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: num,F: num > num,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_605_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_606_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: int,F: num > int,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_607_order__less__le__subst1,axiom,
% 5.64/5.83 ! [A: real,F: num > real,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_subst1
% 5.64/5.83 thf(fact_608_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_609_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_610_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_611_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_612_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_613_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_614_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_615_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_616_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_617_order__le__less__subst2,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst2
% 5.64/5.83 thf(fact_618_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_real @ B @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_619_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_620_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_621_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_nat @ B @ C )
% 5.64/5.83 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_622_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_int @ B @ C )
% 5.64/5.83 => ( ! [X4: int,Y3: int] :
% 5.64/5.83 ( ( ord_less_int @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_623_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: num,F: real > num,B: real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_real @ B @ C )
% 5.64/5.83 => ( ! [X4: real,Y3: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_624_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_625_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: num,F: num > num,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_num @ B @ C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_626_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_nat @ B @ C )
% 5.64/5.83 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_627_order__le__less__subst1,axiom,
% 5.64/5.83 ! [A: num,F: int > num,B: int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_int @ B @ C )
% 5.64/5.83 => ( ! [X4: int,Y3: int] :
% 5.64/5.83 ( ( ord_less_int @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_subst1
% 5.64/5.83 thf(fact_628_order__less__le__trans,axiom,
% 5.64/5.83 ! [X2: set_nat,Y4: set_nat,Z: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_set_nat @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_set_nat @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_trans
% 5.64/5.83 thf(fact_629_order__less__le__trans,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_rat @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_trans
% 5.64/5.83 thf(fact_630_order__less__le__trans,axiom,
% 5.64/5.83 ! [X2: num,Y4: num,Z: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_num @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_trans
% 5.64/5.83 thf(fact_631_order__less__le__trans,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_nat @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_trans
% 5.64/5.83 thf(fact_632_order__less__le__trans,axiom,
% 5.64/5.83 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_int @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_trans
% 5.64/5.83 thf(fact_633_order__less__le__trans,axiom,
% 5.64/5.83 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_real @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le_trans
% 5.64/5.83 thf(fact_634_order__le__less__trans,axiom,
% 5.64/5.83 ! [X2: set_nat,Y4: set_nat,Z: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_set_nat @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_set_nat @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_trans
% 5.64/5.83 thf(fact_635_order__le__less__trans,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_rat @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_trans
% 5.64/5.83 thf(fact_636_order__le__less__trans,axiom,
% 5.64/5.83 ! [X2: num,Y4: num,Z: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_num @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_trans
% 5.64/5.83 thf(fact_637_order__le__less__trans,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_nat @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_trans
% 5.64/5.83 thf(fact_638_order__le__less__trans,axiom,
% 5.64/5.83 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_int @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_trans
% 5.64/5.83 thf(fact_639_order__le__less__trans,axiom,
% 5.64/5.83 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_real @ Y4 @ Z )
% 5.64/5.83 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less_trans
% 5.64/5.83 thf(fact_640_order__neq__le__trans,axiom,
% 5.64/5.83 ! [A: set_nat,B: set_nat] :
% 5.64/5.83 ( ( A != B )
% 5.64/5.83 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.83 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_neq_le_trans
% 5.64/5.83 thf(fact_641_order__neq__le__trans,axiom,
% 5.64/5.83 ! [A: rat,B: rat] :
% 5.64/5.83 ( ( A != B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_neq_le_trans
% 5.64/5.83 thf(fact_642_order__neq__le__trans,axiom,
% 5.64/5.83 ! [A: num,B: num] :
% 5.64/5.83 ( ( A != B )
% 5.64/5.83 => ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ord_less_num @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_neq_le_trans
% 5.64/5.83 thf(fact_643_order__neq__le__trans,axiom,
% 5.64/5.83 ! [A: nat,B: nat] :
% 5.64/5.83 ( ( A != B )
% 5.64/5.83 => ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.83 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_neq_le_trans
% 5.64/5.83 thf(fact_644_order__neq__le__trans,axiom,
% 5.64/5.83 ! [A: int,B: int] :
% 5.64/5.83 ( ( A != B )
% 5.64/5.83 => ( ( ord_less_eq_int @ A @ B )
% 5.64/5.83 => ( ord_less_int @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_neq_le_trans
% 5.64/5.83 thf(fact_645_order__neq__le__trans,axiom,
% 5.64/5.83 ! [A: real,B: real] :
% 5.64/5.83 ( ( A != B )
% 5.64/5.83 => ( ( ord_less_eq_real @ A @ B )
% 5.64/5.83 => ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_neq_le_trans
% 5.64/5.83 thf(fact_646_order__le__neq__trans,axiom,
% 5.64/5.83 ! [A: set_nat,B: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.83 => ( ( A != B )
% 5.64/5.83 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_neq_trans
% 5.64/5.83 thf(fact_647_order__le__neq__trans,axiom,
% 5.64/5.83 ! [A: rat,B: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( A != B )
% 5.64/5.83 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_neq_trans
% 5.64/5.83 thf(fact_648_order__le__neq__trans,axiom,
% 5.64/5.83 ! [A: num,B: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( A != B )
% 5.64/5.83 => ( ord_less_num @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_neq_trans
% 5.64/5.83 thf(fact_649_order__le__neq__trans,axiom,
% 5.64/5.83 ! [A: nat,B: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.83 => ( ( A != B )
% 5.64/5.83 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_neq_trans
% 5.64/5.83 thf(fact_650_order__le__neq__trans,axiom,
% 5.64/5.83 ! [A: int,B: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.83 => ( ( A != B )
% 5.64/5.83 => ( ord_less_int @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_neq_trans
% 5.64/5.83 thf(fact_651_order__le__neq__trans,axiom,
% 5.64/5.83 ! [A: real,B: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.83 => ( ( A != B )
% 5.64/5.83 => ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_neq_trans
% 5.64/5.83 thf(fact_652_order__less__imp__le,axiom,
% 5.64/5.83 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_set_nat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_le
% 5.64/5.83 thf(fact_653_order__less__imp__le,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_rat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_le
% 5.64/5.83 thf(fact_654_order__less__imp__le,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_num @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_le
% 5.64/5.83 thf(fact_655_order__less__imp__le,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_nat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_le
% 5.64/5.83 thf(fact_656_order__less__imp__le,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_int @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_le
% 5.64/5.83 thf(fact_657_order__less__imp__le,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_real @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_imp_le
% 5.64/5.83 thf(fact_658_linorder__not__less,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ~ ( ord_less_rat @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_eq_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_less
% 5.64/5.83 thf(fact_659_linorder__not__less,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ~ ( ord_less_num @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_eq_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_less
% 5.64/5.83 thf(fact_660_linorder__not__less,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ~ ( ord_less_nat @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_eq_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_less
% 5.64/5.83 thf(fact_661_linorder__not__less,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ~ ( ord_less_int @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_eq_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_less
% 5.64/5.83 thf(fact_662_linorder__not__less,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ~ ( ord_less_real @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_eq_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_less
% 5.64/5.83 thf(fact_663_linorder__not__le,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_rat @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_le
% 5.64/5.83 thf(fact_664_linorder__not__le,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_num @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_le
% 5.64/5.83 thf(fact_665_linorder__not__le,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_nat @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_le
% 5.64/5.83 thf(fact_666_linorder__not__le,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_int @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_le
% 5.64/5.83 thf(fact_667_linorder__not__le,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_real @ X2 @ Y4 ) )
% 5.64/5.83 = ( ord_less_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_not_le
% 5.64/5.83 thf(fact_668_order__less__le,axiom,
% 5.64/5.83 ( ord_less_set_nat
% 5.64/5.83 = ( ^ [X: set_nat,Y: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.64/5.83 & ( X != Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le
% 5.64/5.83 thf(fact_669_order__less__le,axiom,
% 5.64/5.83 ( ord_less_rat
% 5.64/5.83 = ( ^ [X: rat,Y: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X @ Y )
% 5.64/5.83 & ( X != Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le
% 5.64/5.83 thf(fact_670_order__less__le,axiom,
% 5.64/5.83 ( ord_less_num
% 5.64/5.83 = ( ^ [X: num,Y: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X @ Y )
% 5.64/5.83 & ( X != Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le
% 5.64/5.83 thf(fact_671_order__less__le,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [X: nat,Y: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ X @ Y )
% 5.64/5.83 & ( X != Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le
% 5.64/5.83 thf(fact_672_order__less__le,axiom,
% 5.64/5.83 ( ord_less_int
% 5.64/5.83 = ( ^ [X: int,Y: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ X @ Y )
% 5.64/5.83 & ( X != Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le
% 5.64/5.83 thf(fact_673_order__less__le,axiom,
% 5.64/5.83 ( ord_less_real
% 5.64/5.83 = ( ^ [X: real,Y: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ X @ Y )
% 5.64/5.83 & ( X != Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_less_le
% 5.64/5.83 thf(fact_674_order__le__less,axiom,
% 5.64/5.83 ( ord_less_eq_set_nat
% 5.64/5.83 = ( ^ [X: set_nat,Y: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ X @ Y )
% 5.64/5.83 | ( X = Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less
% 5.64/5.83 thf(fact_675_order__le__less,axiom,
% 5.64/5.83 ( ord_less_eq_rat
% 5.64/5.83 = ( ^ [X: rat,Y: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X @ Y )
% 5.64/5.83 | ( X = Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less
% 5.64/5.83 thf(fact_676_order__le__less,axiom,
% 5.64/5.83 ( ord_less_eq_num
% 5.64/5.83 = ( ^ [X: num,Y: num] :
% 5.64/5.83 ( ( ord_less_num @ X @ Y )
% 5.64/5.83 | ( X = Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less
% 5.64/5.83 thf(fact_677_order__le__less,axiom,
% 5.64/5.83 ( ord_less_eq_nat
% 5.64/5.83 = ( ^ [X: nat,Y: nat] :
% 5.64/5.83 ( ( ord_less_nat @ X @ Y )
% 5.64/5.83 | ( X = Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less
% 5.64/5.83 thf(fact_678_order__le__less,axiom,
% 5.64/5.83 ( ord_less_eq_int
% 5.64/5.83 = ( ^ [X: int,Y: int] :
% 5.64/5.83 ( ( ord_less_int @ X @ Y )
% 5.64/5.83 | ( X = Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less
% 5.64/5.83 thf(fact_679_order__le__less,axiom,
% 5.64/5.83 ( ord_less_eq_real
% 5.64/5.83 = ( ^ [X: real,Y: real] :
% 5.64/5.83 ( ( ord_less_real @ X @ Y )
% 5.64/5.83 | ( X = Y ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_le_less
% 5.64/5.83 thf(fact_680_dual__order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [B: set_nat,A: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ B @ A )
% 5.64/5.83 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_implies_order
% 5.64/5.83 thf(fact_681_dual__order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [B: rat,A: rat] :
% 5.64/5.83 ( ( ord_less_rat @ B @ A )
% 5.64/5.83 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_implies_order
% 5.64/5.83 thf(fact_682_dual__order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [B: num,A: num] :
% 5.64/5.83 ( ( ord_less_num @ B @ A )
% 5.64/5.83 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_implies_order
% 5.64/5.83 thf(fact_683_dual__order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [B: nat,A: nat] :
% 5.64/5.83 ( ( ord_less_nat @ B @ A )
% 5.64/5.83 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_implies_order
% 5.64/5.83 thf(fact_684_dual__order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [B: int,A: int] :
% 5.64/5.83 ( ( ord_less_int @ B @ A )
% 5.64/5.83 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_implies_order
% 5.64/5.83 thf(fact_685_dual__order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [B: real,A: real] :
% 5.64/5.83 ( ( ord_less_real @ B @ A )
% 5.64/5.83 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_implies_order
% 5.64/5.83 thf(fact_686_order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [A: set_nat,B: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ A @ B )
% 5.64/5.83 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_implies_order
% 5.64/5.83 thf(fact_687_order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [A: rat,B: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_implies_order
% 5.64/5.83 thf(fact_688_order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [A: num,B: num] :
% 5.64/5.83 ( ( ord_less_num @ A @ B )
% 5.64/5.83 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_implies_order
% 5.64/5.83 thf(fact_689_order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [A: nat,B: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_implies_order
% 5.64/5.83 thf(fact_690_order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [A: int,B: int] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_implies_order
% 5.64/5.83 thf(fact_691_order_Ostrict__implies__order,axiom,
% 5.64/5.83 ! [A: real,B: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_implies_order
% 5.64/5.83 thf(fact_692_dual__order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_set_nat
% 5.64/5.83 = ( ^ [B3: set_nat,A3: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.64/5.83 & ~ ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_not
% 5.64/5.83 thf(fact_693_dual__order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_rat
% 5.64/5.83 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ B3 @ A3 )
% 5.64/5.83 & ~ ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_not
% 5.64/5.83 thf(fact_694_dual__order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_num
% 5.64/5.83 = ( ^ [B3: num,A3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ B3 @ A3 )
% 5.64/5.83 & ~ ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_not
% 5.64/5.83 thf(fact_695_dual__order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ B3 @ A3 )
% 5.64/5.83 & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_not
% 5.64/5.83 thf(fact_696_dual__order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_int
% 5.64/5.83 = ( ^ [B3: int,A3: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ B3 @ A3 )
% 5.64/5.83 & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_not
% 5.64/5.83 thf(fact_697_dual__order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_real
% 5.64/5.83 = ( ^ [B3: real,A3: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ B3 @ A3 )
% 5.64/5.83 & ~ ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_not
% 5.64/5.83 thf(fact_698_dual__order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ B @ A )
% 5.64/5.83 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.64/5.83 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans2
% 5.64/5.83 thf(fact_699_dual__order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [B: rat,A: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ B @ A )
% 5.64/5.83 => ( ( ord_less_eq_rat @ C @ B )
% 5.64/5.83 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans2
% 5.64/5.83 thf(fact_700_dual__order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [B: num,A: num,C: num] :
% 5.64/5.83 ( ( ord_less_num @ B @ A )
% 5.64/5.83 => ( ( ord_less_eq_num @ C @ B )
% 5.64/5.83 => ( ord_less_num @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans2
% 5.64/5.83 thf(fact_701_dual__order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [B: nat,A: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_nat @ B @ A )
% 5.64/5.83 => ( ( ord_less_eq_nat @ C @ B )
% 5.64/5.83 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans2
% 5.64/5.83 thf(fact_702_dual__order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [B: int,A: int,C: int] :
% 5.64/5.83 ( ( ord_less_int @ B @ A )
% 5.64/5.83 => ( ( ord_less_eq_int @ C @ B )
% 5.64/5.83 => ( ord_less_int @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans2
% 5.64/5.83 thf(fact_703_dual__order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [B: real,A: real,C: real] :
% 5.64/5.83 ( ( ord_less_real @ B @ A )
% 5.64/5.83 => ( ( ord_less_eq_real @ C @ B )
% 5.64/5.83 => ( ord_less_real @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans2
% 5.64/5.83 thf(fact_704_dual__order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ B @ A )
% 5.64/5.83 => ( ( ord_less_set_nat @ C @ B )
% 5.64/5.83 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans1
% 5.64/5.83 thf(fact_705_dual__order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [B: rat,A: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.83 => ( ( ord_less_rat @ C @ B )
% 5.64/5.83 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans1
% 5.64/5.83 thf(fact_706_dual__order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [B: num,A: num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ B @ A )
% 5.64/5.83 => ( ( ord_less_num @ C @ B )
% 5.64/5.83 => ( ord_less_num @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans1
% 5.64/5.83 thf(fact_707_dual__order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [B: nat,A: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.83 => ( ( ord_less_nat @ C @ B )
% 5.64/5.83 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans1
% 5.64/5.83 thf(fact_708_dual__order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [B: int,A: int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.83 => ( ( ord_less_int @ C @ B )
% 5.64/5.83 => ( ord_less_int @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans1
% 5.64/5.83 thf(fact_709_dual__order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [B: real,A: real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.83 => ( ( ord_less_real @ C @ B )
% 5.64/5.83 => ( ord_less_real @ C @ A ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_trans1
% 5.64/5.83 thf(fact_710_dual__order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_set_nat
% 5.64/5.83 = ( ^ [B3: set_nat,A3: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_order
% 5.64/5.83 thf(fact_711_dual__order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_rat
% 5.64/5.83 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ B3 @ A3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_order
% 5.64/5.83 thf(fact_712_dual__order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_num
% 5.64/5.83 = ( ^ [B3: num,A3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ B3 @ A3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_order
% 5.64/5.83 thf(fact_713_dual__order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ B3 @ A3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_order
% 5.64/5.83 thf(fact_714_dual__order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_int
% 5.64/5.83 = ( ^ [B3: int,A3: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ B3 @ A3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_order
% 5.64/5.83 thf(fact_715_dual__order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_real
% 5.64/5.83 = ( ^ [B3: real,A3: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ B3 @ A3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.strict_iff_order
% 5.64/5.83 thf(fact_716_dual__order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_set_nat
% 5.64/5.83 = ( ^ [B3: set_nat,A3: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ B3 @ A3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.order_iff_strict
% 5.64/5.83 thf(fact_717_dual__order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_rat
% 5.64/5.83 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ B3 @ A3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.order_iff_strict
% 5.64/5.83 thf(fact_718_dual__order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_num
% 5.64/5.83 = ( ^ [B3: num,A3: num] :
% 5.64/5.83 ( ( ord_less_num @ B3 @ A3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.order_iff_strict
% 5.64/5.83 thf(fact_719_dual__order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_nat
% 5.64/5.83 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ B3 @ A3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.order_iff_strict
% 5.64/5.83 thf(fact_720_dual__order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_int
% 5.64/5.83 = ( ^ [B3: int,A3: int] :
% 5.64/5.83 ( ( ord_less_int @ B3 @ A3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.order_iff_strict
% 5.64/5.83 thf(fact_721_dual__order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_real
% 5.64/5.83 = ( ^ [B3: real,A3: real] :
% 5.64/5.83 ( ( ord_less_real @ B3 @ A3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dual_order.order_iff_strict
% 5.64/5.83 thf(fact_722_dense__le__bounded,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ! [W2: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X2 @ W2 )
% 5.64/5.83 => ( ( ord_less_rat @ W2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_le_bounded
% 5.64/5.83 thf(fact_723_dense__le__bounded,axiom,
% 5.64/5.83 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( ! [W2: real] :
% 5.64/5.83 ( ( ord_less_real @ X2 @ W2 )
% 5.64/5.83 => ( ( ord_less_real @ W2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_le_bounded
% 5.64/5.83 thf(fact_724_dense__ge__bounded,axiom,
% 5.64/5.83 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ Z @ X2 )
% 5.64/5.83 => ( ! [W2: rat] :
% 5.64/5.83 ( ( ord_less_rat @ Z @ W2 )
% 5.64/5.83 => ( ( ord_less_rat @ W2 @ X2 )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ W2 ) ) )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_ge_bounded
% 5.64/5.83 thf(fact_725_dense__ge__bounded,axiom,
% 5.64/5.83 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_real @ Z @ X2 )
% 5.64/5.83 => ( ! [W2: real] :
% 5.64/5.83 ( ( ord_less_real @ Z @ W2 )
% 5.64/5.83 => ( ( ord_less_real @ W2 @ X2 )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ W2 ) ) )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ Z ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_ge_bounded
% 5.64/5.83 thf(fact_726_order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_set_nat
% 5.64/5.83 = ( ^ [A3: set_nat,B3: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.64/5.83 & ~ ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_not
% 5.64/5.83 thf(fact_727_order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_rat
% 5.64/5.83 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A3 @ B3 )
% 5.64/5.83 & ~ ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_not
% 5.64/5.83 thf(fact_728_order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_num
% 5.64/5.83 = ( ^ [A3: num,B3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A3 @ B3 )
% 5.64/5.83 & ~ ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_not
% 5.64/5.83 thf(fact_729_order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ A3 @ B3 )
% 5.64/5.83 & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_not
% 5.64/5.83 thf(fact_730_order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_int
% 5.64/5.83 = ( ^ [A3: int,B3: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.64/5.83 & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_not
% 5.64/5.83 thf(fact_731_order_Ostrict__iff__not,axiom,
% 5.64/5.83 ( ord_less_real
% 5.64/5.83 = ( ^ [A3: real,B3: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ A3 @ B3 )
% 5.64/5.83 & ~ ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_not
% 5.64/5.83 thf(fact_732_order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.64/5.83 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans2
% 5.64/5.83 thf(fact_733_order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans2
% 5.64/5.83 thf(fact_734_order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [A: num,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.83 => ( ord_less_num @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans2
% 5.64/5.83 thf(fact_735_order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.83 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans2
% 5.64/5.83 thf(fact_736_order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.83 => ( ord_less_int @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans2
% 5.64/5.83 thf(fact_737_order_Ostrict__trans2,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.83 => ( ord_less_real @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans2
% 5.64/5.83 thf(fact_738_order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_set_nat @ B @ C )
% 5.64/5.83 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans1
% 5.64/5.83 thf(fact_739_order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ B @ C )
% 5.64/5.83 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans1
% 5.64/5.83 thf(fact_740_order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [A: num,B: num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ord_less_num @ B @ C )
% 5.64/5.83 => ( ord_less_num @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans1
% 5.64/5.83 thf(fact_741_order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ B @ C )
% 5.64/5.83 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans1
% 5.64/5.83 thf(fact_742_order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ B @ C )
% 5.64/5.83 => ( ord_less_int @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans1
% 5.64/5.83 thf(fact_743_order_Ostrict__trans1,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ B @ C )
% 5.64/5.83 => ( ord_less_real @ A @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_trans1
% 5.64/5.83 thf(fact_744_order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_set_nat
% 5.64/5.83 = ( ^ [A3: set_nat,B3: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_order
% 5.64/5.83 thf(fact_745_order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_rat
% 5.64/5.83 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A3 @ B3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_order
% 5.64/5.83 thf(fact_746_order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_num
% 5.64/5.83 = ( ^ [A3: num,B3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A3 @ B3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_order
% 5.64/5.83 thf(fact_747_order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ A3 @ B3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_order
% 5.64/5.83 thf(fact_748_order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_int
% 5.64/5.83 = ( ^ [A3: int,B3: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_order
% 5.64/5.83 thf(fact_749_order_Ostrict__iff__order,axiom,
% 5.64/5.83 ( ord_less_real
% 5.64/5.83 = ( ^ [A3: real,B3: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ A3 @ B3 )
% 5.64/5.83 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.strict_iff_order
% 5.64/5.83 thf(fact_750_order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_set_nat
% 5.64/5.83 = ( ^ [A3: set_nat,B3: set_nat] :
% 5.64/5.83 ( ( ord_less_set_nat @ A3 @ B3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.order_iff_strict
% 5.64/5.83 thf(fact_751_order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_rat
% 5.64/5.83 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A3 @ B3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.order_iff_strict
% 5.64/5.83 thf(fact_752_order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_num
% 5.64/5.83 = ( ^ [A3: num,B3: num] :
% 5.64/5.83 ( ( ord_less_num @ A3 @ B3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.order_iff_strict
% 5.64/5.83 thf(fact_753_order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_nat
% 5.64/5.83 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A3 @ B3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.order_iff_strict
% 5.64/5.83 thf(fact_754_order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_int
% 5.64/5.83 = ( ^ [A3: int,B3: int] :
% 5.64/5.83 ( ( ord_less_int @ A3 @ B3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.order_iff_strict
% 5.64/5.83 thf(fact_755_order_Oorder__iff__strict,axiom,
% 5.64/5.83 ( ord_less_eq_real
% 5.64/5.83 = ( ^ [A3: real,B3: real] :
% 5.64/5.83 ( ( ord_less_real @ A3 @ B3 )
% 5.64/5.83 | ( A3 = B3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order.order_iff_strict
% 5.64/5.83 thf(fact_756_not__le__imp__less,axiom,
% 5.64/5.83 ! [Y4: rat,X2: rat] :
% 5.64/5.83 ( ~ ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.83 => ( ord_less_rat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_le_imp_less
% 5.64/5.83 thf(fact_757_not__le__imp__less,axiom,
% 5.64/5.83 ! [Y4: num,X2: num] :
% 5.64/5.83 ( ~ ( ord_less_eq_num @ Y4 @ X2 )
% 5.64/5.83 => ( ord_less_num @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_le_imp_less
% 5.64/5.83 thf(fact_758_not__le__imp__less,axiom,
% 5.64/5.83 ! [Y4: nat,X2: nat] :
% 5.64/5.83 ( ~ ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.83 => ( ord_less_nat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_le_imp_less
% 5.64/5.83 thf(fact_759_not__le__imp__less,axiom,
% 5.64/5.83 ! [Y4: int,X2: int] :
% 5.64/5.83 ( ~ ( ord_less_eq_int @ Y4 @ X2 )
% 5.64/5.83 => ( ord_less_int @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_le_imp_less
% 5.64/5.83 thf(fact_760_not__le__imp__less,axiom,
% 5.64/5.83 ! [Y4: real,X2: real] :
% 5.64/5.83 ( ~ ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.83 => ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_le_imp_less
% 5.64/5.83 thf(fact_761_less__le__not__le,axiom,
% 5.64/5.83 ( ord_less_set_nat
% 5.64/5.83 = ( ^ [X: set_nat,Y: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.64/5.83 & ~ ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_le_not_le
% 5.64/5.83 thf(fact_762_less__le__not__le,axiom,
% 5.64/5.83 ( ord_less_rat
% 5.64/5.83 = ( ^ [X: rat,Y: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X @ Y )
% 5.64/5.83 & ~ ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_le_not_le
% 5.64/5.83 thf(fact_763_less__le__not__le,axiom,
% 5.64/5.83 ( ord_less_num
% 5.64/5.83 = ( ^ [X: num,Y: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X @ Y )
% 5.64/5.83 & ~ ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_le_not_le
% 5.64/5.83 thf(fact_764_less__le__not__le,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [X: nat,Y: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ X @ Y )
% 5.64/5.83 & ~ ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_le_not_le
% 5.64/5.83 thf(fact_765_less__le__not__le,axiom,
% 5.64/5.83 ( ord_less_int
% 5.64/5.83 = ( ^ [X: int,Y: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ X @ Y )
% 5.64/5.83 & ~ ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_le_not_le
% 5.64/5.83 thf(fact_766_less__le__not__le,axiom,
% 5.64/5.83 ( ord_less_real
% 5.64/5.83 = ( ^ [X: real,Y: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ X @ Y )
% 5.64/5.83 & ~ ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_le_not_le
% 5.64/5.83 thf(fact_767_dense__le,axiom,
% 5.64/5.83 ! [Y4: rat,Z: rat] :
% 5.64/5.83 ( ! [X4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ X4 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_rat @ X4 @ Z ) )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ Z ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_le
% 5.64/5.83 thf(fact_768_dense__le,axiom,
% 5.64/5.83 ! [Y4: real,Z: real] :
% 5.64/5.83 ( ! [X4: real] :
% 5.64/5.83 ( ( ord_less_real @ X4 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_real @ X4 @ Z ) )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ Z ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_le
% 5.64/5.83 thf(fact_769_dense__ge,axiom,
% 5.64/5.83 ! [Z: rat,Y4: rat] :
% 5.64/5.83 ( ! [X4: rat] :
% 5.64/5.83 ( ( ord_less_rat @ Z @ X4 )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ X4 ) )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ Z ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_ge
% 5.64/5.83 thf(fact_770_dense__ge,axiom,
% 5.64/5.83 ! [Z: real,Y4: real] :
% 5.64/5.83 ( ! [X4: real] :
% 5.64/5.83 ( ( ord_less_real @ Z @ X4 )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ X4 ) )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ Z ) ) ).
% 5.64/5.83
% 5.64/5.83 % dense_ge
% 5.64/5.83 thf(fact_771_antisym__conv2,axiom,
% 5.64/5.83 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ~ ( ord_less_set_nat @ X2 @ Y4 ) )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv2
% 5.64/5.83 thf(fact_772_antisym__conv2,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ~ ( ord_less_rat @ X2 @ Y4 ) )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv2
% 5.64/5.83 thf(fact_773_antisym__conv2,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 => ( ( ~ ( ord_less_num @ X2 @ Y4 ) )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv2
% 5.64/5.83 thf(fact_774_antisym__conv2,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ~ ( ord_less_nat @ X2 @ Y4 ) )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv2
% 5.64/5.83 thf(fact_775_antisym__conv2,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 => ( ( ~ ( ord_less_int @ X2 @ Y4 ) )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv2
% 5.64/5.83 thf(fact_776_antisym__conv2,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 => ( ( ~ ( ord_less_real @ X2 @ Y4 ) )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv2
% 5.64/5.83 thf(fact_777_antisym__conv1,axiom,
% 5.64/5.83 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.83 ( ~ ( ord_less_set_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv1
% 5.64/5.83 thf(fact_778_antisym__conv1,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ~ ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv1
% 5.64/5.83 thf(fact_779_antisym__conv1,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ~ ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv1
% 5.64/5.83 thf(fact_780_antisym__conv1,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ~ ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv1
% 5.64/5.83 thf(fact_781_antisym__conv1,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ~ ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv1
% 5.64/5.83 thf(fact_782_antisym__conv1,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ~ ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % antisym_conv1
% 5.64/5.83 thf(fact_783_nless__le,axiom,
% 5.64/5.83 ! [A: set_nat,B: set_nat] :
% 5.64/5.83 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 5.64/5.83 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.83 | ( A = B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nless_le
% 5.64/5.83 thf(fact_784_nless__le,axiom,
% 5.64/5.83 ! [A: rat,B: rat] :
% 5.64/5.83 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.64/5.83 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 | ( A = B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nless_le
% 5.64/5.83 thf(fact_785_nless__le,axiom,
% 5.64/5.83 ! [A: num,B: num] :
% 5.64/5.83 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.64/5.83 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.64/5.83 | ( A = B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nless_le
% 5.64/5.83 thf(fact_786_nless__le,axiom,
% 5.64/5.83 ! [A: nat,B: nat] :
% 5.64/5.83 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.64/5.83 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.64/5.83 | ( A = B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nless_le
% 5.64/5.83 thf(fact_787_nless__le,axiom,
% 5.64/5.83 ! [A: int,B: int] :
% 5.64/5.83 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.64/5.83 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.64/5.83 | ( A = B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nless_le
% 5.64/5.83 thf(fact_788_nless__le,axiom,
% 5.64/5.83 ! [A: real,B: real] :
% 5.64/5.83 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.64/5.83 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.64/5.83 | ( A = B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nless_le
% 5.64/5.83 thf(fact_789_leI,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ~ ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leI
% 5.64/5.83 thf(fact_790_leI,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ~ ( ord_less_num @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leI
% 5.64/5.83 thf(fact_791_leI,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ~ ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leI
% 5.64/5.83 thf(fact_792_leI,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ~ ( ord_less_int @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leI
% 5.64/5.83 thf(fact_793_leI,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ~ ( ord_less_real @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leI
% 5.64/5.83 thf(fact_794_leD,axiom,
% 5.64/5.83 ! [Y4: set_nat,X2: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ Y4 @ X2 )
% 5.64/5.83 => ~ ( ord_less_set_nat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leD
% 5.64/5.83 thf(fact_795_leD,axiom,
% 5.64/5.83 ! [Y4: rat,X2: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.83 => ~ ( ord_less_rat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leD
% 5.64/5.83 thf(fact_796_leD,axiom,
% 5.64/5.83 ! [Y4: num,X2: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ Y4 @ X2 )
% 5.64/5.83 => ~ ( ord_less_num @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leD
% 5.64/5.83 thf(fact_797_leD,axiom,
% 5.64/5.83 ! [Y4: nat,X2: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.83 => ~ ( ord_less_nat @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leD
% 5.64/5.83 thf(fact_798_leD,axiom,
% 5.64/5.83 ! [Y4: int,X2: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ Y4 @ X2 )
% 5.64/5.83 => ~ ( ord_less_int @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leD
% 5.64/5.83 thf(fact_799_leD,axiom,
% 5.64/5.83 ! [Y4: real,X2: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.83 => ~ ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % leD
% 5.64/5.83 thf(fact_800_verit__comp__simplify1_I3_J,axiom,
% 5.64/5.83 ! [B2: rat,A2: rat] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 5.64/5.83 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % verit_comp_simplify1(3)
% 5.64/5.83 thf(fact_801_verit__comp__simplify1_I3_J,axiom,
% 5.64/5.83 ! [B2: num,A2: num] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 5.64/5.83 = ( ord_less_num @ A2 @ B2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % verit_comp_simplify1(3)
% 5.64/5.83 thf(fact_802_verit__comp__simplify1_I3_J,axiom,
% 5.64/5.83 ! [B2: nat,A2: nat] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 5.64/5.83 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % verit_comp_simplify1(3)
% 5.64/5.83 thf(fact_803_verit__comp__simplify1_I3_J,axiom,
% 5.64/5.83 ! [B2: int,A2: int] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 5.64/5.83 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % verit_comp_simplify1(3)
% 5.64/5.83 thf(fact_804_verit__comp__simplify1_I3_J,axiom,
% 5.64/5.83 ! [B2: real,A2: real] :
% 5.64/5.83 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 5.64/5.83 = ( ord_less_real @ A2 @ B2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % verit_comp_simplify1(3)
% 5.64/5.83 thf(fact_805_size__neq__size__imp__neq,axiom,
% 5.64/5.83 ! [X2: list_VEBT_VEBT,Y4: list_VEBT_VEBT] :
% 5.64/5.83 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 5.64/5.83 != ( size_s6755466524823107622T_VEBT @ Y4 ) )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % size_neq_size_imp_neq
% 5.64/5.83 thf(fact_806_size__neq__size__imp__neq,axiom,
% 5.64/5.83 ! [X2: list_o,Y4: list_o] :
% 5.64/5.83 ( ( ( size_size_list_o @ X2 )
% 5.64/5.83 != ( size_size_list_o @ Y4 ) )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % size_neq_size_imp_neq
% 5.64/5.83 thf(fact_807_size__neq__size__imp__neq,axiom,
% 5.64/5.83 ! [X2: list_nat,Y4: list_nat] :
% 5.64/5.83 ( ( ( size_size_list_nat @ X2 )
% 5.64/5.83 != ( size_size_list_nat @ Y4 ) )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % size_neq_size_imp_neq
% 5.64/5.83 thf(fact_808_size__neq__size__imp__neq,axiom,
% 5.64/5.83 ! [X2: list_int,Y4: list_int] :
% 5.64/5.83 ( ( ( size_size_list_int @ X2 )
% 5.64/5.83 != ( size_size_list_int @ Y4 ) )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % size_neq_size_imp_neq
% 5.64/5.83 thf(fact_809_size__neq__size__imp__neq,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ( ( size_size_num @ X2 )
% 5.64/5.83 != ( size_size_num @ Y4 ) )
% 5.64/5.83 => ( X2 != Y4 ) ) ).
% 5.64/5.83
% 5.64/5.83 % size_neq_size_imp_neq
% 5.64/5.83 thf(fact_810_less__numeral__extra_I4_J,axiom,
% 5.64/5.83 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.64/5.83
% 5.64/5.83 % less_numeral_extra(4)
% 5.64/5.83 thf(fact_811_less__numeral__extra_I4_J,axiom,
% 5.64/5.83 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.64/5.83
% 5.64/5.83 % less_numeral_extra(4)
% 5.64/5.83 thf(fact_812_less__numeral__extra_I4_J,axiom,
% 5.64/5.83 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.64/5.83
% 5.64/5.83 % less_numeral_extra(4)
% 5.64/5.83 thf(fact_813_less__numeral__extra_I4_J,axiom,
% 5.64/5.83 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.64/5.83
% 5.64/5.83 % less_numeral_extra(4)
% 5.64/5.83 thf(fact_814_add__less__imp__less__right,axiom,
% 5.64/5.83 ! [A: real,C: real,B: real] :
% 5.64/5.83 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.64/5.83 => ( ord_less_real @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_right
% 5.64/5.83 thf(fact_815_add__less__imp__less__right,axiom,
% 5.64/5.83 ! [A: rat,C: rat,B: rat] :
% 5.64/5.83 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.83 => ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_right
% 5.64/5.83 thf(fact_816_add__less__imp__less__right,axiom,
% 5.64/5.83 ! [A: nat,C: nat,B: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.83 => ( ord_less_nat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_right
% 5.64/5.83 thf(fact_817_add__less__imp__less__right,axiom,
% 5.64/5.83 ! [A: int,C: int,B: int] :
% 5.64/5.83 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.64/5.83 => ( ord_less_int @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_right
% 5.64/5.83 thf(fact_818_add__less__imp__less__left,axiom,
% 5.64/5.83 ! [C: real,A: real,B: real] :
% 5.64/5.83 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.64/5.83 => ( ord_less_real @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_left
% 5.64/5.83 thf(fact_819_add__less__imp__less__left,axiom,
% 5.64/5.83 ! [C: rat,A: rat,B: rat] :
% 5.64/5.83 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.64/5.83 => ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_left
% 5.64/5.83 thf(fact_820_add__less__imp__less__left,axiom,
% 5.64/5.83 ! [C: nat,A: nat,B: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.64/5.83 => ( ord_less_nat @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_left
% 5.64/5.83 thf(fact_821_add__less__imp__less__left,axiom,
% 5.64/5.83 ! [C: int,A: int,B: int] :
% 5.64/5.83 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.64/5.83 => ( ord_less_int @ A @ B ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_imp_less_left
% 5.64/5.83 thf(fact_822_add__strict__right__mono,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_right_mono
% 5.64/5.83 thf(fact_823_add__strict__right__mono,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_right_mono
% 5.64/5.83 thf(fact_824_add__strict__right__mono,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_right_mono
% 5.64/5.83 thf(fact_825_add__strict__right__mono,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_right_mono
% 5.64/5.83 thf(fact_826_add__strict__left__mono,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_left_mono
% 5.64/5.83 thf(fact_827_add__strict__left__mono,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_left_mono
% 5.64/5.83 thf(fact_828_add__strict__left__mono,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_left_mono
% 5.64/5.83 thf(fact_829_add__strict__left__mono,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_left_mono
% 5.64/5.83 thf(fact_830_add__strict__mono,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ C @ D )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_mono
% 5.64/5.83 thf(fact_831_add__strict__mono,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ C @ D )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_mono
% 5.64/5.83 thf(fact_832_add__strict__mono,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ C @ D )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_mono
% 5.64/5.83 thf(fact_833_add__strict__mono,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ C @ D )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_strict_mono
% 5.64/5.83 thf(fact_834_add__mono__thms__linordered__field_I1_J,axiom,
% 5.64/5.83 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.83 ( ( ( ord_less_real @ I @ J )
% 5.64/5.83 & ( K = L ) )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(1)
% 5.64/5.83 thf(fact_835_add__mono__thms__linordered__field_I1_J,axiom,
% 5.64/5.83 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.83 ( ( ( ord_less_rat @ I @ J )
% 5.64/5.83 & ( K = L ) )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(1)
% 5.64/5.83 thf(fact_836_add__mono__thms__linordered__field_I1_J,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.83 ( ( ( ord_less_nat @ I @ J )
% 5.64/5.83 & ( K = L ) )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(1)
% 5.64/5.83 thf(fact_837_add__mono__thms__linordered__field_I1_J,axiom,
% 5.64/5.83 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.83 ( ( ( ord_less_int @ I @ J )
% 5.64/5.83 & ( K = L ) )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(1)
% 5.64/5.83 thf(fact_838_add__mono__thms__linordered__field_I2_J,axiom,
% 5.64/5.83 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.83 ( ( ( I = J )
% 5.64/5.83 & ( ord_less_real @ K @ L ) )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(2)
% 5.64/5.83 thf(fact_839_add__mono__thms__linordered__field_I2_J,axiom,
% 5.64/5.83 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.83 ( ( ( I = J )
% 5.64/5.83 & ( ord_less_rat @ K @ L ) )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(2)
% 5.64/5.83 thf(fact_840_add__mono__thms__linordered__field_I2_J,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.83 ( ( ( I = J )
% 5.64/5.83 & ( ord_less_nat @ K @ L ) )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(2)
% 5.64/5.83 thf(fact_841_add__mono__thms__linordered__field_I2_J,axiom,
% 5.64/5.83 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.83 ( ( ( I = J )
% 5.64/5.83 & ( ord_less_int @ K @ L ) )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(2)
% 5.64/5.83 thf(fact_842_add__mono__thms__linordered__field_I5_J,axiom,
% 5.64/5.83 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.83 ( ( ( ord_less_real @ I @ J )
% 5.64/5.83 & ( ord_less_real @ K @ L ) )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(5)
% 5.64/5.83 thf(fact_843_add__mono__thms__linordered__field_I5_J,axiom,
% 5.64/5.83 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.83 ( ( ( ord_less_rat @ I @ J )
% 5.64/5.83 & ( ord_less_rat @ K @ L ) )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(5)
% 5.64/5.83 thf(fact_844_add__mono__thms__linordered__field_I5_J,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.83 ( ( ( ord_less_nat @ I @ J )
% 5.64/5.83 & ( ord_less_nat @ K @ L ) )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(5)
% 5.64/5.83 thf(fact_845_add__mono__thms__linordered__field_I5_J,axiom,
% 5.64/5.83 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.83 ( ( ( ord_less_int @ I @ J )
% 5.64/5.83 & ( ord_less_int @ K @ L ) )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(5)
% 5.64/5.83 thf(fact_846_not__less__less__Suc__eq,axiom,
% 5.64/5.83 ! [N: nat,M: nat] :
% 5.64/5.83 ( ~ ( ord_less_nat @ N @ M )
% 5.64/5.83 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.64/5.83 = ( N = M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_less_less_Suc_eq
% 5.64/5.83 thf(fact_847_strict__inc__induct,axiom,
% 5.64/5.83 ! [I: nat,J: nat,P: nat > $o] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ! [I3: nat] :
% 5.64/5.83 ( ( J
% 5.64/5.83 = ( suc @ I3 ) )
% 5.64/5.83 => ( P @ I3 ) )
% 5.64/5.83 => ( ! [I3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I3 @ J )
% 5.64/5.83 => ( ( P @ ( suc @ I3 ) )
% 5.64/5.83 => ( P @ I3 ) ) )
% 5.64/5.83 => ( P @ I ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % strict_inc_induct
% 5.64/5.83 thf(fact_848_less__Suc__induct,axiom,
% 5.64/5.83 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.64/5.83 => ( ! [I3: nat,J2: nat,K3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I3 @ J2 )
% 5.64/5.83 => ( ( ord_less_nat @ J2 @ K3 )
% 5.64/5.83 => ( ( P @ I3 @ J2 )
% 5.64/5.83 => ( ( P @ J2 @ K3 )
% 5.64/5.83 => ( P @ I3 @ K3 ) ) ) ) )
% 5.64/5.83 => ( P @ I @ J ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_Suc_induct
% 5.64/5.83 thf(fact_849_less__trans__Suc,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ( ord_less_nat @ J @ K )
% 5.64/5.83 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_trans_Suc
% 5.64/5.83 thf(fact_850_Suc__less__SucD,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.64/5.83 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_less_SucD
% 5.64/5.83 thf(fact_851_less__antisym,axiom,
% 5.64/5.83 ! [N: nat,M: nat] :
% 5.64/5.83 ( ~ ( ord_less_nat @ N @ M )
% 5.64/5.83 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.64/5.83 => ( M = N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_antisym
% 5.64/5.83 thf(fact_852_Suc__less__eq2,axiom,
% 5.64/5.83 ! [N: nat,M: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.83 = ( ? [M6: nat] :
% 5.64/5.83 ( ( M
% 5.64/5.83 = ( suc @ M6 ) )
% 5.64/5.83 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_less_eq2
% 5.64/5.83 thf(fact_853_All__less__Suc,axiom,
% 5.64/5.83 ! [N: nat,P: nat > $o] :
% 5.64/5.83 ( ( ! [I4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.64/5.83 => ( P @ I4 ) ) )
% 5.64/5.83 = ( ( P @ N )
% 5.64/5.83 & ! [I4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I4 @ N )
% 5.64/5.83 => ( P @ I4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % All_less_Suc
% 5.64/5.83 thf(fact_854_not__less__eq,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.64/5.83 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % not_less_eq
% 5.64/5.83 thf(fact_855_less__Suc__eq,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.64/5.83 = ( ( ord_less_nat @ M @ N )
% 5.64/5.83 | ( M = N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_Suc_eq
% 5.64/5.83 thf(fact_856_Ex__less__Suc,axiom,
% 5.64/5.83 ! [N: nat,P: nat > $o] :
% 5.64/5.83 ( ( ? [I4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.64/5.83 & ( P @ I4 ) ) )
% 5.64/5.83 = ( ( P @ N )
% 5.64/5.83 | ? [I4: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I4 @ N )
% 5.64/5.83 & ( P @ I4 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % Ex_less_Suc
% 5.64/5.83 thf(fact_857_less__SucI,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ N )
% 5.64/5.83 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_SucI
% 5.64/5.83 thf(fact_858_less__SucE,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.64/5.83 => ( ~ ( ord_less_nat @ M @ N )
% 5.64/5.83 => ( M = N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_SucE
% 5.64/5.83 thf(fact_859_Suc__lessI,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ N )
% 5.64/5.83 => ( ( ( suc @ M )
% 5.64/5.83 != N )
% 5.64/5.83 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_lessI
% 5.64/5.83 thf(fact_860_Suc__lessE,axiom,
% 5.64/5.83 ! [I: nat,K: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.64/5.83 => ~ ! [J2: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J2 )
% 5.64/5.83 => ( K
% 5.64/5.83 != ( suc @ J2 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_lessE
% 5.64/5.83 thf(fact_861_Suc__lessD,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.64/5.83 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_lessD
% 5.64/5.83 thf(fact_862_Nat_OlessE,axiom,
% 5.64/5.83 ! [I: nat,K: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ K )
% 5.64/5.83 => ( ( K
% 5.64/5.83 != ( suc @ I ) )
% 5.64/5.83 => ~ ! [J2: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J2 )
% 5.64/5.83 => ( K
% 5.64/5.83 != ( suc @ J2 ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % Nat.lessE
% 5.64/5.83 thf(fact_863_less__mono__imp__le__mono,axiom,
% 5.64/5.83 ! [F: nat > nat,I: nat,J: nat] :
% 5.64/5.83 ( ! [I3: nat,J2: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I3 @ J2 )
% 5.64/5.83 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 5.64/5.83 => ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_mono_imp_le_mono
% 5.64/5.83 thf(fact_864_le__neq__implies__less,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.83 => ( ( M != N )
% 5.64/5.83 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % le_neq_implies_less
% 5.64/5.83 thf(fact_865_less__or__eq__imp__le,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ( ord_less_nat @ M @ N )
% 5.64/5.83 | ( M = N ) )
% 5.64/5.83 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_or_eq_imp_le
% 5.64/5.83 thf(fact_866_le__eq__less__or__eq,axiom,
% 5.64/5.83 ( ord_less_eq_nat
% 5.64/5.83 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M2 @ N2 )
% 5.64/5.83 | ( M2 = N2 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % le_eq_less_or_eq
% 5.64/5.83 thf(fact_867_less__imp__le__nat,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ N )
% 5.64/5.83 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_imp_le_nat
% 5.64/5.83 thf(fact_868_nat__less__le,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.83 & ( M2 != N2 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % nat_less_le
% 5.64/5.83 thf(fact_869_less__add__eq__less,axiom,
% 5.64/5.83 ! [K: nat,L: nat,M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ K @ L )
% 5.64/5.83 => ( ( ( plus_plus_nat @ M @ L )
% 5.64/5.83 = ( plus_plus_nat @ K @ N ) )
% 5.64/5.83 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_add_eq_less
% 5.64/5.83 thf(fact_870_trans__less__add2,axiom,
% 5.64/5.83 ! [I: nat,J: nat,M: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % trans_less_add2
% 5.64/5.83 thf(fact_871_trans__less__add1,axiom,
% 5.64/5.83 ! [I: nat,J: nat,M: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % trans_less_add1
% 5.64/5.83 thf(fact_872_add__less__mono1,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_mono1
% 5.64/5.83 thf(fact_873_not__add__less2,axiom,
% 5.64/5.83 ! [J: nat,I: nat] :
% 5.64/5.83 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.64/5.83
% 5.64/5.83 % not_add_less2
% 5.64/5.83 thf(fact_874_not__add__less1,axiom,
% 5.64/5.83 ! [I: nat,J: nat] :
% 5.64/5.83 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.64/5.83
% 5.64/5.83 % not_add_less1
% 5.64/5.83 thf(fact_875_add__less__mono,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.83 ( ( ord_less_nat @ I @ J )
% 5.64/5.83 => ( ( ord_less_nat @ K @ L )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_mono
% 5.64/5.83 thf(fact_876_add__lessD1,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat] :
% 5.64/5.83 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.64/5.83 => ( ord_less_nat @ I @ K ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_lessD1
% 5.64/5.83 thf(fact_877_add__less__le__mono,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.83 ( ( ord_less_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_rat @ C @ D )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_le_mono
% 5.64/5.83 thf(fact_878_add__less__le__mono,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.83 ( ( ord_less_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_nat @ C @ D )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_le_mono
% 5.64/5.83 thf(fact_879_add__less__le__mono,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.83 ( ( ord_less_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_int @ C @ D )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_le_mono
% 5.64/5.83 thf(fact_880_add__less__le__mono,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.83 ( ( ord_less_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_eq_real @ C @ D )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_less_le_mono
% 5.64/5.83 thf(fact_881_add__le__less__mono,axiom,
% 5.64/5.83 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ord_less_rat @ C @ D )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_le_less_mono
% 5.64/5.83 thf(fact_882_add__le__less__mono,axiom,
% 5.64/5.83 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.83 => ( ( ord_less_nat @ C @ D )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_le_less_mono
% 5.64/5.83 thf(fact_883_add__le__less__mono,axiom,
% 5.64/5.83 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.83 => ( ( ord_less_int @ C @ D )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_le_less_mono
% 5.64/5.83 thf(fact_884_add__le__less__mono,axiom,
% 5.64/5.83 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.83 => ( ( ord_less_real @ C @ D )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_le_less_mono
% 5.64/5.83 thf(fact_885_add__mono__thms__linordered__field_I3_J,axiom,
% 5.64/5.83 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.83 ( ( ( ord_less_rat @ I @ J )
% 5.64/5.83 & ( ord_less_eq_rat @ K @ L ) )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(3)
% 5.64/5.83 thf(fact_886_add__mono__thms__linordered__field_I3_J,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.83 ( ( ( ord_less_nat @ I @ J )
% 5.64/5.83 & ( ord_less_eq_nat @ K @ L ) )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(3)
% 5.64/5.83 thf(fact_887_add__mono__thms__linordered__field_I3_J,axiom,
% 5.64/5.83 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.83 ( ( ( ord_less_int @ I @ J )
% 5.64/5.83 & ( ord_less_eq_int @ K @ L ) )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(3)
% 5.64/5.83 thf(fact_888_add__mono__thms__linordered__field_I3_J,axiom,
% 5.64/5.83 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.83 ( ( ( ord_less_real @ I @ J )
% 5.64/5.83 & ( ord_less_eq_real @ K @ L ) )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(3)
% 5.64/5.83 thf(fact_889_add__mono__thms__linordered__field_I4_J,axiom,
% 5.64/5.83 ! [I: rat,J: rat,K: rat,L: rat] :
% 5.64/5.83 ( ( ( ord_less_eq_rat @ I @ J )
% 5.64/5.83 & ( ord_less_rat @ K @ L ) )
% 5.64/5.83 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(4)
% 5.64/5.83 thf(fact_890_add__mono__thms__linordered__field_I4_J,axiom,
% 5.64/5.83 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.83 ( ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.83 & ( ord_less_nat @ K @ L ) )
% 5.64/5.83 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(4)
% 5.64/5.83 thf(fact_891_add__mono__thms__linordered__field_I4_J,axiom,
% 5.64/5.83 ! [I: int,J: int,K: int,L: int] :
% 5.64/5.83 ( ( ( ord_less_eq_int @ I @ J )
% 5.64/5.83 & ( ord_less_int @ K @ L ) )
% 5.64/5.83 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(4)
% 5.64/5.83 thf(fact_892_add__mono__thms__linordered__field_I4_J,axiom,
% 5.64/5.83 ! [I: real,J: real,K: real,L: real] :
% 5.64/5.83 ( ( ( ord_less_eq_real @ I @ J )
% 5.64/5.83 & ( ord_less_real @ K @ L ) )
% 5.64/5.83 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % add_mono_thms_linordered_field(4)
% 5.64/5.83 thf(fact_893_not__numeral__less__one,axiom,
% 5.64/5.83 ! [N: num] :
% 5.64/5.83 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.64/5.83
% 5.64/5.83 % not_numeral_less_one
% 5.64/5.83 thf(fact_894_not__numeral__less__one,axiom,
% 5.64/5.83 ! [N: num] :
% 5.64/5.83 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.64/5.83
% 5.64/5.83 % not_numeral_less_one
% 5.64/5.83 thf(fact_895_not__numeral__less__one,axiom,
% 5.64/5.83 ! [N: num] :
% 5.64/5.83 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.64/5.83
% 5.64/5.83 % not_numeral_less_one
% 5.64/5.83 thf(fact_896_not__numeral__less__one,axiom,
% 5.64/5.83 ! [N: num] :
% 5.64/5.83 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.64/5.83
% 5.64/5.83 % not_numeral_less_one
% 5.64/5.83 thf(fact_897_Suc__leI,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ N )
% 5.64/5.83 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_leI
% 5.64/5.83 thf(fact_898_Suc__le__eq,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.64/5.83 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_le_eq
% 5.64/5.83 thf(fact_899_dec__induct,axiom,
% 5.64/5.83 ! [I: nat,J: nat,P: nat > $o] :
% 5.64/5.83 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.83 => ( ( P @ I )
% 5.64/5.83 => ( ! [N3: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ I @ N3 )
% 5.64/5.83 => ( ( ord_less_nat @ N3 @ J )
% 5.64/5.83 => ( ( P @ N3 )
% 5.64/5.83 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.64/5.83 => ( P @ J ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dec_induct
% 5.64/5.83 thf(fact_900_inc__induct,axiom,
% 5.64/5.83 ! [I: nat,J: nat,P: nat > $o] :
% 5.64/5.83 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.83 => ( ( P @ J )
% 5.64/5.83 => ( ! [N3: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ I @ N3 )
% 5.64/5.83 => ( ( ord_less_nat @ N3 @ J )
% 5.64/5.83 => ( ( P @ ( suc @ N3 ) )
% 5.64/5.83 => ( P @ N3 ) ) ) )
% 5.64/5.83 => ( P @ I ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % inc_induct
% 5.64/5.83 thf(fact_901_Suc__le__lessD,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.64/5.83 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % Suc_le_lessD
% 5.64/5.83 thf(fact_902_le__less__Suc__eq,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.83 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.64/5.83 = ( N = M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % le_less_Suc_eq
% 5.64/5.83 thf(fact_903_less__Suc__eq__le,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.64/5.83 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_Suc_eq_le
% 5.64/5.83 thf(fact_904_less__eq__Suc__le,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_eq_Suc_le
% 5.64/5.83 thf(fact_905_le__imp__less__Suc,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.83 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % le_imp_less_Suc
% 5.64/5.83 thf(fact_906_dbl__def,axiom,
% 5.64/5.83 ( neg_numeral_dbl_real
% 5.64/5.83 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dbl_def
% 5.64/5.83 thf(fact_907_dbl__def,axiom,
% 5.64/5.83 ( neg_numeral_dbl_rat
% 5.64/5.83 = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dbl_def
% 5.64/5.83 thf(fact_908_dbl__def,axiom,
% 5.64/5.83 ( neg_numeral_dbl_int
% 5.64/5.83 = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % dbl_def
% 5.64/5.83 thf(fact_909_less__natE,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ N )
% 5.64/5.83 => ~ ! [Q2: nat] :
% 5.64/5.83 ( N
% 5.64/5.83 != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_natE
% 5.64/5.83 thf(fact_910_less__add__Suc1,axiom,
% 5.64/5.83 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_add_Suc1
% 5.64/5.83 thf(fact_911_less__add__Suc2,axiom,
% 5.64/5.83 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_add_Suc2
% 5.64/5.83 thf(fact_912_less__iff__Suc__add,axiom,
% 5.64/5.83 ( ord_less_nat
% 5.64/5.83 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.83 ? [K2: nat] :
% 5.64/5.83 ( N2
% 5.64/5.83 = ( suc @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_iff_Suc_add
% 5.64/5.83 thf(fact_913_less__imp__Suc__add,axiom,
% 5.64/5.83 ! [M: nat,N: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M @ N )
% 5.64/5.83 => ? [K3: nat] :
% 5.64/5.83 ( N
% 5.64/5.83 = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % less_imp_Suc_add
% 5.64/5.83 thf(fact_914_mono__nat__linear__lb,axiom,
% 5.64/5.83 ! [F: nat > nat,M: nat,K: nat] :
% 5.64/5.83 ( ! [M4: nat,N3: nat] :
% 5.64/5.83 ( ( ord_less_nat @ M4 @ N3 )
% 5.64/5.83 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 5.64/5.83 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % mono_nat_linear_lb
% 5.64/5.83 thf(fact_915_order__antisym__conv,axiom,
% 5.64/5.83 ! [Y4: set_nat,X2: set_nat] :
% 5.64/5.83 ( ( ord_less_eq_set_nat @ Y4 @ X2 )
% 5.64/5.83 => ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_antisym_conv
% 5.64/5.83 thf(fact_916_order__antisym__conv,axiom,
% 5.64/5.83 ! [Y4: rat,X2: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.83 => ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_antisym_conv
% 5.64/5.83 thf(fact_917_order__antisym__conv,axiom,
% 5.64/5.83 ! [Y4: num,X2: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ Y4 @ X2 )
% 5.64/5.83 => ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_antisym_conv
% 5.64/5.83 thf(fact_918_order__antisym__conv,axiom,
% 5.64/5.83 ! [Y4: nat,X2: nat] :
% 5.64/5.83 ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.83 => ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_antisym_conv
% 5.64/5.83 thf(fact_919_order__antisym__conv,axiom,
% 5.64/5.83 ! [Y4: int,X2: int] :
% 5.64/5.83 ( ( ord_less_eq_int @ Y4 @ X2 )
% 5.64/5.83 => ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_antisym_conv
% 5.64/5.83 thf(fact_920_order__antisym__conv,axiom,
% 5.64/5.83 ! [Y4: real,X2: real] :
% 5.64/5.83 ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.83 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 = ( X2 = Y4 ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % order_antisym_conv
% 5.64/5.83 thf(fact_921_linorder__le__cases,axiom,
% 5.64/5.83 ! [X2: rat,Y4: rat] :
% 5.64/5.83 ( ~ ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_rat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_cases
% 5.64/5.83 thf(fact_922_linorder__le__cases,axiom,
% 5.64/5.83 ! [X2: num,Y4: num] :
% 5.64/5.83 ( ~ ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_num @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_cases
% 5.64/5.83 thf(fact_923_linorder__le__cases,axiom,
% 5.64/5.83 ! [X2: nat,Y4: nat] :
% 5.64/5.83 ( ~ ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_nat @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_cases
% 5.64/5.83 thf(fact_924_linorder__le__cases,axiom,
% 5.64/5.83 ! [X2: int,Y4: int] :
% 5.64/5.83 ( ~ ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_int @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_cases
% 5.64/5.83 thf(fact_925_linorder__le__cases,axiom,
% 5.64/5.83 ! [X2: real,Y4: real] :
% 5.64/5.83 ( ~ ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.83 => ( ord_less_eq_real @ Y4 @ X2 ) ) ).
% 5.64/5.83
% 5.64/5.83 % linorder_le_cases
% 5.64/5.83 thf(fact_926_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_927_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_928_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_929_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_930_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_931_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_932_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > num,C: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_933_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_934_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > int,C: int] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_935_ord__le__eq__subst,axiom,
% 5.64/5.83 ! [A: num,B: num,F: num > real,C: real] :
% 5.64/5.83 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.83 => ( ( ( F @ B )
% 5.64/5.83 = C )
% 5.64/5.83 => ( ! [X4: num,Y3: num] :
% 5.64/5.83 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_le_eq_subst
% 5.64/5.83 thf(fact_936_ord__eq__le__subst,axiom,
% 5.64/5.83 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.64/5.83 ( ( A
% 5.64/5.83 = ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_eq_le_subst
% 5.64/5.83 thf(fact_937_ord__eq__le__subst,axiom,
% 5.64/5.83 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.64/5.83 ( ( A
% 5.64/5.83 = ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.83 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.83
% 5.64/5.83 % ord_eq_le_subst
% 5.64/5.83 thf(fact_938_ord__eq__le__subst,axiom,
% 5.64/5.83 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.64/5.83 ( ( A
% 5.64/5.83 = ( F @ B ) )
% 5.64/5.83 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.83 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.83 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.83 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_939_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_940_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_941_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_942_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: num,F: num > num,B: num,C: num] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_943_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_944_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: int,F: num > int,B: num,C: num] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_945_ord__eq__le__subst,axiom,
% 5.64/5.84 ! [A: real,F: num > real,B: num,C: num] :
% 5.64/5.84 ( ( A
% 5.64/5.84 = ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_subst
% 5.64/5.84 thf(fact_946_linorder__linear,axiom,
% 5.64/5.84 ! [X2: rat,Y4: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.84 | ( ord_less_eq_rat @ Y4 @ X2 ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_linear
% 5.64/5.84 thf(fact_947_linorder__linear,axiom,
% 5.64/5.84 ! [X2: num,Y4: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.84 | ( ord_less_eq_num @ Y4 @ X2 ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_linear
% 5.64/5.84 thf(fact_948_linorder__linear,axiom,
% 5.64/5.84 ! [X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.84 | ( ord_less_eq_nat @ Y4 @ X2 ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_linear
% 5.64/5.84 thf(fact_949_linorder__linear,axiom,
% 5.64/5.84 ! [X2: int,Y4: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.84 | ( ord_less_eq_int @ Y4 @ X2 ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_linear
% 5.64/5.84 thf(fact_950_linorder__linear,axiom,
% 5.64/5.84 ! [X2: real,Y4: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.84 | ( ord_less_eq_real @ Y4 @ X2 ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_linear
% 5.64/5.84 thf(fact_951_verit__la__disequality,axiom,
% 5.64/5.84 ! [A: rat,B: rat] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 | ~ ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.64/5.84
% 5.64/5.84 % verit_la_disequality
% 5.64/5.84 thf(fact_952_verit__la__disequality,axiom,
% 5.64/5.84 ! [A: num,B: num] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 | ~ ( ord_less_eq_num @ A @ B )
% 5.64/5.84 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.64/5.84
% 5.64/5.84 % verit_la_disequality
% 5.64/5.84 thf(fact_953_verit__la__disequality,axiom,
% 5.64/5.84 ! [A: nat,B: nat] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 | ~ ( ord_less_eq_nat @ A @ B )
% 5.64/5.84 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.64/5.84
% 5.64/5.84 % verit_la_disequality
% 5.64/5.84 thf(fact_954_verit__la__disequality,axiom,
% 5.64/5.84 ! [A: int,B: int] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 | ~ ( ord_less_eq_int @ A @ B )
% 5.64/5.84 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.64/5.84
% 5.64/5.84 % verit_la_disequality
% 5.64/5.84 thf(fact_955_verit__la__disequality,axiom,
% 5.64/5.84 ! [A: real,B: real] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 | ~ ( ord_less_eq_real @ A @ B )
% 5.64/5.84 | ~ ( ord_less_eq_real @ B @ A ) ) ).
% 5.64/5.84
% 5.64/5.84 % verit_la_disequality
% 5.64/5.84 thf(fact_956_order__eq__refl,axiom,
% 5.64/5.84 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.84 ( ( X2 = Y4 )
% 5.64/5.84 => ( ord_less_eq_set_nat @ X2 @ Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_eq_refl
% 5.64/5.84 thf(fact_957_order__eq__refl,axiom,
% 5.64/5.84 ! [X2: rat,Y4: rat] :
% 5.64/5.84 ( ( X2 = Y4 )
% 5.64/5.84 => ( ord_less_eq_rat @ X2 @ Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_eq_refl
% 5.64/5.84 thf(fact_958_order__eq__refl,axiom,
% 5.64/5.84 ! [X2: num,Y4: num] :
% 5.64/5.84 ( ( X2 = Y4 )
% 5.64/5.84 => ( ord_less_eq_num @ X2 @ Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_eq_refl
% 5.64/5.84 thf(fact_959_order__eq__refl,axiom,
% 5.64/5.84 ! [X2: nat,Y4: nat] :
% 5.64/5.84 ( ( X2 = Y4 )
% 5.64/5.84 => ( ord_less_eq_nat @ X2 @ Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_eq_refl
% 5.64/5.84 thf(fact_960_order__eq__refl,axiom,
% 5.64/5.84 ! [X2: int,Y4: int] :
% 5.64/5.84 ( ( X2 = Y4 )
% 5.64/5.84 => ( ord_less_eq_int @ X2 @ Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_eq_refl
% 5.64/5.84 thf(fact_961_order__eq__refl,axiom,
% 5.64/5.84 ! [X2: real,Y4: real] :
% 5.64/5.84 ( ( X2 = Y4 )
% 5.64/5.84 => ( ord_less_eq_real @ X2 @ Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_eq_refl
% 5.64/5.84 thf(fact_962_order__subst2,axiom,
% 5.64/5.84 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_963_order__subst2,axiom,
% 5.64/5.84 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_964_order__subst2,axiom,
% 5.64/5.84 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_965_order__subst2,axiom,
% 5.64/5.84 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_966_order__subst2,axiom,
% 5.64/5.84 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_967_order__subst2,axiom,
% 5.64/5.84 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_968_order__subst2,axiom,
% 5.64/5.84 ! [A: num,B: num,F: num > num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_969_order__subst2,axiom,
% 5.64/5.84 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_970_order__subst2,axiom,
% 5.64/5.84 ! [A: num,B: num,F: num > int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_int @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_971_order__subst2,axiom,
% 5.64/5.84 ! [A: num,B: num,F: num > real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst2
% 5.64/5.84 thf(fact_972_order__subst1,axiom,
% 5.64/5.84 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_973_order__subst1,axiom,
% 5.64/5.84 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_974_order__subst1,axiom,
% 5.64/5.84 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.84 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_975_order__subst1,axiom,
% 5.64/5.84 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.84 => ( ! [X4: int,Y3: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_976_order__subst1,axiom,
% 5.64/5.84 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.84 => ( ! [X4: real,Y3: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_977_order__subst1,axiom,
% 5.64/5.84 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.84 => ( ! [X4: rat,Y3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_978_order__subst1,axiom,
% 5.64/5.84 ! [A: num,F: num > num,B: num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ! [X4: num,Y3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_979_order__subst1,axiom,
% 5.64/5.84 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.84 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_980_order__subst1,axiom,
% 5.64/5.84 ! [A: num,F: int > num,B: int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.84 => ( ! [X4: int,Y3: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_981_order__subst1,axiom,
% 5.64/5.84 ! [A: num,F: real > num,B: real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.64/5.84 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.84 => ( ! [X4: real,Y3: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ X4 @ Y3 )
% 5.64/5.84 => ( ord_less_eq_num @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.64/5.84 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_subst1
% 5.64/5.84 thf(fact_982_Orderings_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: set_nat,B3: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.64/5.84 & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % Orderings.order_eq_iff
% 5.64/5.84 thf(fact_983_Orderings_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A3 @ B3 )
% 5.64/5.84 & ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % Orderings.order_eq_iff
% 5.64/5.84 thf(fact_984_Orderings_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: num,B3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A3 @ B3 )
% 5.64/5.84 & ( ord_less_eq_num @ B3 @ A3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % Orderings.order_eq_iff
% 5.64/5.84 thf(fact_985_Orderings_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ A3 @ B3 )
% 5.64/5.84 & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % Orderings.order_eq_iff
% 5.64/5.84 thf(fact_986_Orderings_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: int,B3: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.64/5.84 & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % Orderings.order_eq_iff
% 5.64/5.84 thf(fact_987_Orderings_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: real,B3: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ A3 @ B3 )
% 5.64/5.84 & ( ord_less_eq_real @ B3 @ A3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % Orderings.order_eq_iff
% 5.64/5.84 thf(fact_988_antisym,axiom,
% 5.64/5.84 ! [A: set_nat,B: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % antisym
% 5.64/5.84 thf(fact_989_antisym,axiom,
% 5.64/5.84 ! [A: rat,B: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % antisym
% 5.64/5.84 thf(fact_990_antisym,axiom,
% 5.64/5.84 ! [A: num,B: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ A )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % antisym
% 5.64/5.84 thf(fact_991_antisym,axiom,
% 5.64/5.84 ! [A: nat,B: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % antisym
% 5.64/5.84 thf(fact_992_antisym,axiom,
% 5.64/5.84 ! [A: int,B: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_int @ B @ A )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % antisym
% 5.64/5.84 thf(fact_993_antisym,axiom,
% 5.64/5.84 ! [A: real,B: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_real @ B @ A )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % antisym
% 5.64/5.84 thf(fact_994_dual__order_Otrans,axiom,
% 5.64/5.84 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.64/5.84 => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.trans
% 5.64/5.84 thf(fact_995_dual__order_Otrans,axiom,
% 5.64/5.84 ! [B: rat,A: rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_rat @ C @ B )
% 5.64/5.84 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.trans
% 5.64/5.84 thf(fact_996_dual__order_Otrans,axiom,
% 5.64/5.84 ! [B: num,A: num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_num @ C @ B )
% 5.64/5.84 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.trans
% 5.64/5.84 thf(fact_997_dual__order_Otrans,axiom,
% 5.64/5.84 ! [B: nat,A: nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_nat @ C @ B )
% 5.64/5.84 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.trans
% 5.64/5.84 thf(fact_998_dual__order_Otrans,axiom,
% 5.64/5.84 ! [B: int,A: int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_int @ C @ B )
% 5.64/5.84 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.trans
% 5.64/5.84 thf(fact_999_dual__order_Otrans,axiom,
% 5.64/5.84 ! [B: real,A: real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_real @ C @ B )
% 5.64/5.84 => ( ord_less_eq_real @ C @ A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.trans
% 5.64/5.84 thf(fact_1000_dual__order_Oantisym,axiom,
% 5.64/5.84 ! [B: set_nat,A: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.antisym
% 5.64/5.84 thf(fact_1001_dual__order_Oantisym,axiom,
% 5.64/5.84 ! [B: rat,A: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.antisym
% 5.64/5.84 thf(fact_1002_dual__order_Oantisym,axiom,
% 5.64/5.84 ! [B: num,A: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.antisym
% 5.64/5.84 thf(fact_1003_dual__order_Oantisym,axiom,
% 5.64/5.84 ! [B: nat,A: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.antisym
% 5.64/5.84 thf(fact_1004_dual__order_Oantisym,axiom,
% 5.64/5.84 ! [B: int,A: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_int @ A @ B )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.antisym
% 5.64/5.84 thf(fact_1005_dual__order_Oantisym,axiom,
% 5.64/5.84 ! [B: real,A: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.84 => ( ( ord_less_eq_real @ A @ B )
% 5.64/5.84 => ( A = B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.antisym
% 5.64/5.84 thf(fact_1006_dual__order_Oeq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: set_nat,B3: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.64/5.84 & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.eq_iff
% 5.64/5.84 thf(fact_1007_dual__order_Oeq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ B3 @ A3 )
% 5.64/5.84 & ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.eq_iff
% 5.64/5.84 thf(fact_1008_dual__order_Oeq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: num,B3: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ B3 @ A3 )
% 5.64/5.84 & ( ord_less_eq_num @ A3 @ B3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.eq_iff
% 5.64/5.84 thf(fact_1009_dual__order_Oeq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ B3 @ A3 )
% 5.64/5.84 & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.eq_iff
% 5.64/5.84 thf(fact_1010_dual__order_Oeq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: int,B3: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ B3 @ A3 )
% 5.64/5.84 & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.eq_iff
% 5.64/5.84 thf(fact_1011_dual__order_Oeq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [A3: real,B3: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ B3 @ A3 )
% 5.64/5.84 & ( ord_less_eq_real @ A3 @ B3 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % dual_order.eq_iff
% 5.64/5.84 thf(fact_1012_linorder__wlog,axiom,
% 5.64/5.84 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.64/5.84 ( ! [A5: rat,B5: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( ! [A5: rat,B5: rat] :
% 5.64/5.84 ( ( P @ B5 @ A5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( P @ A @ B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_wlog
% 5.64/5.84 thf(fact_1013_linorder__wlog,axiom,
% 5.64/5.84 ! [P: num > num > $o,A: num,B: num] :
% 5.64/5.84 ( ! [A5: num,B5: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( ! [A5: num,B5: num] :
% 5.64/5.84 ( ( P @ B5 @ A5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( P @ A @ B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_wlog
% 5.64/5.84 thf(fact_1014_linorder__wlog,axiom,
% 5.64/5.84 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.64/5.84 ( ! [A5: nat,B5: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( ! [A5: nat,B5: nat] :
% 5.64/5.84 ( ( P @ B5 @ A5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( P @ A @ B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_wlog
% 5.64/5.84 thf(fact_1015_linorder__wlog,axiom,
% 5.64/5.84 ! [P: int > int > $o,A: int,B: int] :
% 5.64/5.84 ( ! [A5: int,B5: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( ! [A5: int,B5: int] :
% 5.64/5.84 ( ( P @ B5 @ A5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( P @ A @ B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_wlog
% 5.64/5.84 thf(fact_1016_linorder__wlog,axiom,
% 5.64/5.84 ! [P: real > real > $o,A: real,B: real] :
% 5.64/5.84 ( ! [A5: real,B5: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ A5 @ B5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( ! [A5: real,B5: real] :
% 5.64/5.84 ( ( P @ B5 @ A5 )
% 5.64/5.84 => ( P @ A5 @ B5 ) )
% 5.64/5.84 => ( P @ A @ B ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % linorder_wlog
% 5.64/5.84 thf(fact_1017_order__trans,axiom,
% 5.64/5.84 ! [X2: set_nat,Y4: set_nat,Z: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ Y4 @ Z )
% 5.64/5.84 => ( ord_less_eq_set_nat @ X2 @ Z ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_trans
% 5.64/5.84 thf(fact_1018_order__trans,axiom,
% 5.64/5.84 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_rat @ Y4 @ Z )
% 5.64/5.84 => ( ord_less_eq_rat @ X2 @ Z ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_trans
% 5.64/5.84 thf(fact_1019_order__trans,axiom,
% 5.64/5.84 ! [X2: num,Y4: num,Z: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_num @ Y4 @ Z )
% 5.64/5.84 => ( ord_less_eq_num @ X2 @ Z ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_trans
% 5.64/5.84 thf(fact_1020_order__trans,axiom,
% 5.64/5.84 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_nat @ Y4 @ Z )
% 5.64/5.84 => ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_trans
% 5.64/5.84 thf(fact_1021_order__trans,axiom,
% 5.64/5.84 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_int @ Y4 @ Z )
% 5.64/5.84 => ( ord_less_eq_int @ X2 @ Z ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_trans
% 5.64/5.84 thf(fact_1022_order__trans,axiom,
% 5.64/5.84 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_real @ Y4 @ Z )
% 5.64/5.84 => ( ord_less_eq_real @ X2 @ Z ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_trans
% 5.64/5.84 thf(fact_1023_order_Otrans,axiom,
% 5.64/5.84 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.64/5.84 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order.trans
% 5.64/5.84 thf(fact_1024_order_Otrans,axiom,
% 5.64/5.84 ! [A: rat,B: rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order.trans
% 5.64/5.84 thf(fact_1025_order_Otrans,axiom,
% 5.64/5.84 ! [A: num,B: num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order.trans
% 5.64/5.84 thf(fact_1026_order_Otrans,axiom,
% 5.64/5.84 ! [A: nat,B: nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.84 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order.trans
% 5.64/5.84 thf(fact_1027_order_Otrans,axiom,
% 5.64/5.84 ! [A: int,B: int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.84 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order.trans
% 5.64/5.84 thf(fact_1028_order_Otrans,axiom,
% 5.64/5.84 ! [A: real,B: real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.84 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.84 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order.trans
% 5.64/5.84 thf(fact_1029_order__antisym,axiom,
% 5.64/5.84 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ Y4 @ X2 )
% 5.64/5.84 => ( X2 = Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_antisym
% 5.64/5.84 thf(fact_1030_order__antisym,axiom,
% 5.64/5.84 ! [X2: rat,Y4: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.84 => ( X2 = Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_antisym
% 5.64/5.84 thf(fact_1031_order__antisym,axiom,
% 5.64/5.84 ! [X2: num,Y4: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_num @ Y4 @ X2 )
% 5.64/5.84 => ( X2 = Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_antisym
% 5.64/5.84 thf(fact_1032_order__antisym,axiom,
% 5.64/5.84 ! [X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.84 => ( X2 = Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_antisym
% 5.64/5.84 thf(fact_1033_order__antisym,axiom,
% 5.64/5.84 ! [X2: int,Y4: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_int @ Y4 @ X2 )
% 5.64/5.84 => ( X2 = Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_antisym
% 5.64/5.84 thf(fact_1034_order__antisym,axiom,
% 5.64/5.84 ! [X2: real,Y4: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.84 => ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.84 => ( X2 = Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_antisym
% 5.64/5.84 thf(fact_1035_ord__le__eq__trans,axiom,
% 5.64/5.84 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.84 => ( ( B = C )
% 5.64/5.84 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_le_eq_trans
% 5.64/5.84 thf(fact_1036_ord__le__eq__trans,axiom,
% 5.64/5.84 ! [A: rat,B: rat,C: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.84 => ( ( B = C )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_le_eq_trans
% 5.64/5.84 thf(fact_1037_ord__le__eq__trans,axiom,
% 5.64/5.84 ! [A: num,B: num,C: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.84 => ( ( B = C )
% 5.64/5.84 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_le_eq_trans
% 5.64/5.84 thf(fact_1038_ord__le__eq__trans,axiom,
% 5.64/5.84 ! [A: nat,B: nat,C: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.84 => ( ( B = C )
% 5.64/5.84 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_le_eq_trans
% 5.64/5.84 thf(fact_1039_ord__le__eq__trans,axiom,
% 5.64/5.84 ! [A: int,B: int,C: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.84 => ( ( B = C )
% 5.64/5.84 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_le_eq_trans
% 5.64/5.84 thf(fact_1040_ord__le__eq__trans,axiom,
% 5.64/5.84 ! [A: real,B: real,C: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.84 => ( ( B = C )
% 5.64/5.84 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_le_eq_trans
% 5.64/5.84 thf(fact_1041_ord__eq__le__trans,axiom,
% 5.64/5.84 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.64/5.84 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_trans
% 5.64/5.84 thf(fact_1042_ord__eq__le__trans,axiom,
% 5.64/5.84 ! [A: rat,B: rat,C: rat] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.84 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_trans
% 5.64/5.84 thf(fact_1043_ord__eq__le__trans,axiom,
% 5.64/5.84 ! [A: num,B: num,C: num] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 => ( ( ord_less_eq_num @ B @ C )
% 5.64/5.84 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_trans
% 5.64/5.84 thf(fact_1044_ord__eq__le__trans,axiom,
% 5.64/5.84 ! [A: nat,B: nat,C: nat] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.84 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_trans
% 5.64/5.84 thf(fact_1045_ord__eq__le__trans,axiom,
% 5.64/5.84 ! [A: int,B: int,C: int] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.84 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_trans
% 5.64/5.84 thf(fact_1046_ord__eq__le__trans,axiom,
% 5.64/5.84 ! [A: real,B: real,C: real] :
% 5.64/5.84 ( ( A = B )
% 5.64/5.84 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.84 => ( ord_less_eq_real @ A @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ord_eq_le_trans
% 5.64/5.84 thf(fact_1047_order__class_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: set_nat,Z3: set_nat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [X: set_nat,Y: set_nat] :
% 5.64/5.84 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.64/5.84 & ( ord_less_eq_set_nat @ Y @ X ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_class.order_eq_iff
% 5.64/5.84 thf(fact_1048_order__class_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [X: rat,Y: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ X @ Y )
% 5.64/5.84 & ( ord_less_eq_rat @ Y @ X ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_class.order_eq_iff
% 5.64/5.84 thf(fact_1049_order__class_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: num,Z3: num] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [X: num,Y: num] :
% 5.64/5.84 ( ( ord_less_eq_num @ X @ Y )
% 5.64/5.84 & ( ord_less_eq_num @ Y @ X ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_class.order_eq_iff
% 5.64/5.84 thf(fact_1050_order__class_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [X: nat,Y: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ X @ Y )
% 5.64/5.84 & ( ord_less_eq_nat @ Y @ X ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_class.order_eq_iff
% 5.64/5.84 thf(fact_1051_order__class_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [X: int,Y: int] :
% 5.64/5.84 ( ( ord_less_eq_int @ X @ Y )
% 5.64/5.84 & ( ord_less_eq_int @ Y @ X ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_class.order_eq_iff
% 5.64/5.84 thf(fact_1052_order__class_Oorder__eq__iff,axiom,
% 5.64/5.84 ( ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 ) )
% 5.64/5.84 = ( ^ [X: real,Y: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ X @ Y )
% 5.64/5.84 & ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % order_class.order_eq_iff
% 5.64/5.84 thf(fact_1053_le__cases3,axiom,
% 5.64/5.84 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.84 ( ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_rat @ Y4 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_rat @ X2 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_rat @ X2 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_rat @ Z @ Y4 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_rat @ Z @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_rat @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_rat @ Y4 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_rat @ Z @ X2 ) )
% 5.64/5.84 => ~ ( ( ord_less_eq_rat @ Z @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_rat @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_cases3
% 5.64/5.84 thf(fact_1054_le__cases3,axiom,
% 5.64/5.84 ! [X2: num,Y4: num,Z: num] :
% 5.64/5.84 ( ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_num @ Y4 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_num @ Y4 @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_num @ Z @ Y4 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_num @ Z @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_num @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_num @ Y4 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 5.64/5.84 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_num @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_cases3
% 5.64/5.84 thf(fact_1055_le__cases3,axiom,
% 5.64/5.84 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.84 ( ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_nat @ Y4 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_nat @ Z @ Y4 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_nat @ Z @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_nat @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_nat @ Y4 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 5.64/5.84 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_nat @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_cases3
% 5.64/5.84 thf(fact_1056_le__cases3,axiom,
% 5.64/5.84 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.84 ( ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_int @ Y4 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_int @ Y4 @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_int @ X2 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_int @ X2 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_int @ Z @ Y4 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_int @ Z @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_int @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_int @ Y4 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_int @ Z @ X2 ) )
% 5.64/5.84 => ~ ( ( ord_less_eq_int @ Z @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_int @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_cases3
% 5.64/5.84 thf(fact_1057_le__cases3,axiom,
% 5.64/5.84 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.84 ( ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_real @ Y4 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_real @ X2 @ Z ) )
% 5.64/5.84 => ( ( ( ord_less_eq_real @ X2 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_real @ Z @ Y4 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_real @ Z @ Y4 )
% 5.64/5.84 => ~ ( ord_less_eq_real @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( ( ord_less_eq_real @ Y4 @ Z )
% 5.64/5.84 => ~ ( ord_less_eq_real @ Z @ X2 ) )
% 5.64/5.84 => ~ ( ( ord_less_eq_real @ Z @ X2 )
% 5.64/5.84 => ~ ( ord_less_eq_real @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_cases3
% 5.64/5.84 thf(fact_1058_nle__le,axiom,
% 5.64/5.84 ! [A: rat,B: rat] :
% 5.64/5.84 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.64/5.84 = ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.84 & ( B != A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nle_le
% 5.64/5.84 thf(fact_1059_nle__le,axiom,
% 5.64/5.84 ! [A: num,B: num] :
% 5.64/5.84 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.64/5.84 = ( ( ord_less_eq_num @ B @ A )
% 5.64/5.84 & ( B != A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nle_le
% 5.64/5.84 thf(fact_1060_nle__le,axiom,
% 5.64/5.84 ! [A: nat,B: nat] :
% 5.64/5.84 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.64/5.84 = ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.84 & ( B != A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nle_le
% 5.64/5.84 thf(fact_1061_nle__le,axiom,
% 5.64/5.84 ! [A: int,B: int] :
% 5.64/5.84 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.64/5.84 = ( ( ord_less_eq_int @ B @ A )
% 5.64/5.84 & ( B != A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nle_le
% 5.64/5.84 thf(fact_1062_nle__le,axiom,
% 5.64/5.84 ! [A: real,B: real] :
% 5.64/5.84 ( ( ~ ( ord_less_eq_real @ A @ B ) )
% 5.64/5.84 = ( ( ord_less_eq_real @ B @ A )
% 5.64/5.84 & ( B != A ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nle_le
% 5.64/5.84 thf(fact_1063_verit__comp__simplify1_I2_J,axiom,
% 5.64/5.84 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.64/5.84
% 5.64/5.84 % verit_comp_simplify1(2)
% 5.64/5.84 thf(fact_1064_verit__comp__simplify1_I2_J,axiom,
% 5.64/5.84 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.64/5.84
% 5.64/5.84 % verit_comp_simplify1(2)
% 5.64/5.84 thf(fact_1065_verit__comp__simplify1_I2_J,axiom,
% 5.64/5.84 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.64/5.84
% 5.64/5.84 % verit_comp_simplify1(2)
% 5.64/5.84 thf(fact_1066_verit__comp__simplify1_I2_J,axiom,
% 5.64/5.84 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.64/5.84
% 5.64/5.84 % verit_comp_simplify1(2)
% 5.64/5.84 thf(fact_1067_verit__comp__simplify1_I2_J,axiom,
% 5.64/5.84 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.64/5.84
% 5.64/5.84 % verit_comp_simplify1(2)
% 5.64/5.84 thf(fact_1068_verit__comp__simplify1_I2_J,axiom,
% 5.64/5.84 ! [A: real] : ( ord_less_eq_real @ A @ A ) ).
% 5.64/5.84
% 5.64/5.84 % verit_comp_simplify1(2)
% 5.64/5.84 thf(fact_1069_verit__eq__simplify_I10_J,axiom,
% 5.64/5.84 ! [X22: num] :
% 5.64/5.84 ( one
% 5.64/5.84 != ( bit0 @ X22 ) ) ).
% 5.64/5.84
% 5.64/5.84 % verit_eq_simplify(10)
% 5.64/5.84 thf(fact_1070_maxt__corr,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_maxt @ T )
% 5.64/5.84 = ( some_nat @ X2 ) )
% 5.64/5.84 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % maxt_corr
% 5.64/5.84 thf(fact_1071_maxt__sound,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.64/5.84 => ( ( vEBT_vebt_maxt @ T )
% 5.64/5.84 = ( some_nat @ X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % maxt_sound
% 5.64/5.84 thf(fact_1072_succ__min,axiom,
% 5.64/5.84 ! [Deg: nat,X2: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.84 => ( ( ord_less_nat @ X2 @ Mi )
% 5.64/5.84 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 = ( some_nat @ Mi ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % succ_min
% 5.64/5.84 thf(fact_1073_pred__max,axiom,
% 5.64/5.84 ! [Deg: nat,Ma: nat,X2: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.84 => ( ( ord_less_nat @ Ma @ X2 )
% 5.64/5.84 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 = ( some_nat @ Ma ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % pred_max
% 5.64/5.84 thf(fact_1074_power__increasing__iff,axiom,
% 5.64/5.84 ! [B: rat,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_rat @ one_one_rat @ B )
% 5.64/5.84 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_eq_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing_iff
% 5.64/5.84 thf(fact_1075_power__increasing__iff,axiom,
% 5.64/5.84 ! [B: nat,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ one_one_nat @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_eq_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing_iff
% 5.64/5.84 thf(fact_1076_power__increasing__iff,axiom,
% 5.64/5.84 ! [B: int,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_int @ one_one_int @ B )
% 5.64/5.84 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_eq_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing_iff
% 5.64/5.84 thf(fact_1077_power__increasing__iff,axiom,
% 5.64/5.84 ! [B: real,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.84 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_eq_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing_iff
% 5.64/5.84 thf(fact_1078_less__shift,axiom,
% 5.64/5.84 ( ord_less_nat
% 5.64/5.84 = ( ^ [X: nat,Y: nat] : ( vEBT_VEBT_less @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % less_shift
% 5.64/5.84 thf(fact_1079_greater__shift,axiom,
% 5.64/5.84 ( ord_less_nat
% 5.64/5.84 = ( ^ [Y: nat,X: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X ) @ ( some_nat @ Y ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % greater_shift
% 5.64/5.84 thf(fact_1080_helpyd,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.64/5.84 = ( some_nat @ Y4 ) )
% 5.64/5.84 => ( ord_less_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % helpyd
% 5.64/5.84 thf(fact_1081_helpypredd,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.64/5.84 = ( some_nat @ Y4 ) )
% 5.64/5.84 => ( ord_less_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % helpypredd
% 5.64/5.84 thf(fact_1082_misiz,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( some_nat @ M )
% 5.64/5.84 = ( vEBT_vebt_mint @ T ) )
% 5.64/5.84 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % misiz
% 5.64/5.84 thf(fact_1083_power__strict__increasing__iff,axiom,
% 5.64/5.84 ! [B: real,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.84 => ( ( ord_less_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing_iff
% 5.64/5.84 thf(fact_1084_power__strict__increasing__iff,axiom,
% 5.64/5.84 ! [B: rat,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_rat @ one_one_rat @ B )
% 5.64/5.84 => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing_iff
% 5.64/5.84 thf(fact_1085_power__strict__increasing__iff,axiom,
% 5.64/5.84 ! [B: nat,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ one_one_nat @ B )
% 5.64/5.84 => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing_iff
% 5.64/5.84 thf(fact_1086_power__strict__increasing__iff,axiom,
% 5.64/5.84 ! [B: int,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_int @ one_one_int @ B )
% 5.64/5.84 => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y4 ) )
% 5.64/5.84 = ( ord_less_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing_iff
% 5.64/5.84 thf(fact_1087_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N: nat] :
% 5.64/5.84 ( ! [X4: product_prod_nat_nat] :
% 5.64/5.84 ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1088_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_complex,P: complex > $o,N: nat] :
% 5.64/5.84 ( ! [X4: complex] :
% 5.64/5.84 ( ( member_complex @ X4 @ ( set_complex2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1089_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_real,P: real > $o,N: nat] :
% 5.64/5.84 ( ! [X4: real] :
% 5.64/5.84 ( ( member_real @ X4 @ ( set_real2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1090_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.64/5.84 ( ! [X4: vEBT_VEBT] :
% 5.64/5.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1091_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_o,P: $o > $o,N: nat] :
% 5.64/5.84 ( ! [X4: $o] :
% 5.64/5.84 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1092_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_nat,P: nat > $o,N: nat] :
% 5.64/5.84 ( ! [X4: nat] :
% 5.64/5.84 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1093_inthall,axiom,
% 5.64/5.84 ! [Xs2: list_int,P: int > $o,N: nat] :
% 5.64/5.84 ( ! [X4: int] :
% 5.64/5.84 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % inthall
% 5.64/5.84 thf(fact_1094_set__vebt__set__vebt_H__valid,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( vEBT_set_vebt @ T )
% 5.64/5.84 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % set_vebt_set_vebt'_valid
% 5.64/5.84 thf(fact_1095_mint__member,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_mint @ T )
% 5.64/5.84 = ( some_nat @ Maxi ) )
% 5.64/5.84 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mint_member
% 5.64/5.84 thf(fact_1096_local_Opower__def,axiom,
% 5.64/5.84 ( vEBT_VEBT_power
% 5.64/5.84 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.64/5.84
% 5.64/5.84 % local.power_def
% 5.64/5.84 thf(fact_1097_mint__corr__help,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,Mini: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_mint @ T )
% 5.64/5.84 = ( some_nat @ Mini ) )
% 5.64/5.84 => ( ( vEBT_vebt_member @ T @ X2 )
% 5.64/5.84 => ( ord_less_eq_nat @ Mini @ X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mint_corr_help
% 5.64/5.84 thf(fact_1098_mint__sound,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 )
% 5.64/5.84 => ( ( vEBT_vebt_mint @ T )
% 5.64/5.84 = ( some_nat @ X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mint_sound
% 5.64/5.84 thf(fact_1099_mint__corr,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_mint @ T )
% 5.64/5.84 = ( some_nat @ X2 ) )
% 5.64/5.84 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mint_corr
% 5.64/5.84 thf(fact_1100_power__one,axiom,
% 5.64/5.84 ! [N: nat] :
% 5.64/5.84 ( ( power_power_rat @ one_one_rat @ N )
% 5.64/5.84 = one_one_rat ) ).
% 5.64/5.84
% 5.64/5.84 % power_one
% 5.64/5.84 thf(fact_1101_power__one,axiom,
% 5.64/5.84 ! [N: nat] :
% 5.64/5.84 ( ( power_power_nat @ one_one_nat @ N )
% 5.64/5.84 = one_one_nat ) ).
% 5.64/5.84
% 5.64/5.84 % power_one
% 5.64/5.84 thf(fact_1102_power__one,axiom,
% 5.64/5.84 ! [N: nat] :
% 5.64/5.84 ( ( power_power_real @ one_one_real @ N )
% 5.64/5.84 = one_one_real ) ).
% 5.64/5.84
% 5.64/5.84 % power_one
% 5.64/5.84 thf(fact_1103_power__one,axiom,
% 5.64/5.84 ! [N: nat] :
% 5.64/5.84 ( ( power_power_int @ one_one_int @ N )
% 5.64/5.84 = one_one_int ) ).
% 5.64/5.84
% 5.64/5.84 % power_one
% 5.64/5.84 thf(fact_1104_power__one,axiom,
% 5.64/5.84 ! [N: nat] :
% 5.64/5.84 ( ( power_power_complex @ one_one_complex @ N )
% 5.64/5.84 = one_one_complex ) ).
% 5.64/5.84
% 5.64/5.84 % power_one
% 5.64/5.84 thf(fact_1105_power__one__right,axiom,
% 5.64/5.84 ! [A: nat] :
% 5.64/5.84 ( ( power_power_nat @ A @ one_one_nat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % power_one_right
% 5.64/5.84 thf(fact_1106_power__one__right,axiom,
% 5.64/5.84 ! [A: real] :
% 5.64/5.84 ( ( power_power_real @ A @ one_one_nat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % power_one_right
% 5.64/5.84 thf(fact_1107_power__one__right,axiom,
% 5.64/5.84 ! [A: int] :
% 5.64/5.84 ( ( power_power_int @ A @ one_one_nat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % power_one_right
% 5.64/5.84 thf(fact_1108_power__one__right,axiom,
% 5.64/5.84 ! [A: complex] :
% 5.64/5.84 ( ( power_power_complex @ A @ one_one_nat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % power_one_right
% 5.64/5.84 thf(fact_1109_semiring__norm_I78_J,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.84 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.84
% 5.64/5.84 % semiring_norm(78)
% 5.64/5.84 thf(fact_1110_semiring__norm_I75_J,axiom,
% 5.64/5.84 ! [M: num] :
% 5.64/5.84 ~ ( ord_less_num @ M @ one ) ).
% 5.64/5.84
% 5.64/5.84 % semiring_norm(75)
% 5.64/5.84 thf(fact_1111_power__inject__exp,axiom,
% 5.64/5.84 ! [A: real,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.84 => ( ( ( power_power_real @ A @ M )
% 5.64/5.84 = ( power_power_real @ A @ N ) )
% 5.64/5.84 = ( M = N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_inject_exp
% 5.64/5.84 thf(fact_1112_power__inject__exp,axiom,
% 5.64/5.84 ! [A: rat,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ( ( power_power_rat @ A @ M )
% 5.64/5.84 = ( power_power_rat @ A @ N ) )
% 5.64/5.84 = ( M = N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_inject_exp
% 5.64/5.84 thf(fact_1113_power__inject__exp,axiom,
% 5.64/5.84 ! [A: nat,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ( ( power_power_nat @ A @ M )
% 5.64/5.84 = ( power_power_nat @ A @ N ) )
% 5.64/5.84 = ( M = N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_inject_exp
% 5.64/5.84 thf(fact_1114_power__inject__exp,axiom,
% 5.64/5.84 ! [A: int,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.84 => ( ( ( power_power_int @ A @ M )
% 5.64/5.84 = ( power_power_int @ A @ N ) )
% 5.64/5.84 = ( M = N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_inject_exp
% 5.64/5.84 thf(fact_1115_semiring__norm_I76_J,axiom,
% 5.64/5.84 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.64/5.84
% 5.64/5.84 % semiring_norm(76)
% 5.64/5.84 thf(fact_1116_enat__ord__number_I2_J,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.64/5.84 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % enat_ord_number(2)
% 5.64/5.84 thf(fact_1117_succ__member,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y4 )
% 5.64/5.84 = ( ( vEBT_vebt_member @ T @ Y4 )
% 5.64/5.84 & ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.84 & ! [Z4: nat] :
% 5.64/5.84 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.64/5.84 & ( ord_less_nat @ X2 @ Z4 ) )
% 5.64/5.84 => ( ord_less_eq_nat @ Y4 @ Z4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % succ_member
% 5.64/5.84 thf(fact_1118_pred__member,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,X2: nat,Y4: nat] :
% 5.64/5.84 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Y4 )
% 5.64/5.84 = ( ( vEBT_vebt_member @ T @ Y4 )
% 5.64/5.84 & ( ord_less_nat @ Y4 @ X2 )
% 5.64/5.84 & ! [Z4: nat] :
% 5.64/5.84 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 5.64/5.84 & ( ord_less_nat @ Z4 @ X2 ) )
% 5.64/5.84 => ( ord_less_eq_nat @ Z4 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % pred_member
% 5.64/5.84 thf(fact_1119_pred__corr,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat,Px: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.64/5.84 = ( some_nat @ Px ) )
% 5.64/5.84 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Px ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % pred_corr
% 5.64/5.84 thf(fact_1120_succ__corr,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.64/5.84 = ( some_nat @ Sx ) )
% 5.64/5.84 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % succ_corr
% 5.64/5.84 thf(fact_1121_pred__correct,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.64/5.84 = ( some_nat @ Sx ) )
% 5.64/5.84 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % pred_correct
% 5.64/5.84 thf(fact_1122_succ__correct,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat,X2: nat,Sx: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.64/5.84 = ( some_nat @ Sx ) )
% 5.64/5.84 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X2 @ Sx ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % succ_correct
% 5.64/5.84 thf(fact_1123_one__le__power,axiom,
% 5.64/5.84 ! [A: rat,N: nat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % one_le_power
% 5.64/5.84 thf(fact_1124_one__le__power,axiom,
% 5.64/5.84 ! [A: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % one_le_power
% 5.64/5.84 thf(fact_1125_one__le__power,axiom,
% 5.64/5.84 ! [A: int,N: nat] :
% 5.64/5.84 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.64/5.84 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % one_le_power
% 5.64/5.84 thf(fact_1126_one__le__power,axiom,
% 5.64/5.84 ! [A: real,N: nat] :
% 5.64/5.84 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.64/5.84 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % one_le_power
% 5.64/5.84 thf(fact_1127_power__gt1,axiom,
% 5.64/5.84 ! [A: real,N: nat] :
% 5.64/5.84 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.84 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_gt1
% 5.64/5.84 thf(fact_1128_power__gt1,axiom,
% 5.64/5.84 ! [A: rat,N: nat] :
% 5.64/5.84 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_gt1
% 5.64/5.84 thf(fact_1129_power__gt1,axiom,
% 5.64/5.84 ! [A: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_gt1
% 5.64/5.84 thf(fact_1130_power__gt1,axiom,
% 5.64/5.84 ! [A: int,N: nat] :
% 5.64/5.84 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.84 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_gt1
% 5.64/5.84 thf(fact_1131_power__less__imp__less__exp,axiom,
% 5.64/5.84 ! [A: real,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.84 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.64/5.84 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_less_imp_less_exp
% 5.64/5.84 thf(fact_1132_power__less__imp__less__exp,axiom,
% 5.64/5.84 ! [A: rat,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.64/5.84 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_less_imp_less_exp
% 5.64/5.84 thf(fact_1133_power__less__imp__less__exp,axiom,
% 5.64/5.84 ! [A: nat,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.64/5.84 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_less_imp_less_exp
% 5.64/5.84 thf(fact_1134_power__less__imp__less__exp,axiom,
% 5.64/5.84 ! [A: int,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.84 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.64/5.84 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_less_imp_less_exp
% 5.64/5.84 thf(fact_1135_power__strict__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: real] :
% 5.64/5.84 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.84 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing
% 5.64/5.84 thf(fact_1136_power__strict__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: rat] :
% 5.64/5.84 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing
% 5.64/5.84 thf(fact_1137_power__strict__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: nat] :
% 5.64/5.84 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing
% 5.64/5.84 thf(fact_1138_power__strict__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: int] :
% 5.64/5.84 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.84 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_strict_increasing
% 5.64/5.84 thf(fact_1139_power__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: rat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing
% 5.64/5.84 thf(fact_1140_power__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing
% 5.64/5.84 thf(fact_1141_power__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: int] :
% 5.64/5.84 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.64/5.84 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing
% 5.64/5.84 thf(fact_1142_power__increasing,axiom,
% 5.64/5.84 ! [N: nat,N5: nat,A: real] :
% 5.64/5.84 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.84 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.64/5.84 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N5 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_increasing
% 5.64/5.84 thf(fact_1143_power__le__imp__le__exp,axiom,
% 5.64/5.84 ! [A: rat,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.84 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.64/5.84 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_le_imp_le_exp
% 5.64/5.84 thf(fact_1144_power__le__imp__le__exp,axiom,
% 5.64/5.84 ! [A: nat,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.64/5.84 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_le_imp_le_exp
% 5.64/5.84 thf(fact_1145_power__le__imp__le__exp,axiom,
% 5.64/5.84 ! [A: int,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.84 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.64/5.84 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_le_imp_le_exp
% 5.64/5.84 thf(fact_1146_power__le__imp__le__exp,axiom,
% 5.64/5.84 ! [A: real,M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.84 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.64/5.84 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_le_imp_le_exp
% 5.64/5.84 thf(fact_1147_one__power2,axiom,
% 5.64/5.84 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.84 = one_one_rat ) ).
% 5.64/5.84
% 5.64/5.84 % one_power2
% 5.64/5.84 thf(fact_1148_one__power2,axiom,
% 5.64/5.84 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.84 = one_one_nat ) ).
% 5.64/5.84
% 5.64/5.84 % one_power2
% 5.64/5.84 thf(fact_1149_one__power2,axiom,
% 5.64/5.84 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.84 = one_one_real ) ).
% 5.64/5.84
% 5.64/5.84 % one_power2
% 5.64/5.84 thf(fact_1150_one__power2,axiom,
% 5.64/5.84 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.84 = one_one_int ) ).
% 5.64/5.84
% 5.64/5.84 % one_power2
% 5.64/5.84 thf(fact_1151_one__power2,axiom,
% 5.64/5.84 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.84 = one_one_complex ) ).
% 5.64/5.84
% 5.64/5.84 % one_power2
% 5.64/5.84 thf(fact_1152_less__exp,axiom,
% 5.64/5.84 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.84
% 5.64/5.84 % less_exp
% 5.64/5.84 thf(fact_1153_power2__nat__le__imp__le,axiom,
% 5.64/5.84 ! [M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.64/5.84 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.84
% 5.64/5.84 % power2_nat_le_imp_le
% 5.64/5.84 thf(fact_1154_power2__nat__le__eq__le,axiom,
% 5.64/5.84 ! [M: nat,N: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.84 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.84
% 5.64/5.84 % power2_nat_le_eq_le
% 5.64/5.84 thf(fact_1155_self__le__ge2__pow,axiom,
% 5.64/5.84 ! [K: nat,M: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.64/5.84 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % self_le_ge2_pow
% 5.64/5.84 thf(fact_1156_ex__power__ivl1,axiom,
% 5.64/5.84 ! [B: nat,K: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.64/5.84 => ? [N3: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.64/5.84 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ex_power_ivl1
% 5.64/5.84 thf(fact_1157_ex__power__ivl2,axiom,
% 5.64/5.84 ! [B: nat,K: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.64/5.84 => ? [N3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.64/5.84 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ex_power_ivl2
% 5.64/5.84 thf(fact_1158_two__powr__height__bound__deg,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.84 => ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( vEBT_VEBT_height @ T ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % two_powr_height_bound_deg
% 5.64/5.84 thf(fact_1159_vebt__maxt_Osimps_I3_J,axiom,
% 5.64/5.84 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.64/5.84 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.64/5.84 = ( some_nat @ Ma ) ) ).
% 5.64/5.84
% 5.64/5.84 % vebt_maxt.simps(3)
% 5.64/5.84 thf(fact_1160__C5_Ohyps_C_I9_J,axiom,
% 5.64/5.84 ( ( mi != ma )
% 5.64/5.84 => ! [I2: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.64/5.84 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.64/5.84 = I2 )
% 5.64/5.84 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.64/5.84 & ! [X3: nat] :
% 5.64/5.84 ( ( ( ( vEBT_VEBT_high @ X3 @ na )
% 5.64/5.84 = I2 )
% 5.64/5.84 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ X3 @ na ) ) )
% 5.64/5.84 => ( ( ord_less_nat @ mi @ X3 )
% 5.64/5.84 & ( ord_less_eq_nat @ X3 @ ma ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % "5.hyps"(9)
% 5.64/5.84 thf(fact_1161_vebt__mint_Osimps_I3_J,axiom,
% 5.64/5.84 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.64/5.84 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.64/5.84 = ( some_nat @ Mi ) ) ).
% 5.64/5.84
% 5.64/5.84 % vebt_mint.simps(3)
% 5.64/5.84 thf(fact_1162_geqmaxNone,axiom,
% 5.64/5.84 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.84 => ( ( ord_less_eq_nat @ Ma @ X2 )
% 5.64/5.84 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 = none_nat ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % geqmaxNone
% 5.64/5.84 thf(fact_1163_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_P6011104703257516679at_nat] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.64/5.84 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1164_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_complex] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.64/5.84 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1165_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_real] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.64/5.84 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1166_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.84 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1167_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_o] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.84 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1168_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_nat] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.84 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1169_nth__mem,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_int] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.84 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nth_mem
% 5.64/5.84 thf(fact_1170_list__ball__nth,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.84 => ( ! [X4: vEBT_VEBT] :
% 5.64/5.84 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % list_ball_nth
% 5.64/5.84 thf(fact_1171_list__ball__nth,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_o,P: $o > $o] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.84 => ( ! [X4: $o] :
% 5.64/5.84 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( P @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % list_ball_nth
% 5.64/5.84 thf(fact_1172_list__ball__nth,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_nat,P: nat > $o] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.84 => ( ! [X4: nat] :
% 5.64/5.84 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( P @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % list_ball_nth
% 5.64/5.84 thf(fact_1173_list__ball__nth,axiom,
% 5.64/5.84 ! [N: nat,Xs2: list_int,P: int > $o] :
% 5.64/5.84 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.84 => ( ! [X4: int] :
% 5.64/5.84 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X4 ) )
% 5.64/5.84 => ( P @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % list_ball_nth
% 5.64/5.84 thf(fact_1174_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.64/5.84 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.64/5.84 & ( ( nth_Pr7617993195940197384at_nat @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1175_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: complex,Xs2: list_complex] :
% 5.64/5.84 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.64/5.84 & ( ( nth_complex @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1176_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: real,Xs2: list_real] :
% 5.64/5.84 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs2 ) )
% 5.64/5.84 & ( ( nth_real @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1177_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.64/5.84 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.84 & ( ( nth_VEBT_VEBT @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1178_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: $o,Xs2: list_o] :
% 5.64/5.84 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.84 & ( ( nth_o @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1179_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: nat,Xs2: list_nat] :
% 5.64/5.84 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.84 & ( ( nth_nat @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1180_in__set__conv__nth,axiom,
% 5.64/5.84 ! [X2: int,Xs2: list_int] :
% 5.64/5.84 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.64/5.84 = ( ? [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.84 & ( ( nth_int @ Xs2 @ I4 )
% 5.64/5.84 = X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % in_set_conv_nth
% 5.64/5.84 thf(fact_1181_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1182_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_complex,P: complex > $o,X2: complex] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_complex @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1183_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_real,P: real > $o,X2: real] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_real @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1184_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1185_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_o,P: $o > $o,X2: $o] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_o @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1186_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_nat,P: nat > $o,X2: nat] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_nat @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1187_all__nth__imp__all__set,axiom,
% 5.64/5.84 ! [Xs2: list_int,P: int > $o,X2: int] :
% 5.64/5.84 ( ! [I3: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_int @ Xs2 @ I3 ) ) )
% 5.64/5.84 => ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_nth_imp_all_set
% 5.64/5.84 thf(fact_1188_all__set__conv__all__nth,axiom,
% 5.64/5.84 ! [Xs2: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.64/5.84 ( ( ! [X: vEBT_VEBT] :
% 5.64/5.84 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X ) ) )
% 5.64/5.84 = ( ! [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_VEBT_VEBT @ Xs2 @ I4 ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_set_conv_all_nth
% 5.64/5.84 thf(fact_1189_all__set__conv__all__nth,axiom,
% 5.64/5.84 ! [Xs2: list_o,P: $o > $o] :
% 5.64/5.84 ( ( ! [X: $o] :
% 5.64/5.84 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X ) ) )
% 5.64/5.84 = ( ! [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_o @ Xs2 @ I4 ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_set_conv_all_nth
% 5.64/5.84 thf(fact_1190_all__set__conv__all__nth,axiom,
% 5.64/5.84 ! [Xs2: list_nat,P: nat > $o] :
% 5.64/5.84 ( ( ! [X: nat] :
% 5.64/5.84 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X ) ) )
% 5.64/5.84 = ( ! [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_nat @ Xs2 @ I4 ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_set_conv_all_nth
% 5.64/5.84 thf(fact_1191_all__set__conv__all__nth,axiom,
% 5.64/5.84 ! [Xs2: list_int,P: int > $o] :
% 5.64/5.84 ( ( ! [X: int] :
% 5.64/5.84 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.64/5.84 => ( P @ X ) ) )
% 5.64/5.84 = ( ! [I4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.84 => ( P @ ( nth_int @ Xs2 @ I4 ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % all_set_conv_all_nth
% 5.64/5.84 thf(fact_1192_pow__sum,axiom,
% 5.64/5.84 ! [A: nat,B: nat] :
% 5.64/5.84 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.84 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % pow_sum
% 5.64/5.84 thf(fact_1193_minNullmin,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT] :
% 5.64/5.84 ( ( vEBT_VEBT_minNull @ T )
% 5.64/5.84 => ( ( vEBT_vebt_mint @ T )
% 5.64/5.84 = none_nat ) ) ).
% 5.64/5.84
% 5.64/5.84 % minNullmin
% 5.64/5.84 thf(fact_1194_minminNull,axiom,
% 5.64/5.84 ! [T: vEBT_VEBT] :
% 5.64/5.84 ( ( ( vEBT_vebt_mint @ T )
% 5.64/5.84 = none_nat )
% 5.64/5.84 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.64/5.84
% 5.64/5.84 % minminNull
% 5.64/5.84 thf(fact_1195_bit__split__inv,axiom,
% 5.64/5.84 ! [X2: nat,D: nat] :
% 5.64/5.84 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X2 @ D ) @ ( vEBT_VEBT_low @ X2 @ D ) @ D )
% 5.64/5.84 = X2 ) ).
% 5.64/5.84
% 5.64/5.84 % bit_split_inv
% 5.64/5.84 thf(fact_1196_high__def,axiom,
% 5.64/5.84 ( vEBT_VEBT_high
% 5.64/5.84 = ( ^ [X: nat,N2: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % high_def
% 5.64/5.84 thf(fact_1197_high__bound__aux,axiom,
% 5.64/5.84 ! [Ma: nat,N: nat,M: nat] :
% 5.64/5.84 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.64/5.84 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % high_bound_aux
% 5.64/5.84 thf(fact_1198_mult__numeral__left__semiring__numeral,axiom,
% 5.64/5.84 ! [V: num,W: num,Z: complex] :
% 5.64/5.84 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.64/5.84 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult_numeral_left_semiring_numeral
% 5.64/5.84 thf(fact_1199_mult__numeral__left__semiring__numeral,axiom,
% 5.64/5.84 ! [V: num,W: num,Z: real] :
% 5.64/5.84 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.64/5.84 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult_numeral_left_semiring_numeral
% 5.64/5.84 thf(fact_1200_mult__numeral__left__semiring__numeral,axiom,
% 5.64/5.84 ! [V: num,W: num,Z: rat] :
% 5.64/5.84 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.64/5.84 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult_numeral_left_semiring_numeral
% 5.64/5.84 thf(fact_1201_mult__numeral__left__semiring__numeral,axiom,
% 5.64/5.84 ! [V: num,W: num,Z: nat] :
% 5.64/5.84 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.64/5.84 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult_numeral_left_semiring_numeral
% 5.64/5.84 thf(fact_1202_mult__numeral__left__semiring__numeral,axiom,
% 5.64/5.84 ! [V: num,W: num,Z: int] :
% 5.64/5.84 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.64/5.84 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult_numeral_left_semiring_numeral
% 5.64/5.84 thf(fact_1203_numeral__times__numeral,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.84 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % numeral_times_numeral
% 5.64/5.84 thf(fact_1204_numeral__times__numeral,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.84 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % numeral_times_numeral
% 5.64/5.84 thf(fact_1205_numeral__times__numeral,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.84 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % numeral_times_numeral
% 5.64/5.84 thf(fact_1206_numeral__times__numeral,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.84 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % numeral_times_numeral
% 5.64/5.84 thf(fact_1207_numeral__times__numeral,axiom,
% 5.64/5.84 ! [M: num,N: num] :
% 5.64/5.84 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.84 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % numeral_times_numeral
% 5.64/5.84 thf(fact_1208_high__inv,axiom,
% 5.64/5.84 ! [X2: nat,N: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.84 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.64/5.84 = Y4 ) ) ).
% 5.64/5.84
% 5.64/5.84 % high_inv
% 5.64/5.84 thf(fact_1209_low__inv,axiom,
% 5.64/5.84 ! [X2: nat,N: nat,Y4: nat] :
% 5.64/5.84 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.84 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X2 ) @ N )
% 5.64/5.84 = X2 ) ) ).
% 5.64/5.84
% 5.64/5.84 % low_inv
% 5.64/5.84 thf(fact_1210_mult__1,axiom,
% 5.64/5.84 ! [A: complex] :
% 5.64/5.84 ( ( times_times_complex @ one_one_complex @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult_1
% 5.64/5.84 thf(fact_1211_mult__1,axiom,
% 5.64/5.84 ! [A: real] :
% 5.64/5.84 ( ( times_times_real @ one_one_real @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult_1
% 5.64/5.84 thf(fact_1212_mult__1,axiom,
% 5.64/5.84 ! [A: rat] :
% 5.64/5.84 ( ( times_times_rat @ one_one_rat @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult_1
% 5.64/5.84 thf(fact_1213_mult__1,axiom,
% 5.64/5.84 ! [A: nat] :
% 5.64/5.84 ( ( times_times_nat @ one_one_nat @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult_1
% 5.64/5.84 thf(fact_1214_mult__1,axiom,
% 5.64/5.84 ! [A: int] :
% 5.64/5.84 ( ( times_times_int @ one_one_int @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult_1
% 5.64/5.84 thf(fact_1215_mult_Oright__neutral,axiom,
% 5.64/5.84 ! [A: complex] :
% 5.64/5.84 ( ( times_times_complex @ A @ one_one_complex )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.right_neutral
% 5.64/5.84 thf(fact_1216_mult_Oright__neutral,axiom,
% 5.64/5.84 ! [A: real] :
% 5.64/5.84 ( ( times_times_real @ A @ one_one_real )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.right_neutral
% 5.64/5.84 thf(fact_1217_mult_Oright__neutral,axiom,
% 5.64/5.84 ! [A: rat] :
% 5.64/5.84 ( ( times_times_rat @ A @ one_one_rat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.right_neutral
% 5.64/5.84 thf(fact_1218_mult_Oright__neutral,axiom,
% 5.64/5.84 ! [A: nat] :
% 5.64/5.84 ( ( times_times_nat @ A @ one_one_nat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.right_neutral
% 5.64/5.84 thf(fact_1219_mult_Oright__neutral,axiom,
% 5.64/5.84 ! [A: int] :
% 5.64/5.84 ( ( times_times_int @ A @ one_one_int )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.right_neutral
% 5.64/5.84 thf(fact_1220_not__Some__eq,axiom,
% 5.64/5.84 ! [X2: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( ! [Y: product_prod_nat_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( some_P7363390416028606310at_nat @ Y ) ) )
% 5.64/5.84 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 5.64/5.84
% 5.64/5.84 % not_Some_eq
% 5.64/5.84 thf(fact_1221_not__Some__eq,axiom,
% 5.64/5.84 ! [X2: option_nat] :
% 5.64/5.84 ( ( ! [Y: nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( some_nat @ Y ) ) )
% 5.64/5.84 = ( X2 = none_nat ) ) ).
% 5.64/5.84
% 5.64/5.84 % not_Some_eq
% 5.64/5.84 thf(fact_1222_not__Some__eq,axiom,
% 5.64/5.84 ! [X2: option_num] :
% 5.64/5.84 ( ( ! [Y: num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( some_num @ Y ) ) )
% 5.64/5.84 = ( X2 = none_num ) ) ).
% 5.64/5.84
% 5.64/5.84 % not_Some_eq
% 5.64/5.84 thf(fact_1223_not__None__eq,axiom,
% 5.64/5.84 ! [X2: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( X2 != none_P5556105721700978146at_nat )
% 5.64/5.84 = ( ? [Y: product_prod_nat_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ Y ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % not_None_eq
% 5.64/5.84 thf(fact_1224_not__None__eq,axiom,
% 5.64/5.84 ! [X2: option_nat] :
% 5.64/5.84 ( ( X2 != none_nat )
% 5.64/5.84 = ( ? [Y: nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 = ( some_nat @ Y ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % not_None_eq
% 5.64/5.84 thf(fact_1225_not__None__eq,axiom,
% 5.64/5.84 ! [X2: option_num] :
% 5.64/5.84 ( ( X2 != none_num )
% 5.64/5.84 = ( ? [Y: num] :
% 5.64/5.84 ( X2
% 5.64/5.84 = ( some_num @ Y ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % not_None_eq
% 5.64/5.84 thf(fact_1226_nat__mult__eq__1__iff,axiom,
% 5.64/5.84 ! [M: nat,N: nat] :
% 5.64/5.84 ( ( ( times_times_nat @ M @ N )
% 5.64/5.84 = one_one_nat )
% 5.64/5.84 = ( ( M = one_one_nat )
% 5.64/5.84 & ( N = one_one_nat ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nat_mult_eq_1_iff
% 5.64/5.84 thf(fact_1227_nat__1__eq__mult__iff,axiom,
% 5.64/5.84 ! [M: nat,N: nat] :
% 5.64/5.84 ( ( one_one_nat
% 5.64/5.84 = ( times_times_nat @ M @ N ) )
% 5.64/5.84 = ( ( M = one_one_nat )
% 5.64/5.84 & ( N = one_one_nat ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % nat_1_eq_mult_iff
% 5.64/5.84 thf(fact_1228_bit__concat__def,axiom,
% 5.64/5.84 ( vEBT_VEBT_bit_concat
% 5.64/5.84 = ( ^ [H: nat,L2: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L2 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % bit_concat_def
% 5.64/5.84 thf(fact_1229_distrib__right__numeral,axiom,
% 5.64/5.84 ! [A: complex,B: complex,V: num] :
% 5.64/5.84 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.64/5.84 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_right_numeral
% 5.64/5.84 thf(fact_1230_distrib__right__numeral,axiom,
% 5.64/5.84 ! [A: real,B: real,V: num] :
% 5.64/5.84 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.84 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_right_numeral
% 5.64/5.84 thf(fact_1231_distrib__right__numeral,axiom,
% 5.64/5.84 ! [A: rat,B: rat,V: num] :
% 5.64/5.84 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.84 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_right_numeral
% 5.64/5.84 thf(fact_1232_distrib__right__numeral,axiom,
% 5.64/5.84 ! [A: nat,B: nat,V: num] :
% 5.64/5.84 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.84 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_right_numeral
% 5.64/5.84 thf(fact_1233_distrib__right__numeral,axiom,
% 5.64/5.84 ! [A: int,B: int,V: num] :
% 5.64/5.84 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.84 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_right_numeral
% 5.64/5.84 thf(fact_1234_distrib__left__numeral,axiom,
% 5.64/5.84 ! [V: num,B: complex,C: complex] :
% 5.64/5.84 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.64/5.84 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_left_numeral
% 5.64/5.84 thf(fact_1235_distrib__left__numeral,axiom,
% 5.64/5.84 ! [V: num,B: real,C: real] :
% 5.64/5.84 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.64/5.84 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_left_numeral
% 5.64/5.84 thf(fact_1236_distrib__left__numeral,axiom,
% 5.64/5.84 ! [V: num,B: rat,C: rat] :
% 5.64/5.84 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.84 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_left_numeral
% 5.64/5.84 thf(fact_1237_distrib__left__numeral,axiom,
% 5.64/5.84 ! [V: num,B: nat,C: nat] :
% 5.64/5.84 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.84 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_left_numeral
% 5.64/5.84 thf(fact_1238_distrib__left__numeral,axiom,
% 5.64/5.84 ! [V: num,B: int,C: int] :
% 5.64/5.84 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.64/5.84 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % distrib_left_numeral
% 5.64/5.84 thf(fact_1239_mult__Suc__right,axiom,
% 5.64/5.84 ! [M: nat,N: nat] :
% 5.64/5.84 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.64/5.84 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult_Suc_right
% 5.64/5.84 thf(fact_1240_both__member__options__ding,axiom,
% 5.64/5.84 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.84 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.84 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.64/5.84 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.84 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % both_member_options_ding
% 5.64/5.84 thf(fact_1241_succ__list__to__short,axiom,
% 5.64/5.84 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.84 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.84 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 = none_nat ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % succ_list_to_short
% 5.64/5.84 thf(fact_1242_pred__list__to__short,axiom,
% 5.64/5.84 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.64/5.84 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.84 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList ) @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.84 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 = none_nat ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % pred_list_to_short
% 5.64/5.84 thf(fact_1243_both__member__options__from__complete__tree__to__child,axiom,
% 5.64/5.84 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.84 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.64/5.84 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.84 | ( X2 = Mi )
% 5.64/5.84 | ( X2 = Ma ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % both_member_options_from_complete_tree_to_child
% 5.64/5.84 thf(fact_1244_member__inv,axiom,
% 5.64/5.84 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.84 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.84 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.84 & ( ( X2 = Mi )
% 5.64/5.84 | ( X2 = Ma )
% 5.64/5.84 | ( ( ord_less_nat @ X2 @ Ma )
% 5.64/5.84 & ( ord_less_nat @ Mi @ X2 )
% 5.64/5.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.84 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % member_inv
% 5.64/5.84 thf(fact_1245_divide__le__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [B: rat,W: num,A: rat] :
% 5.64/5.84 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.64/5.84 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % divide_le_eq_numeral1(1)
% 5.64/5.84 thf(fact_1246_divide__le__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [B: real,W: num,A: real] :
% 5.64/5.84 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.64/5.84 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % divide_le_eq_numeral1(1)
% 5.64/5.84 thf(fact_1247_le__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [A: rat,B: rat,W: num] :
% 5.64/5.84 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.84 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_divide_eq_numeral1(1)
% 5.64/5.84 thf(fact_1248_le__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [A: real,B: real,W: num] :
% 5.64/5.84 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.84 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % le_divide_eq_numeral1(1)
% 5.64/5.84 thf(fact_1249_divide__less__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [B: real,W: num,A: real] :
% 5.64/5.84 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.64/5.84 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % divide_less_eq_numeral1(1)
% 5.64/5.84 thf(fact_1250_divide__less__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [B: rat,W: num,A: rat] :
% 5.64/5.84 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.64/5.84 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % divide_less_eq_numeral1(1)
% 5.64/5.84 thf(fact_1251_less__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [A: real,B: real,W: num] :
% 5.64/5.84 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.84 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % less_divide_eq_numeral1(1)
% 5.64/5.84 thf(fact_1252_less__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.84 ! [A: rat,B: rat,W: num] :
% 5.64/5.84 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.84 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % less_divide_eq_numeral1(1)
% 5.64/5.84 thf(fact_1253_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.64/5.84 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.64/5.84 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.84 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.64/5.84 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.84 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % both_member_options_from_chilf_to_complete_tree
% 5.64/5.84 thf(fact_1254_power__add__numeral2,axiom,
% 5.64/5.84 ! [A: complex,M: num,N: num,B: complex] :
% 5.64/5.84 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.64/5.84 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral2
% 5.64/5.84 thf(fact_1255_power__add__numeral2,axiom,
% 5.64/5.84 ! [A: real,M: num,N: num,B: real] :
% 5.64/5.84 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.64/5.84 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral2
% 5.64/5.84 thf(fact_1256_power__add__numeral2,axiom,
% 5.64/5.84 ! [A: rat,M: num,N: num,B: rat] :
% 5.64/5.84 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.64/5.84 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral2
% 5.64/5.84 thf(fact_1257_power__add__numeral2,axiom,
% 5.64/5.84 ! [A: nat,M: num,N: num,B: nat] :
% 5.64/5.84 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.64/5.84 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral2
% 5.64/5.84 thf(fact_1258_power__add__numeral2,axiom,
% 5.64/5.84 ! [A: int,M: num,N: num,B: int] :
% 5.64/5.84 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.64/5.84 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral2
% 5.64/5.84 thf(fact_1259_power__add__numeral,axiom,
% 5.64/5.84 ! [A: complex,M: num,N: num] :
% 5.64/5.84 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.64/5.84 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral
% 5.64/5.84 thf(fact_1260_power__add__numeral,axiom,
% 5.64/5.84 ! [A: real,M: num,N: num] :
% 5.64/5.84 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.64/5.84 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral
% 5.64/5.84 thf(fact_1261_power__add__numeral,axiom,
% 5.64/5.84 ! [A: rat,M: num,N: num] :
% 5.64/5.84 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.64/5.84 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral
% 5.64/5.84 thf(fact_1262_power__add__numeral,axiom,
% 5.64/5.84 ! [A: nat,M: num,N: num] :
% 5.64/5.84 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.64/5.84 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral
% 5.64/5.84 thf(fact_1263_power__add__numeral,axiom,
% 5.64/5.84 ! [A: int,M: num,N: num] :
% 5.64/5.84 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.64/5.84 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_add_numeral
% 5.64/5.84 thf(fact_1264_enat__less__induct,axiom,
% 5.64/5.84 ! [P: extended_enat > $o,N: extended_enat] :
% 5.64/5.84 ( ! [N3: extended_enat] :
% 5.64/5.84 ( ! [M5: extended_enat] :
% 5.64/5.84 ( ( ord_le72135733267957522d_enat @ M5 @ N3 )
% 5.64/5.84 => ( P @ M5 ) )
% 5.64/5.84 => ( P @ N3 ) )
% 5.64/5.84 => ( P @ N ) ) ).
% 5.64/5.84
% 5.64/5.84 % enat_less_induct
% 5.64/5.84 thf(fact_1265_mult_Oleft__commute,axiom,
% 5.64/5.84 ! [B: real,A: real,C: real] :
% 5.64/5.84 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.64/5.84 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.left_commute
% 5.64/5.84 thf(fact_1266_mult_Oleft__commute,axiom,
% 5.64/5.84 ! [B: rat,A: rat,C: rat] :
% 5.64/5.84 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.64/5.84 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.left_commute
% 5.64/5.84 thf(fact_1267_mult_Oleft__commute,axiom,
% 5.64/5.84 ! [B: nat,A: nat,C: nat] :
% 5.64/5.84 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.64/5.84 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.left_commute
% 5.64/5.84 thf(fact_1268_mult_Oleft__commute,axiom,
% 5.64/5.84 ! [B: int,A: int,C: int] :
% 5.64/5.84 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.64/5.84 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.left_commute
% 5.64/5.84 thf(fact_1269_mult_Ocommute,axiom,
% 5.64/5.84 ( times_times_real
% 5.64/5.84 = ( ^ [A3: real,B3: real] : ( times_times_real @ B3 @ A3 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.commute
% 5.64/5.84 thf(fact_1270_mult_Ocommute,axiom,
% 5.64/5.84 ( times_times_rat
% 5.64/5.84 = ( ^ [A3: rat,B3: rat] : ( times_times_rat @ B3 @ A3 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.commute
% 5.64/5.84 thf(fact_1271_mult_Ocommute,axiom,
% 5.64/5.84 ( times_times_nat
% 5.64/5.84 = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.commute
% 5.64/5.84 thf(fact_1272_mult_Ocommute,axiom,
% 5.64/5.84 ( times_times_int
% 5.64/5.84 = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.commute
% 5.64/5.84 thf(fact_1273_mult_Oassoc,axiom,
% 5.64/5.84 ! [A: real,B: real,C: real] :
% 5.64/5.84 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.assoc
% 5.64/5.84 thf(fact_1274_mult_Oassoc,axiom,
% 5.64/5.84 ! [A: rat,B: rat,C: rat] :
% 5.64/5.84 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.assoc
% 5.64/5.84 thf(fact_1275_mult_Oassoc,axiom,
% 5.64/5.84 ! [A: nat,B: nat,C: nat] :
% 5.64/5.84 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.assoc
% 5.64/5.84 thf(fact_1276_mult_Oassoc,axiom,
% 5.64/5.84 ! [A: int,B: int,C: int] :
% 5.64/5.84 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % mult.assoc
% 5.64/5.84 thf(fact_1277_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.64/5.84 ! [A: real,B: real,C: real] :
% 5.64/5.84 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ab_semigroup_mult_class.mult_ac(1)
% 5.64/5.84 thf(fact_1278_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.64/5.84 ! [A: rat,B: rat,C: rat] :
% 5.64/5.84 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ab_semigroup_mult_class.mult_ac(1)
% 5.64/5.84 thf(fact_1279_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.64/5.84 ! [A: nat,B: nat,C: nat] :
% 5.64/5.84 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ab_semigroup_mult_class.mult_ac(1)
% 5.64/5.84 thf(fact_1280_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.64/5.84 ! [A: int,B: int,C: int] :
% 5.64/5.84 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.84 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % ab_semigroup_mult_class.mult_ac(1)
% 5.64/5.84 thf(fact_1281_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.64/5.84 ! [X2: produc5542196010084753463at_nat] :
% 5.64/5.84 ( ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc2899441246263362727at_nat @ Uu @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv ) ) )
% 5.64/5.84 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc2899441246263362727at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.64/5.84 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B5 ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_shift.cases
% 5.64/5.84 thf(fact_1282_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.64/5.84 ! [X2: produc8306885398267862888on_nat] :
% 5.64/5.84 ( ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc8929957630744042906on_nat @ Uu @ ( produc5098337634421038937on_nat @ none_nat @ Uv ) ) )
% 5.64/5.84 => ( ! [Uw: nat > nat > nat,V2: nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc8929957630744042906on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.64/5.84 => ~ ! [F2: nat > nat > nat,A5: nat,B5: nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B5 ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_shift.cases
% 5.64/5.84 thf(fact_1283_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.64/5.84 ! [X2: produc1193250871479095198on_num] :
% 5.64/5.84 ( ! [Uu: num > num > num,Uv: option_num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc5778274026573060048on_num @ Uu @ ( produc8585076106096196333on_num @ none_num @ Uv ) ) )
% 5.64/5.84 => ( ! [Uw: num > num > num,V2: num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc5778274026573060048on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.64/5.84 => ~ ! [F2: num > num > num,A5: num,B5: num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B5 ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_shift.cases
% 5.64/5.84 thf(fact_1284_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.64/5.84 ! [X2: produc5491161045314408544at_nat] :
% 5.64/5.84 ( ! [Uu: product_prod_nat_nat > product_prod_nat_nat > $o,Uv: option4927543243414619207at_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc3994169339658061776at_nat @ Uu @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv ) ) )
% 5.64/5.84 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc3994169339658061776at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.64/5.84 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X4 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_comp_shift.cases
% 5.64/5.84 thf(fact_1285_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.64/5.84 ! [X2: produc2233624965454879586on_nat] :
% 5.64/5.84 ( ! [Uu: nat > nat > $o,Uv: option_nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc4035269172776083154on_nat @ Uu @ ( produc5098337634421038937on_nat @ none_nat @ Uv ) ) )
% 5.64/5.84 => ( ! [Uw: nat > nat > $o,V2: nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc4035269172776083154on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.64/5.84 => ~ ! [F2: nat > nat > $o,X4: nat,Y3: nat] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X4 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_comp_shift.cases
% 5.64/5.84 thf(fact_1286_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.64/5.84 ! [X2: produc7036089656553540234on_num] :
% 5.64/5.84 ( ! [Uu: num > num > $o,Uv: option_num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc3576312749637752826on_num @ Uu @ ( produc8585076106096196333on_num @ none_num @ Uv ) ) )
% 5.64/5.84 => ( ! [Uw: num > num > $o,V2: num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc3576312749637752826on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.64/5.84 => ~ ! [F2: num > num > $o,X4: num,Y3: num] :
% 5.64/5.84 ( X2
% 5.64/5.84 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X4 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_comp_shift.cases
% 5.64/5.84 thf(fact_1287_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.64/5.84 ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( vEBT_V1502963449132264192at_nat @ Uu2 @ none_P5556105721700978146at_nat @ Uv2 )
% 5.64/5.84 = none_P5556105721700978146at_nat ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_shift.simps(1)
% 5.64/5.84 thf(fact_1288_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.64/5.84 ! [Uu2: num > num > num,Uv2: option_num] :
% 5.64/5.84 ( ( vEBT_V819420779217536731ft_num @ Uu2 @ none_num @ Uv2 )
% 5.64/5.84 = none_num ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_shift.simps(1)
% 5.64/5.84 thf(fact_1289_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.64/5.84 ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.64/5.84 ( ( vEBT_V4262088993061758097ft_nat @ Uu2 @ none_nat @ Uv2 )
% 5.64/5.84 = none_nat ) ).
% 5.64/5.84
% 5.64/5.84 % VEBT_internal.option_shift.simps(1)
% 5.64/5.84 thf(fact_1290_power__divide,axiom,
% 5.64/5.84 ! [A: complex,B: complex,N: nat] :
% 5.64/5.84 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.64/5.84 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_divide
% 5.64/5.84 thf(fact_1291_power__divide,axiom,
% 5.64/5.84 ! [A: real,B: real,N: nat] :
% 5.64/5.84 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.64/5.84 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_divide
% 5.64/5.84 thf(fact_1292_power__divide,axiom,
% 5.64/5.84 ! [A: rat,B: rat,N: nat] :
% 5.64/5.84 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.64/5.84 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_divide
% 5.64/5.84 thf(fact_1293_mult_Ocomm__neutral,axiom,
% 5.64/5.84 ! [A: complex] :
% 5.64/5.84 ( ( times_times_complex @ A @ one_one_complex )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.comm_neutral
% 5.64/5.84 thf(fact_1294_mult_Ocomm__neutral,axiom,
% 5.64/5.84 ! [A: real] :
% 5.64/5.84 ( ( times_times_real @ A @ one_one_real )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.comm_neutral
% 5.64/5.84 thf(fact_1295_mult_Ocomm__neutral,axiom,
% 5.64/5.84 ! [A: rat] :
% 5.64/5.84 ( ( times_times_rat @ A @ one_one_rat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.comm_neutral
% 5.64/5.84 thf(fact_1296_mult_Ocomm__neutral,axiom,
% 5.64/5.84 ! [A: nat] :
% 5.64/5.84 ( ( times_times_nat @ A @ one_one_nat )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.comm_neutral
% 5.64/5.84 thf(fact_1297_mult_Ocomm__neutral,axiom,
% 5.64/5.84 ! [A: int] :
% 5.64/5.84 ( ( times_times_int @ A @ one_one_int )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % mult.comm_neutral
% 5.64/5.84 thf(fact_1298_comm__monoid__mult__class_Omult__1,axiom,
% 5.64/5.84 ! [A: complex] :
% 5.64/5.84 ( ( times_times_complex @ one_one_complex @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % comm_monoid_mult_class.mult_1
% 5.64/5.84 thf(fact_1299_comm__monoid__mult__class_Omult__1,axiom,
% 5.64/5.84 ! [A: real] :
% 5.64/5.84 ( ( times_times_real @ one_one_real @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % comm_monoid_mult_class.mult_1
% 5.64/5.84 thf(fact_1300_comm__monoid__mult__class_Omult__1,axiom,
% 5.64/5.84 ! [A: rat] :
% 5.64/5.84 ( ( times_times_rat @ one_one_rat @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % comm_monoid_mult_class.mult_1
% 5.64/5.84 thf(fact_1301_comm__monoid__mult__class_Omult__1,axiom,
% 5.64/5.84 ! [A: nat] :
% 5.64/5.84 ( ( times_times_nat @ one_one_nat @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % comm_monoid_mult_class.mult_1
% 5.64/5.84 thf(fact_1302_comm__monoid__mult__class_Omult__1,axiom,
% 5.64/5.84 ! [A: int] :
% 5.64/5.84 ( ( times_times_int @ one_one_int @ A )
% 5.64/5.84 = A ) ).
% 5.64/5.84
% 5.64/5.84 % comm_monoid_mult_class.mult_1
% 5.64/5.84 thf(fact_1303_power__commutes,axiom,
% 5.64/5.84 ! [A: complex,N: nat] :
% 5.64/5.84 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.64/5.84 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commutes
% 5.64/5.84 thf(fact_1304_power__commutes,axiom,
% 5.64/5.84 ! [A: real,N: nat] :
% 5.64/5.84 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.64/5.84 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commutes
% 5.64/5.84 thf(fact_1305_power__commutes,axiom,
% 5.64/5.84 ! [A: rat,N: nat] :
% 5.64/5.84 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.64/5.84 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commutes
% 5.64/5.84 thf(fact_1306_power__commutes,axiom,
% 5.64/5.84 ! [A: nat,N: nat] :
% 5.64/5.84 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.64/5.84 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commutes
% 5.64/5.84 thf(fact_1307_power__commutes,axiom,
% 5.64/5.84 ! [A: int,N: nat] :
% 5.64/5.84 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.64/5.84 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commutes
% 5.64/5.84 thf(fact_1308_power__mult__distrib,axiom,
% 5.64/5.84 ! [A: complex,B: complex,N: nat] :
% 5.64/5.84 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.64/5.84 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_mult_distrib
% 5.64/5.84 thf(fact_1309_power__mult__distrib,axiom,
% 5.64/5.84 ! [A: real,B: real,N: nat] :
% 5.64/5.84 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.64/5.84 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_mult_distrib
% 5.64/5.84 thf(fact_1310_power__mult__distrib,axiom,
% 5.64/5.84 ! [A: rat,B: rat,N: nat] :
% 5.64/5.84 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.64/5.84 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_mult_distrib
% 5.64/5.84 thf(fact_1311_power__mult__distrib,axiom,
% 5.64/5.84 ! [A: nat,B: nat,N: nat] :
% 5.64/5.84 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.64/5.84 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_mult_distrib
% 5.64/5.84 thf(fact_1312_power__mult__distrib,axiom,
% 5.64/5.84 ! [A: int,B: int,N: nat] :
% 5.64/5.84 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.64/5.84 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_mult_distrib
% 5.64/5.84 thf(fact_1313_power__commuting__commutes,axiom,
% 5.64/5.84 ! [X2: complex,Y4: complex,N: nat] :
% 5.64/5.84 ( ( ( times_times_complex @ X2 @ Y4 )
% 5.64/5.84 = ( times_times_complex @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ Y4 )
% 5.64/5.84 = ( times_times_complex @ Y4 @ ( power_power_complex @ X2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commuting_commutes
% 5.64/5.84 thf(fact_1314_power__commuting__commutes,axiom,
% 5.64/5.84 ! [X2: real,Y4: real,N: nat] :
% 5.64/5.84 ( ( ( times_times_real @ X2 @ Y4 )
% 5.64/5.84 = ( times_times_real @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ Y4 )
% 5.64/5.84 = ( times_times_real @ Y4 @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commuting_commutes
% 5.64/5.84 thf(fact_1315_power__commuting__commutes,axiom,
% 5.64/5.84 ! [X2: rat,Y4: rat,N: nat] :
% 5.64/5.84 ( ( ( times_times_rat @ X2 @ Y4 )
% 5.64/5.84 = ( times_times_rat @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ Y4 )
% 5.64/5.84 = ( times_times_rat @ Y4 @ ( power_power_rat @ X2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commuting_commutes
% 5.64/5.84 thf(fact_1316_power__commuting__commutes,axiom,
% 5.64/5.84 ! [X2: nat,Y4: nat,N: nat] :
% 5.64/5.84 ( ( ( times_times_nat @ X2 @ Y4 )
% 5.64/5.84 = ( times_times_nat @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ Y4 )
% 5.64/5.84 = ( times_times_nat @ Y4 @ ( power_power_nat @ X2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commuting_commutes
% 5.64/5.84 thf(fact_1317_power__commuting__commutes,axiom,
% 5.64/5.84 ! [X2: int,Y4: int,N: nat] :
% 5.64/5.84 ( ( ( times_times_int @ X2 @ Y4 )
% 5.64/5.84 = ( times_times_int @ Y4 @ X2 ) )
% 5.64/5.84 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ Y4 )
% 5.64/5.84 = ( times_times_int @ Y4 @ ( power_power_int @ X2 @ N ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % power_commuting_commutes
% 5.64/5.84 thf(fact_1318_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y4: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_P5556105721700978146at_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1319_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y4: option_nat] :
% 5.64/5.84 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: product_prod_nat_nat,B5: nat] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_nat @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1320_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y4: option_num] :
% 5.64/5.84 ( ( ( X2 = none_P5556105721700978146at_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_num )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: product_prod_nat_nat,B5: num] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_num @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1321_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y4: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( ( X2 = none_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_P5556105721700978146at_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: nat,B5: product_prod_nat_nat] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_nat @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1322_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option_nat,P: option_nat > option_nat > $o,Y4: option_nat] :
% 5.64/5.84 ( ( ( X2 = none_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: nat,B5: nat] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_nat @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_nat @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1323_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option_nat,P: option_nat > option_num > $o,Y4: option_num] :
% 5.64/5.84 ( ( ( X2 = none_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_num )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: nat,B5: num] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_nat @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_num @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1324_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option_num,P: option_num > option4927543243414619207at_nat > $o,Y4: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( ( X2 = none_num )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_P5556105721700978146at_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: num,B5: product_prod_nat_nat] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_num @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1325_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option_num,P: option_num > option_nat > $o,Y4: option_nat] :
% 5.64/5.84 ( ( ( X2 = none_num )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_nat )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: num,B5: nat] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_num @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_nat @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1326_combine__options__cases,axiom,
% 5.64/5.84 ! [X2: option_num,P: option_num > option_num > $o,Y4: option_num] :
% 5.64/5.84 ( ( ( X2 = none_num )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ( ( Y4 = none_num )
% 5.64/5.84 => ( P @ X2 @ Y4 ) )
% 5.64/5.84 => ( ! [A5: num,B5: num] :
% 5.64/5.84 ( ( X2
% 5.64/5.84 = ( some_num @ A5 ) )
% 5.64/5.84 => ( ( Y4
% 5.64/5.84 = ( some_num @ B5 ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) )
% 5.64/5.84 => ( P @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % combine_options_cases
% 5.64/5.84 thf(fact_1327_split__option__all,axiom,
% 5.64/5.84 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.64/5.84 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.64/5.84 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.64/5.84 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.64/5.84 & ! [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % split_option_all
% 5.64/5.84 thf(fact_1328_split__option__all,axiom,
% 5.64/5.84 ( ( ^ [P3: option_nat > $o] :
% 5.64/5.84 ! [X6: option_nat] : ( P3 @ X6 ) )
% 5.64/5.84 = ( ^ [P4: option_nat > $o] :
% 5.64/5.84 ( ( P4 @ none_nat )
% 5.64/5.84 & ! [X: nat] : ( P4 @ ( some_nat @ X ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % split_option_all
% 5.64/5.84 thf(fact_1329_split__option__all,axiom,
% 5.64/5.84 ( ( ^ [P3: option_num > $o] :
% 5.64/5.84 ! [X6: option_num] : ( P3 @ X6 ) )
% 5.64/5.84 = ( ^ [P4: option_num > $o] :
% 5.64/5.84 ( ( P4 @ none_num )
% 5.64/5.84 & ! [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % split_option_all
% 5.64/5.84 thf(fact_1330_split__option__ex,axiom,
% 5.64/5.84 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.64/5.84 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.64/5.84 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.64/5.84 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.64/5.84 | ? [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % split_option_ex
% 5.64/5.84 thf(fact_1331_split__option__ex,axiom,
% 5.64/5.84 ( ( ^ [P3: option_nat > $o] :
% 5.64/5.84 ? [X6: option_nat] : ( P3 @ X6 ) )
% 5.64/5.84 = ( ^ [P4: option_nat > $o] :
% 5.64/5.84 ( ( P4 @ none_nat )
% 5.64/5.84 | ? [X: nat] : ( P4 @ ( some_nat @ X ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % split_option_ex
% 5.64/5.84 thf(fact_1332_split__option__ex,axiom,
% 5.64/5.84 ( ( ^ [P3: option_num > $o] :
% 5.64/5.84 ? [X6: option_num] : ( P3 @ X6 ) )
% 5.64/5.84 = ( ^ [P4: option_num > $o] :
% 5.64/5.84 ( ( P4 @ none_num )
% 5.64/5.84 | ? [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % split_option_ex
% 5.64/5.84 thf(fact_1333_option_Oexhaust,axiom,
% 5.64/5.84 ! [Y4: option4927543243414619207at_nat] :
% 5.64/5.84 ( ( Y4 != none_P5556105721700978146at_nat )
% 5.64/5.84 => ~ ! [X23: product_prod_nat_nat] :
% 5.64/5.84 ( Y4
% 5.64/5.84 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % option.exhaust
% 5.64/5.84 thf(fact_1334_option_Oexhaust,axiom,
% 5.64/5.84 ! [Y4: option_nat] :
% 5.64/5.84 ( ( Y4 != none_nat )
% 5.64/5.84 => ~ ! [X23: nat] :
% 5.64/5.84 ( Y4
% 5.64/5.84 != ( some_nat @ X23 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % option.exhaust
% 5.64/5.84 thf(fact_1335_option_Oexhaust,axiom,
% 5.64/5.84 ! [Y4: option_num] :
% 5.64/5.84 ( ( Y4 != none_num )
% 5.64/5.84 => ~ ! [X23: num] :
% 5.64/5.84 ( Y4
% 5.64/5.84 != ( some_num @ X23 ) ) ) ).
% 5.64/5.84
% 5.64/5.84 % option.exhaust
% 5.64/5.84 thf(fact_1336_option_OdiscI,axiom,
% 5.64/5.84 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.64/5.85 ( ( Option
% 5.64/5.85 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.64/5.85 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.discI
% 5.64/5.85 thf(fact_1337_option_OdiscI,axiom,
% 5.64/5.85 ! [Option: option_nat,X22: nat] :
% 5.64/5.85 ( ( Option
% 5.64/5.85 = ( some_nat @ X22 ) )
% 5.64/5.85 => ( Option != none_nat ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.discI
% 5.64/5.85 thf(fact_1338_option_OdiscI,axiom,
% 5.64/5.85 ! [Option: option_num,X22: num] :
% 5.64/5.85 ( ( Option
% 5.64/5.85 = ( some_num @ X22 ) )
% 5.64/5.85 => ( Option != none_num ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.discI
% 5.64/5.85 thf(fact_1339_option_Odistinct_I1_J,axiom,
% 5.64/5.85 ! [X22: product_prod_nat_nat] :
% 5.64/5.85 ( none_P5556105721700978146at_nat
% 5.64/5.85 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.distinct(1)
% 5.64/5.85 thf(fact_1340_option_Odistinct_I1_J,axiom,
% 5.64/5.85 ! [X22: nat] :
% 5.64/5.85 ( none_nat
% 5.64/5.85 != ( some_nat @ X22 ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.distinct(1)
% 5.64/5.85 thf(fact_1341_option_Odistinct_I1_J,axiom,
% 5.64/5.85 ! [X22: num] :
% 5.64/5.85 ( none_num
% 5.64/5.85 != ( some_num @ X22 ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.distinct(1)
% 5.64/5.85 thf(fact_1342_Suc__mult__cancel1,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.64/5.85 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.64/5.85 = ( M = N ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_mult_cancel1
% 5.64/5.85 thf(fact_1343_power__mult,axiom,
% 5.64/5.85 ! [A: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.64/5.85 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult
% 5.64/5.85 thf(fact_1344_power__mult,axiom,
% 5.64/5.85 ! [A: real,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.64/5.85 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult
% 5.64/5.85 thf(fact_1345_power__mult,axiom,
% 5.64/5.85 ! [A: int,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.64/5.85 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult
% 5.64/5.85 thf(fact_1346_power__mult,axiom,
% 5.64/5.85 ! [A: complex,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.64/5.85 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult
% 5.64/5.85 thf(fact_1347_mult__le__mono2,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_le_mono2
% 5.64/5.85 thf(fact_1348_mult__le__mono1,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_le_mono1
% 5.64/5.85 thf(fact_1349_mult__le__mono,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat,L: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ( ord_less_eq_nat @ K @ L )
% 5.64/5.85 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_le_mono
% 5.64/5.85 thf(fact_1350_le__square,axiom,
% 5.64/5.85 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_square
% 5.64/5.85 thf(fact_1351_le__cube,axiom,
% 5.64/5.85 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_cube
% 5.64/5.85 thf(fact_1352_add__mult__distrib2,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_mult_distrib2
% 5.64/5.85 thf(fact_1353_add__mult__distrib,axiom,
% 5.64/5.85 ! [M: nat,N: nat,K: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_mult_distrib
% 5.64/5.85 thf(fact_1354_left__add__mult__distrib,axiom,
% 5.64/5.85 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_add_mult_distrib
% 5.64/5.85 thf(fact_1355_nat__mult__1__right,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ( ( times_times_nat @ N @ one_one_nat )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % nat_mult_1_right
% 5.64/5.85 thf(fact_1356_nat__mult__1,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ( ( times_times_nat @ one_one_nat @ N )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % nat_mult_1
% 5.64/5.85 thf(fact_1357_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.64/5.85 ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.64/5.85 ( ( vEBT_V1502963449132264192at_nat @ Uw2 @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.64/5.85 = none_P5556105721700978146at_nat ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.simps(2)
% 5.64/5.85 thf(fact_1358_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.64/5.85 ! [Uw2: num > num > num,V: num] :
% 5.64/5.85 ( ( vEBT_V819420779217536731ft_num @ Uw2 @ ( some_num @ V ) @ none_num )
% 5.64/5.85 = none_num ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.simps(2)
% 5.64/5.85 thf(fact_1359_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.64/5.85 ! [Uw2: nat > nat > nat,V: nat] :
% 5.64/5.85 ( ( vEBT_V4262088993061758097ft_nat @ Uw2 @ ( some_nat @ V ) @ none_nat )
% 5.64/5.85 = none_nat ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.simps(2)
% 5.64/5.85 thf(fact_1360_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.64/5.85 ! [X2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y4: option4927543243414619207at_nat] :
% 5.64/5.85 ( ( ( vEBT_V1502963449132264192at_nat @ X2 @ Xa2 @ Xb )
% 5.64/5.85 = Y4 )
% 5.64/5.85 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.64/5.85 => ( Y4 != none_P5556105721700978146at_nat ) )
% 5.64/5.85 => ( ( ? [V2: product_prod_nat_nat] :
% 5.64/5.85 ( Xa2
% 5.64/5.85 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.64/5.85 => ( ( Xb = none_P5556105721700978146at_nat )
% 5.64/5.85 => ( Y4 != none_P5556105721700978146at_nat ) ) )
% 5.64/5.85 => ~ ! [A5: product_prod_nat_nat] :
% 5.64/5.85 ( ( Xa2
% 5.64/5.85 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.64/5.85 => ! [B5: product_prod_nat_nat] :
% 5.64/5.85 ( ( Xb
% 5.64/5.85 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.64/5.85 => ( Y4
% 5.64/5.85 != ( some_P7363390416028606310at_nat @ ( X2 @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.elims
% 5.64/5.85 thf(fact_1361_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.64/5.85 ! [X2: num > num > num,Xa2: option_num,Xb: option_num,Y4: option_num] :
% 5.64/5.85 ( ( ( vEBT_V819420779217536731ft_num @ X2 @ Xa2 @ Xb )
% 5.64/5.85 = Y4 )
% 5.64/5.85 => ( ( ( Xa2 = none_num )
% 5.64/5.85 => ( Y4 != none_num ) )
% 5.64/5.85 => ( ( ? [V2: num] :
% 5.64/5.85 ( Xa2
% 5.64/5.85 = ( some_num @ V2 ) )
% 5.64/5.85 => ( ( Xb = none_num )
% 5.64/5.85 => ( Y4 != none_num ) ) )
% 5.64/5.85 => ~ ! [A5: num] :
% 5.64/5.85 ( ( Xa2
% 5.64/5.85 = ( some_num @ A5 ) )
% 5.64/5.85 => ! [B5: num] :
% 5.64/5.85 ( ( Xb
% 5.64/5.85 = ( some_num @ B5 ) )
% 5.64/5.85 => ( Y4
% 5.64/5.85 != ( some_num @ ( X2 @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.elims
% 5.64/5.85 thf(fact_1362_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.64/5.85 ! [X2: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y4: option_nat] :
% 5.64/5.85 ( ( ( vEBT_V4262088993061758097ft_nat @ X2 @ Xa2 @ Xb )
% 5.64/5.85 = Y4 )
% 5.64/5.85 => ( ( ( Xa2 = none_nat )
% 5.64/5.85 => ( Y4 != none_nat ) )
% 5.64/5.85 => ( ( ? [V2: nat] :
% 5.64/5.85 ( Xa2
% 5.64/5.85 = ( some_nat @ V2 ) )
% 5.64/5.85 => ( ( Xb = none_nat )
% 5.64/5.85 => ( Y4 != none_nat ) ) )
% 5.64/5.85 => ~ ! [A5: nat] :
% 5.64/5.85 ( ( Xa2
% 5.64/5.85 = ( some_nat @ A5 ) )
% 5.64/5.85 => ! [B5: nat] :
% 5.64/5.85 ( ( Xb
% 5.64/5.85 = ( some_nat @ B5 ) )
% 5.64/5.85 => ( Y4
% 5.64/5.85 != ( some_nat @ ( X2 @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.elims
% 5.64/5.85 thf(fact_1363_divide__numeral__1,axiom,
% 5.64/5.85 ! [A: complex] :
% 5.64/5.85 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % divide_numeral_1
% 5.64/5.85 thf(fact_1364_divide__numeral__1,axiom,
% 5.64/5.85 ! [A: real] :
% 5.64/5.85 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % divide_numeral_1
% 5.64/5.85 thf(fact_1365_divide__numeral__1,axiom,
% 5.64/5.85 ! [A: rat] :
% 5.64/5.85 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % divide_numeral_1
% 5.64/5.85 thf(fact_1366_power__one__over,axiom,
% 5.64/5.85 ! [A: complex,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.64/5.85 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_one_over
% 5.64/5.85 thf(fact_1367_power__one__over,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.64/5.85 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_one_over
% 5.64/5.85 thf(fact_1368_power__one__over,axiom,
% 5.64/5.85 ! [A: rat,N: nat] :
% 5.64/5.85 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.64/5.85 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_one_over
% 5.64/5.85 thf(fact_1369_mult__numeral__1,axiom,
% 5.64/5.85 ! [A: complex] :
% 5.64/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1
% 5.64/5.85 thf(fact_1370_mult__numeral__1,axiom,
% 5.64/5.85 ! [A: real] :
% 5.64/5.85 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1
% 5.64/5.85 thf(fact_1371_mult__numeral__1,axiom,
% 5.64/5.85 ! [A: rat] :
% 5.64/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1
% 5.64/5.85 thf(fact_1372_mult__numeral__1,axiom,
% 5.64/5.85 ! [A: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1
% 5.64/5.85 thf(fact_1373_mult__numeral__1,axiom,
% 5.64/5.85 ! [A: int] :
% 5.64/5.85 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1
% 5.64/5.85 thf(fact_1374_mult__numeral__1__right,axiom,
% 5.64/5.85 ! [A: complex] :
% 5.64/5.85 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1_right
% 5.64/5.85 thf(fact_1375_mult__numeral__1__right,axiom,
% 5.64/5.85 ! [A: real] :
% 5.64/5.85 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1_right
% 5.64/5.85 thf(fact_1376_mult__numeral__1__right,axiom,
% 5.64/5.85 ! [A: rat] :
% 5.64/5.85 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1_right
% 5.64/5.85 thf(fact_1377_mult__numeral__1__right,axiom,
% 5.64/5.85 ! [A: nat] :
% 5.64/5.85 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1_right
% 5.64/5.85 thf(fact_1378_mult__numeral__1__right,axiom,
% 5.64/5.85 ! [A: int] :
% 5.64/5.85 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % mult_numeral_1_right
% 5.64/5.85 thf(fact_1379_left__right__inverse__power,axiom,
% 5.64/5.85 ! [X2: complex,Y4: complex,N: nat] :
% 5.64/5.85 ( ( ( times_times_complex @ X2 @ Y4 )
% 5.64/5.85 = one_one_complex )
% 5.64/5.85 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y4 @ N ) )
% 5.64/5.85 = one_one_complex ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_right_inverse_power
% 5.64/5.85 thf(fact_1380_left__right__inverse__power,axiom,
% 5.64/5.85 ! [X2: real,Y4: real,N: nat] :
% 5.64/5.85 ( ( ( times_times_real @ X2 @ Y4 )
% 5.64/5.85 = one_one_real )
% 5.64/5.85 => ( ( times_times_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y4 @ N ) )
% 5.64/5.85 = one_one_real ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_right_inverse_power
% 5.64/5.85 thf(fact_1381_left__right__inverse__power,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat,N: nat] :
% 5.64/5.85 ( ( ( times_times_rat @ X2 @ Y4 )
% 5.64/5.85 = one_one_rat )
% 5.64/5.85 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y4 @ N ) )
% 5.64/5.85 = one_one_rat ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_right_inverse_power
% 5.64/5.85 thf(fact_1382_left__right__inverse__power,axiom,
% 5.64/5.85 ! [X2: nat,Y4: nat,N: nat] :
% 5.64/5.85 ( ( ( times_times_nat @ X2 @ Y4 )
% 5.64/5.85 = one_one_nat )
% 5.64/5.85 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y4 @ N ) )
% 5.64/5.85 = one_one_nat ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_right_inverse_power
% 5.64/5.85 thf(fact_1383_left__right__inverse__power,axiom,
% 5.64/5.85 ! [X2: int,Y4: int,N: nat] :
% 5.64/5.85 ( ( ( times_times_int @ X2 @ Y4 )
% 5.64/5.85 = one_one_int )
% 5.64/5.85 => ( ( times_times_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y4 @ N ) )
% 5.64/5.85 = one_one_int ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_right_inverse_power
% 5.64/5.85 thf(fact_1384_power__Suc2,axiom,
% 5.64/5.85 ! [A: complex,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc2
% 5.64/5.85 thf(fact_1385_power__Suc2,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc2
% 5.64/5.85 thf(fact_1386_power__Suc2,axiom,
% 5.64/5.85 ! [A: rat,N: nat] :
% 5.64/5.85 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc2
% 5.64/5.85 thf(fact_1387_power__Suc2,axiom,
% 5.64/5.85 ! [A: nat,N: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc2
% 5.64/5.85 thf(fact_1388_power__Suc2,axiom,
% 5.64/5.85 ! [A: int,N: nat] :
% 5.64/5.85 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc2
% 5.64/5.85 thf(fact_1389_power__Suc,axiom,
% 5.64/5.85 ! [A: complex,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc
% 5.64/5.85 thf(fact_1390_power__Suc,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc
% 5.64/5.85 thf(fact_1391_power__Suc,axiom,
% 5.64/5.85 ! [A: rat,N: nat] :
% 5.64/5.85 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc
% 5.64/5.85 thf(fact_1392_power__Suc,axiom,
% 5.64/5.85 ! [A: nat,N: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc
% 5.64/5.85 thf(fact_1393_power__Suc,axiom,
% 5.64/5.85 ! [A: int,N: nat] :
% 5.64/5.85 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.64/5.85 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_Suc
% 5.64/5.85 thf(fact_1394_Suc__mult__less__cancel1,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.64/5.85 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_mult_less_cancel1
% 5.64/5.85 thf(fact_1395_power__add,axiom,
% 5.64/5.85 ! [A: complex,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.85 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_add
% 5.64/5.85 thf(fact_1396_power__add,axiom,
% 5.64/5.85 ! [A: real,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.85 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_add
% 5.64/5.85 thf(fact_1397_power__add,axiom,
% 5.64/5.85 ! [A: rat,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.85 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_add
% 5.64/5.85 thf(fact_1398_power__add,axiom,
% 5.64/5.85 ! [A: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.85 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_add
% 5.64/5.85 thf(fact_1399_power__add,axiom,
% 5.64/5.85 ! [A: int,M: nat,N: nat] :
% 5.64/5.85 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.85 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_add
% 5.64/5.85 thf(fact_1400_Suc__mult__le__cancel1,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.64/5.85 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_mult_le_cancel1
% 5.64/5.85 thf(fact_1401_mult__Suc,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.64/5.85 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_Suc
% 5.64/5.85 thf(fact_1402_power__odd__eq,axiom,
% 5.64/5.85 ! [A: complex,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.85 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_odd_eq
% 5.64/5.85 thf(fact_1403_power__odd__eq,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.85 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_odd_eq
% 5.64/5.85 thf(fact_1404_power__odd__eq,axiom,
% 5.64/5.85 ! [A: rat,N: nat] :
% 5.64/5.85 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.85 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_odd_eq
% 5.64/5.85 thf(fact_1405_power__odd__eq,axiom,
% 5.64/5.85 ! [A: nat,N: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.85 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_odd_eq
% 5.64/5.85 thf(fact_1406_power__odd__eq,axiom,
% 5.64/5.85 ! [A: int,N: nat] :
% 5.64/5.85 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.85 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_odd_eq
% 5.64/5.85 thf(fact_1407_power__less__power__Suc,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.85 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_less_power_Suc
% 5.64/5.85 thf(fact_1408_power__less__power__Suc,axiom,
% 5.64/5.85 ! [A: rat,N: nat] :
% 5.64/5.85 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.85 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_less_power_Suc
% 5.64/5.85 thf(fact_1409_power__less__power__Suc,axiom,
% 5.64/5.85 ! [A: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.85 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_less_power_Suc
% 5.64/5.85 thf(fact_1410_power__less__power__Suc,axiom,
% 5.64/5.85 ! [A: int,N: nat] :
% 5.64/5.85 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.85 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_less_power_Suc
% 5.64/5.85 thf(fact_1411_power__gt1__lemma,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.85 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_gt1_lemma
% 5.64/5.85 thf(fact_1412_power__gt1__lemma,axiom,
% 5.64/5.85 ! [A: rat,N: nat] :
% 5.64/5.85 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.85 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_gt1_lemma
% 5.64/5.85 thf(fact_1413_power__gt1__lemma,axiom,
% 5.64/5.85 ! [A: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.85 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_gt1_lemma
% 5.64/5.85 thf(fact_1414_power__gt1__lemma,axiom,
% 5.64/5.85 ! [A: int,N: nat] :
% 5.64/5.85 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.85 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_gt1_lemma
% 5.64/5.85 thf(fact_1415_subset__code_I1_J,axiom,
% 5.64/5.85 ! [Xs2: list_P6011104703257516679at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.64/5.85 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ B4 )
% 5.64/5.85 = ( ! [X: product_prod_nat_nat] :
% 5.64/5.85 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.64/5.85 => ( member8440522571783428010at_nat @ X @ B4 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % subset_code(1)
% 5.64/5.85 thf(fact_1416_subset__code_I1_J,axiom,
% 5.64/5.85 ! [Xs2: list_complex,B4: set_complex] :
% 5.64/5.85 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ B4 )
% 5.64/5.85 = ( ! [X: complex] :
% 5.64/5.85 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 5.64/5.85 => ( member_complex @ X @ B4 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % subset_code(1)
% 5.64/5.85 thf(fact_1417_subset__code_I1_J,axiom,
% 5.64/5.85 ! [Xs2: list_real,B4: set_real] :
% 5.64/5.85 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ B4 )
% 5.64/5.85 = ( ! [X: real] :
% 5.64/5.85 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 5.64/5.85 => ( member_real @ X @ B4 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % subset_code(1)
% 5.64/5.85 thf(fact_1418_subset__code_I1_J,axiom,
% 5.64/5.85 ! [Xs2: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 5.64/5.85 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ B4 )
% 5.64/5.85 = ( ! [X: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.85 => ( member_VEBT_VEBT @ X @ B4 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % subset_code(1)
% 5.64/5.85 thf(fact_1419_subset__code_I1_J,axiom,
% 5.64/5.85 ! [Xs2: list_int,B4: set_int] :
% 5.64/5.85 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ B4 )
% 5.64/5.85 = ( ! [X: int] :
% 5.64/5.85 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 5.64/5.85 => ( member_int @ X @ B4 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % subset_code(1)
% 5.64/5.85 thf(fact_1420_subset__code_I1_J,axiom,
% 5.64/5.85 ! [Xs2: list_nat,B4: set_nat] :
% 5.64/5.85 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ B4 )
% 5.64/5.85 = ( ! [X: nat] :
% 5.64/5.85 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 5.64/5.85 => ( member_nat @ X @ B4 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % subset_code(1)
% 5.64/5.85 thf(fact_1421_Ex__list__of__length,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ? [Xs3: list_VEBT_VEBT] :
% 5.64/5.85 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % Ex_list_of_length
% 5.64/5.85 thf(fact_1422_Ex__list__of__length,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ? [Xs3: list_o] :
% 5.64/5.85 ( ( size_size_list_o @ Xs3 )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % Ex_list_of_length
% 5.64/5.85 thf(fact_1423_Ex__list__of__length,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ? [Xs3: list_nat] :
% 5.64/5.85 ( ( size_size_list_nat @ Xs3 )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % Ex_list_of_length
% 5.64/5.85 thf(fact_1424_Ex__list__of__length,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ? [Xs3: list_int] :
% 5.64/5.85 ( ( size_size_list_int @ Xs3 )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % Ex_list_of_length
% 5.64/5.85 thf(fact_1425_neq__if__length__neq,axiom,
% 5.64/5.85 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.64/5.85 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.64/5.85 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.64/5.85 => ( Xs2 != Ys ) ) ).
% 5.64/5.85
% 5.64/5.85 % neq_if_length_neq
% 5.64/5.85 thf(fact_1426_neq__if__length__neq,axiom,
% 5.64/5.85 ! [Xs2: list_o,Ys: list_o] :
% 5.64/5.85 ( ( ( size_size_list_o @ Xs2 )
% 5.64/5.85 != ( size_size_list_o @ Ys ) )
% 5.64/5.85 => ( Xs2 != Ys ) ) ).
% 5.64/5.85
% 5.64/5.85 % neq_if_length_neq
% 5.64/5.85 thf(fact_1427_neq__if__length__neq,axiom,
% 5.64/5.85 ! [Xs2: list_nat,Ys: list_nat] :
% 5.64/5.85 ( ( ( size_size_list_nat @ Xs2 )
% 5.64/5.85 != ( size_size_list_nat @ Ys ) )
% 5.64/5.85 => ( Xs2 != Ys ) ) ).
% 5.64/5.85
% 5.64/5.85 % neq_if_length_neq
% 5.64/5.85 thf(fact_1428_neq__if__length__neq,axiom,
% 5.64/5.85 ! [Xs2: list_int,Ys: list_int] :
% 5.64/5.85 ( ( ( size_size_list_int @ Xs2 )
% 5.64/5.85 != ( size_size_list_int @ Ys ) )
% 5.64/5.85 => ( Xs2 != Ys ) ) ).
% 5.64/5.85
% 5.64/5.85 % neq_if_length_neq
% 5.64/5.85 thf(fact_1429_mult__2,axiom,
% 5.64/5.85 ! [Z: complex] :
% 5.64/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.64/5.85 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2
% 5.64/5.85 thf(fact_1430_mult__2,axiom,
% 5.64/5.85 ! [Z: real] :
% 5.64/5.85 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.64/5.85 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2
% 5.64/5.85 thf(fact_1431_mult__2,axiom,
% 5.64/5.85 ! [Z: rat] :
% 5.64/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.64/5.85 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2
% 5.64/5.85 thf(fact_1432_mult__2,axiom,
% 5.64/5.85 ! [Z: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.64/5.85 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2
% 5.64/5.85 thf(fact_1433_mult__2,axiom,
% 5.64/5.85 ! [Z: int] :
% 5.64/5.85 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.64/5.85 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2
% 5.64/5.85 thf(fact_1434_mult__2__right,axiom,
% 5.64/5.85 ! [Z: complex] :
% 5.64/5.85 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2_right
% 5.64/5.85 thf(fact_1435_mult__2__right,axiom,
% 5.64/5.85 ! [Z: real] :
% 5.64/5.85 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2_right
% 5.64/5.85 thf(fact_1436_mult__2__right,axiom,
% 5.64/5.85 ! [Z: rat] :
% 5.64/5.85 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2_right
% 5.64/5.85 thf(fact_1437_mult__2__right,axiom,
% 5.64/5.85 ! [Z: nat] :
% 5.64/5.85 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2_right
% 5.64/5.85 thf(fact_1438_mult__2__right,axiom,
% 5.64/5.85 ! [Z: int] :
% 5.64/5.85 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_2_right
% 5.64/5.85 thf(fact_1439_left__add__twice,axiom,
% 5.64/5.85 ! [A: complex,B: complex] :
% 5.64/5.85 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.64/5.85 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_add_twice
% 5.64/5.85 thf(fact_1440_left__add__twice,axiom,
% 5.64/5.85 ! [A: real,B: real] :
% 5.64/5.85 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_add_twice
% 5.64/5.85 thf(fact_1441_left__add__twice,axiom,
% 5.64/5.85 ! [A: rat,B: rat] :
% 5.64/5.85 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_add_twice
% 5.64/5.85 thf(fact_1442_left__add__twice,axiom,
% 5.64/5.85 ! [A: nat,B: nat] :
% 5.64/5.85 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_add_twice
% 5.64/5.85 thf(fact_1443_left__add__twice,axiom,
% 5.64/5.85 ! [A: int,B: int] :
% 5.64/5.85 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.64/5.85 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_add_twice
% 5.64/5.85 thf(fact_1444_power4__eq__xxxx,axiom,
% 5.64/5.85 ! [X2: complex] :
% 5.64/5.85 ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % power4_eq_xxxx
% 5.64/5.85 thf(fact_1445_power4__eq__xxxx,axiom,
% 5.64/5.85 ! [X2: real] :
% 5.64/5.85 ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % power4_eq_xxxx
% 5.64/5.85 thf(fact_1446_power4__eq__xxxx,axiom,
% 5.64/5.85 ! [X2: rat] :
% 5.64/5.85 ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % power4_eq_xxxx
% 5.64/5.85 thf(fact_1447_power4__eq__xxxx,axiom,
% 5.64/5.85 ! [X2: nat] :
% 5.64/5.85 ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % power4_eq_xxxx
% 5.64/5.85 thf(fact_1448_power4__eq__xxxx,axiom,
% 5.64/5.85 ! [X2: int] :
% 5.64/5.85 ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % power4_eq_xxxx
% 5.64/5.85 thf(fact_1449_power2__eq__square,axiom,
% 5.64/5.85 ! [A: complex] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( times_times_complex @ A @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_eq_square
% 5.64/5.85 thf(fact_1450_power2__eq__square,axiom,
% 5.64/5.85 ! [A: real] :
% 5.64/5.85 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( times_times_real @ A @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_eq_square
% 5.64/5.85 thf(fact_1451_power2__eq__square,axiom,
% 5.64/5.85 ! [A: rat] :
% 5.64/5.85 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( times_times_rat @ A @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_eq_square
% 5.64/5.85 thf(fact_1452_power2__eq__square,axiom,
% 5.64/5.85 ! [A: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( times_times_nat @ A @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_eq_square
% 5.64/5.85 thf(fact_1453_power2__eq__square,axiom,
% 5.64/5.85 ! [A: int] :
% 5.64/5.85 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( times_times_int @ A @ A ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_eq_square
% 5.64/5.85 thf(fact_1454_power__even__eq,axiom,
% 5.64/5.85 ! [A: nat,N: nat] :
% 5.64/5.85 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.85 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_even_eq
% 5.64/5.85 thf(fact_1455_power__even__eq,axiom,
% 5.64/5.85 ! [A: real,N: nat] :
% 5.64/5.85 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.85 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_even_eq
% 5.64/5.85 thf(fact_1456_power__even__eq,axiom,
% 5.64/5.85 ! [A: int,N: nat] :
% 5.64/5.85 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.85 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_even_eq
% 5.64/5.85 thf(fact_1457_power__even__eq,axiom,
% 5.64/5.85 ! [A: complex,N: nat] :
% 5.64/5.85 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.85 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_even_eq
% 5.64/5.85 thf(fact_1458_power2__sum,axiom,
% 5.64/5.85 ! [X2: complex,Y4: complex] :
% 5.64/5.85 ( ( power_power_complex @ ( plus_plus_complex @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_sum
% 5.64/5.85 thf(fact_1459_power2__sum,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] :
% 5.64/5.85 ( ( power_power_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_sum
% 5.64/5.85 thf(fact_1460_power2__sum,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat] :
% 5.64/5.85 ( ( power_power_rat @ ( plus_plus_rat @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_sum
% 5.64/5.85 thf(fact_1461_power2__sum,axiom,
% 5.64/5.85 ! [X2: nat,Y4: nat] :
% 5.64/5.85 ( ( power_power_nat @ ( plus_plus_nat @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_sum
% 5.64/5.85 thf(fact_1462_power2__sum,axiom,
% 5.64/5.85 ! [X2: int,Y4: int] :
% 5.64/5.85 ( ( power_power_int @ ( plus_plus_int @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_sum
% 5.64/5.85 thf(fact_1463_length__induct,axiom,
% 5.64/5.85 ! [P: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 5.64/5.85 ( ! [Xs3: list_VEBT_VEBT] :
% 5.64/5.85 ( ! [Ys2: list_VEBT_VEBT] :
% 5.64/5.85 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.64/5.85 => ( P @ Ys2 ) )
% 5.64/5.85 => ( P @ Xs3 ) )
% 5.64/5.85 => ( P @ Xs2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % length_induct
% 5.64/5.85 thf(fact_1464_length__induct,axiom,
% 5.64/5.85 ! [P: list_o > $o,Xs2: list_o] :
% 5.64/5.85 ( ! [Xs3: list_o] :
% 5.64/5.85 ( ! [Ys2: list_o] :
% 5.64/5.85 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.64/5.85 => ( P @ Ys2 ) )
% 5.64/5.85 => ( P @ Xs3 ) )
% 5.64/5.85 => ( P @ Xs2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % length_induct
% 5.64/5.85 thf(fact_1465_length__induct,axiom,
% 5.64/5.85 ! [P: list_nat > $o,Xs2: list_nat] :
% 5.64/5.85 ( ! [Xs3: list_nat] :
% 5.64/5.85 ( ! [Ys2: list_nat] :
% 5.64/5.85 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.64/5.85 => ( P @ Ys2 ) )
% 5.64/5.85 => ( P @ Xs3 ) )
% 5.64/5.85 => ( P @ Xs2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % length_induct
% 5.64/5.85 thf(fact_1466_length__induct,axiom,
% 5.64/5.85 ! [P: list_int > $o,Xs2: list_int] :
% 5.64/5.85 ( ! [Xs3: list_int] :
% 5.64/5.85 ( ! [Ys2: list_int] :
% 5.64/5.85 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.64/5.85 => ( P @ Ys2 ) )
% 5.64/5.85 => ( P @ Xs3 ) )
% 5.64/5.85 => ( P @ Xs2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % length_induct
% 5.64/5.85 thf(fact_1467_invar__vebt_Ointros_I4_J,axiom,
% 5.64/5.85 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.64/5.85 ( ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.64/5.85 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.64/5.85 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.64/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( M = N )
% 5.64/5.85 => ( ( Deg
% 5.64/5.85 = ( plus_plus_nat @ N @ M ) )
% 5.64/5.85 => ( ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X5 ) )
% 5.64/5.85 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.64/5.85 => ( ( ( Mi = Ma )
% 5.64/5.85 => ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.64/5.85 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.64/5.85 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.64/5.85 => ( ( ( Mi != Ma )
% 5.64/5.85 => ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.64/5.85 = I3 )
% 5.64/5.85 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.64/5.85 & ! [X4: nat] :
% 5.64/5.85 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.64/5.85 = I3 )
% 5.64/5.85 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.64/5.85 => ( ( ord_less_nat @ Mi @ X4 )
% 5.64/5.85 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % invar_vebt.intros(4)
% 5.64/5.85 thf(fact_1468_invar__vebt_Ointros_I5_J,axiom,
% 5.64/5.85 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.64/5.85 ( ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.64/5.85 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.64/5.85 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.64/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( M
% 5.64/5.85 = ( suc @ N ) )
% 5.64/5.85 => ( ( Deg
% 5.64/5.85 = ( plus_plus_nat @ N @ M ) )
% 5.64/5.85 => ( ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X5 ) )
% 5.64/5.85 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.64/5.85 => ( ( ( Mi = Ma )
% 5.64/5.85 => ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.64/5.85 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.64/5.85 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.64/5.85 => ( ( ( Mi != Ma )
% 5.64/5.85 => ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.64/5.85 = I3 )
% 5.64/5.85 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.64/5.85 & ! [X4: nat] :
% 5.64/5.85 ( ( ( ( vEBT_VEBT_high @ X4 @ N )
% 5.64/5.85 = I3 )
% 5.64/5.85 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X4 @ N ) ) )
% 5.64/5.85 => ( ( ord_less_nat @ Mi @ X4 )
% 5.64/5.85 & ( ord_less_eq_nat @ X4 @ Ma ) ) ) ) ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % invar_vebt.intros(5)
% 5.64/5.85 thf(fact_1469_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.64/5.85 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.64/5.85 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.64/5.85 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.simps(3)
% 5.64/5.85 thf(fact_1470_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.64/5.85 ! [F: num > num > num,A: num,B: num] :
% 5.64/5.85 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.64/5.85 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.simps(3)
% 5.64/5.85 thf(fact_1471_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.64/5.85 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.64/5.85 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.64/5.85 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % VEBT_internal.option_shift.simps(3)
% 5.64/5.85 thf(fact_1472_nth__equalityI,axiom,
% 5.64/5.85 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.64/5.85 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.64/5.85 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.64/5.85 => ( ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.85 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 5.64/5.85 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 5.64/5.85 => ( Xs2 = Ys ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nth_equalityI
% 5.64/5.85 thf(fact_1473_nth__equalityI,axiom,
% 5.64/5.85 ! [Xs2: list_o,Ys: list_o] :
% 5.64/5.85 ( ( ( size_size_list_o @ Xs2 )
% 5.64/5.85 = ( size_size_list_o @ Ys ) )
% 5.64/5.85 => ( ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.85 => ( ( nth_o @ Xs2 @ I3 )
% 5.64/5.85 = ( nth_o @ Ys @ I3 ) ) )
% 5.64/5.85 => ( Xs2 = Ys ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nth_equalityI
% 5.64/5.85 thf(fact_1474_nth__equalityI,axiom,
% 5.64/5.85 ! [Xs2: list_nat,Ys: list_nat] :
% 5.64/5.85 ( ( ( size_size_list_nat @ Xs2 )
% 5.64/5.85 = ( size_size_list_nat @ Ys ) )
% 5.64/5.85 => ( ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.85 => ( ( nth_nat @ Xs2 @ I3 )
% 5.64/5.85 = ( nth_nat @ Ys @ I3 ) ) )
% 5.64/5.85 => ( Xs2 = Ys ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nth_equalityI
% 5.64/5.85 thf(fact_1475_nth__equalityI,axiom,
% 5.64/5.85 ! [Xs2: list_int,Ys: list_int] :
% 5.64/5.85 ( ( ( size_size_list_int @ Xs2 )
% 5.64/5.85 = ( size_size_list_int @ Ys ) )
% 5.64/5.85 => ( ! [I3: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.85 => ( ( nth_int @ Xs2 @ I3 )
% 5.64/5.85 = ( nth_int @ Ys @ I3 ) ) )
% 5.64/5.85 => ( Xs2 = Ys ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nth_equalityI
% 5.64/5.85 thf(fact_1476_Skolem__list__nth,axiom,
% 5.64/5.85 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.64/5.85 ( ( ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ? [X5: vEBT_VEBT] : ( P @ I4 @ X5 ) ) )
% 5.64/5.85 = ( ? [Xs: list_VEBT_VEBT] :
% 5.64/5.85 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.64/5.85 = K )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ( P @ I4 @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Skolem_list_nth
% 5.64/5.85 thf(fact_1477_Skolem__list__nth,axiom,
% 5.64/5.85 ! [K: nat,P: nat > $o > $o] :
% 5.64/5.85 ( ( ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ? [X5: $o] : ( P @ I4 @ X5 ) ) )
% 5.64/5.85 = ( ? [Xs: list_o] :
% 5.64/5.85 ( ( ( size_size_list_o @ Xs )
% 5.64/5.85 = K )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ( P @ I4 @ ( nth_o @ Xs @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Skolem_list_nth
% 5.64/5.85 thf(fact_1478_Skolem__list__nth,axiom,
% 5.64/5.85 ! [K: nat,P: nat > nat > $o] :
% 5.64/5.85 ( ( ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ? [X5: nat] : ( P @ I4 @ X5 ) ) )
% 5.64/5.85 = ( ? [Xs: list_nat] :
% 5.64/5.85 ( ( ( size_size_list_nat @ Xs )
% 5.64/5.85 = K )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ( P @ I4 @ ( nth_nat @ Xs @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Skolem_list_nth
% 5.64/5.85 thf(fact_1479_Skolem__list__nth,axiom,
% 5.64/5.85 ! [K: nat,P: nat > int > $o] :
% 5.64/5.85 ( ( ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ? [X5: int] : ( P @ I4 @ X5 ) ) )
% 5.64/5.85 = ( ? [Xs: list_int] :
% 5.64/5.85 ( ( ( size_size_list_int @ Xs )
% 5.64/5.85 = K )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ K )
% 5.64/5.85 => ( P @ I4 @ ( nth_int @ Xs @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Skolem_list_nth
% 5.64/5.85 thf(fact_1480_list__eq__iff__nth__eq,axiom,
% 5.64/5.85 ( ( ^ [Y6: list_VEBT_VEBT,Z3: list_VEBT_VEBT] : ( Y6 = Z3 ) )
% 5.64/5.85 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.64/5.85 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.64/5.85 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.64/5.85 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.64/5.85 = ( nth_VEBT_VEBT @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % list_eq_iff_nth_eq
% 5.64/5.85 thf(fact_1481_list__eq__iff__nth__eq,axiom,
% 5.64/5.85 ( ( ^ [Y6: list_o,Z3: list_o] : ( Y6 = Z3 ) )
% 5.64/5.85 = ( ^ [Xs: list_o,Ys3: list_o] :
% 5.64/5.85 ( ( ( size_size_list_o @ Xs )
% 5.64/5.85 = ( size_size_list_o @ Ys3 ) )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.64/5.85 => ( ( nth_o @ Xs @ I4 )
% 5.64/5.85 = ( nth_o @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % list_eq_iff_nth_eq
% 5.64/5.85 thf(fact_1482_list__eq__iff__nth__eq,axiom,
% 5.64/5.85 ( ( ^ [Y6: list_nat,Z3: list_nat] : ( Y6 = Z3 ) )
% 5.64/5.85 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 5.64/5.85 ( ( ( size_size_list_nat @ Xs )
% 5.64/5.85 = ( size_size_list_nat @ Ys3 ) )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.64/5.85 => ( ( nth_nat @ Xs @ I4 )
% 5.64/5.85 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % list_eq_iff_nth_eq
% 5.64/5.85 thf(fact_1483_list__eq__iff__nth__eq,axiom,
% 5.64/5.85 ( ( ^ [Y6: list_int,Z3: list_int] : ( Y6 = Z3 ) )
% 5.64/5.85 = ( ^ [Xs: list_int,Ys3: list_int] :
% 5.64/5.85 ( ( ( size_size_list_int @ Xs )
% 5.64/5.85 = ( size_size_list_int @ Ys3 ) )
% 5.64/5.85 & ! [I4: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.64/5.85 => ( ( nth_int @ Xs @ I4 )
% 5.64/5.85 = ( nth_int @ Ys3 @ I4 ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % list_eq_iff_nth_eq
% 5.64/5.85 thf(fact_1484_in__children__def,axiom,
% 5.64/5.85 ( vEBT_V5917875025757280293ildren
% 5.64/5.85 = ( ^ [N2: nat,TreeList3: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X @ N2 ) ) @ ( vEBT_VEBT_low @ X @ N2 ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % in_children_def
% 5.64/5.85 thf(fact_1485_nested__mint,axiom,
% 5.64/5.85 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.64/5.85 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.85 => ( ( N
% 5.64/5.85 = ( suc @ ( suc @ Va ) ) )
% 5.64/5.85 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.64/5.85 => ( ( Ma != Mi )
% 5.64/5.85 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nested_mint
% 5.64/5.85 thf(fact_1486_add__self__div__2,axiom,
% 5.64/5.85 ! [M: nat] :
% 5.64/5.85 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = M ) ).
% 5.64/5.85
% 5.64/5.85 % add_self_div_2
% 5.64/5.85 thf(fact_1487_div2__Suc__Suc,axiom,
% 5.64/5.85 ! [M: nat] :
% 5.64/5.85 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div2_Suc_Suc
% 5.64/5.85 thf(fact_1488_mintlistlength,axiom,
% 5.64/5.85 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.64/5.85 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N )
% 5.64/5.85 => ( ( Mi != Ma )
% 5.64/5.85 => ( ( ord_less_nat @ Mi @ Ma )
% 5.64/5.85 & ? [M4: nat] :
% 5.64/5.85 ( ( ( some_nat @ M4 )
% 5.64/5.85 = ( vEBT_vebt_mint @ Summary ) )
% 5.64/5.85 & ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mintlistlength
% 5.64/5.85 thf(fact_1489_summaxma,axiom,
% 5.64/5.85 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.85 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 5.64/5.85 => ( ( Mi != Ma )
% 5.64/5.85 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.64/5.85 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % summaxma
% 5.64/5.85 thf(fact_1490_sum__squares__bound,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % sum_squares_bound
% 5.64/5.85 thf(fact_1491_sum__squares__bound,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % sum_squares_bound
% 5.64/5.85 thf(fact_1492_mul__def,axiom,
% 5.64/5.85 ( vEBT_VEBT_mul
% 5.64/5.85 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.64/5.85
% 5.64/5.85 % mul_def
% 5.64/5.85 thf(fact_1493_div__exp__eq,axiom,
% 5.64/5.85 ! [A: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.85 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_exp_eq
% 5.64/5.85 thf(fact_1494_div__exp__eq,axiom,
% 5.64/5.85 ! [A: int,M: nat,N: nat] :
% 5.64/5.85 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.85 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_exp_eq
% 5.64/5.85 thf(fact_1495_field__less__half__sum,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] :
% 5.64/5.85 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.85 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % field_less_half_sum
% 5.64/5.85 thf(fact_1496_field__less__half__sum,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat] :
% 5.64/5.85 ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.85 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % field_less_half_sum
% 5.64/5.85 thf(fact_1497_div__nat__eqI,axiom,
% 5.64/5.85 ! [N: nat,Q3: nat,M: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q3 ) @ M )
% 5.64/5.85 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q3 ) ) )
% 5.64/5.85 => ( ( divide_divide_nat @ M @ N )
% 5.64/5.85 = Q3 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_nat_eqI
% 5.64/5.85 thf(fact_1498_mul__shift,axiom,
% 5.64/5.85 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.85 ( ( ( times_times_nat @ X2 @ Y4 )
% 5.64/5.85 = Z )
% 5.64/5.85 = ( ( vEBT_VEBT_mul @ ( some_nat @ X2 ) @ ( some_nat @ Y4 ) )
% 5.64/5.85 = ( some_nat @ Z ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mul_shift
% 5.64/5.85 thf(fact_1499_power__minus__is__div,axiom,
% 5.64/5.85 ! [B: nat,A: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.85 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.85 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_minus_is_div
% 5.64/5.85 thf(fact_1500_add__diff__cancel,axiom,
% 5.64/5.85 ! [A: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel
% 5.64/5.85 thf(fact_1501_add__diff__cancel,axiom,
% 5.64/5.85 ! [A: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel
% 5.64/5.85 thf(fact_1502_add__diff__cancel,axiom,
% 5.64/5.85 ! [A: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel
% 5.64/5.85 thf(fact_1503_diff__add__cancel,axiom,
% 5.64/5.85 ! [A: real,B: real] :
% 5.64/5.85 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_cancel
% 5.64/5.85 thf(fact_1504_diff__add__cancel,axiom,
% 5.64/5.85 ! [A: rat,B: rat] :
% 5.64/5.85 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_cancel
% 5.64/5.85 thf(fact_1505_diff__add__cancel,axiom,
% 5.64/5.85 ! [A: int,B: int] :
% 5.64/5.85 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_cancel
% 5.64/5.85 thf(fact_1506_add__diff__cancel__left,axiom,
% 5.64/5.85 ! [C: real,A: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.64/5.85 = ( minus_minus_real @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left
% 5.64/5.85 thf(fact_1507_add__diff__cancel__left,axiom,
% 5.64/5.85 ! [C: rat,A: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.64/5.85 = ( minus_minus_rat @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left
% 5.64/5.85 thf(fact_1508_add__diff__cancel__left,axiom,
% 5.64/5.85 ! [C: nat,A: nat,B: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.64/5.85 = ( minus_minus_nat @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left
% 5.64/5.85 thf(fact_1509_add__diff__cancel__left,axiom,
% 5.64/5.85 ! [C: int,A: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.64/5.85 = ( minus_minus_int @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left
% 5.64/5.85 thf(fact_1510_add__diff__cancel__left_H,axiom,
% 5.64/5.85 ! [A: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.64/5.85 = B ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left'
% 5.64/5.85 thf(fact_1511_add__diff__cancel__left_H,axiom,
% 5.64/5.85 ! [A: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.64/5.85 = B ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left'
% 5.64/5.85 thf(fact_1512_add__diff__cancel__left_H,axiom,
% 5.64/5.85 ! [A: nat,B: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.64/5.85 = B ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left'
% 5.64/5.85 thf(fact_1513_add__diff__cancel__left_H,axiom,
% 5.64/5.85 ! [A: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.64/5.85 = B ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_left'
% 5.64/5.85 thf(fact_1514_add__diff__cancel__right,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.64/5.85 = ( minus_minus_real @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right
% 5.64/5.85 thf(fact_1515_add__diff__cancel__right,axiom,
% 5.64/5.85 ! [A: rat,C: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.85 = ( minus_minus_rat @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right
% 5.64/5.85 thf(fact_1516_add__diff__cancel__right,axiom,
% 5.64/5.85 ! [A: nat,C: nat,B: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.85 = ( minus_minus_nat @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right
% 5.64/5.85 thf(fact_1517_add__diff__cancel__right,axiom,
% 5.64/5.85 ! [A: int,C: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.64/5.85 = ( minus_minus_int @ A @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right
% 5.64/5.85 thf(fact_1518_add__diff__cancel__right_H,axiom,
% 5.64/5.85 ! [A: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right'
% 5.64/5.85 thf(fact_1519_add__diff__cancel__right_H,axiom,
% 5.64/5.85 ! [A: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right'
% 5.64/5.85 thf(fact_1520_add__diff__cancel__right_H,axiom,
% 5.64/5.85 ! [A: nat,B: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right'
% 5.64/5.85 thf(fact_1521_add__diff__cancel__right_H,axiom,
% 5.64/5.85 ! [A: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_cancel_right'
% 5.64/5.85 thf(fact_1522_bits__div__by__1,axiom,
% 5.64/5.85 ! [A: nat] :
% 5.64/5.85 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % bits_div_by_1
% 5.64/5.85 thf(fact_1523_bits__div__by__1,axiom,
% 5.64/5.85 ! [A: int] :
% 5.64/5.85 ( ( divide_divide_int @ A @ one_one_int )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % bits_div_by_1
% 5.64/5.85 thf(fact_1524_diff__Suc__Suc,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.64/5.85 = ( minus_minus_nat @ M @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_Suc_Suc
% 5.64/5.85 thf(fact_1525_Suc__diff__diff,axiom,
% 5.64/5.85 ! [M: nat,N: nat,K: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.64/5.85 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_diff_diff
% 5.64/5.85 thf(fact_1526_diff__diff__cancel,axiom,
% 5.64/5.85 ! [I: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ N )
% 5.64/5.85 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.64/5.85 = I ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_cancel
% 5.64/5.85 thf(fact_1527_diff__diff__left,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.64/5.85 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_left
% 5.64/5.85 thf(fact_1528_semiring__norm_I13_J,axiom,
% 5.64/5.85 ! [M: num,N: num] :
% 5.64/5.85 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.85 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % semiring_norm(13)
% 5.64/5.85 thf(fact_1529_semiring__norm_I11_J,axiom,
% 5.64/5.85 ! [M: num] :
% 5.64/5.85 ( ( times_times_num @ M @ one )
% 5.64/5.85 = M ) ).
% 5.64/5.85
% 5.64/5.85 % semiring_norm(11)
% 5.64/5.85 thf(fact_1530_semiring__norm_I12_J,axiom,
% 5.64/5.85 ! [N: num] :
% 5.64/5.85 ( ( times_times_num @ one @ N )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % semiring_norm(12)
% 5.64/5.85 thf(fact_1531_left__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [A: complex,B: complex,V: num] :
% 5.64/5.85 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.64/5.85 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_diff_distrib_numeral
% 5.64/5.85 thf(fact_1532_left__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [A: real,B: real,V: num] :
% 5.64/5.85 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.85 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_diff_distrib_numeral
% 5.64/5.85 thf(fact_1533_left__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [A: rat,B: rat,V: num] :
% 5.64/5.85 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.85 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_diff_distrib_numeral
% 5.64/5.85 thf(fact_1534_left__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [A: int,B: int,V: num] :
% 5.64/5.85 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.85 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % left_diff_distrib_numeral
% 5.64/5.85 thf(fact_1535_right__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [V: num,B: complex,C: complex] :
% 5.64/5.85 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.64/5.85 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % right_diff_distrib_numeral
% 5.64/5.85 thf(fact_1536_right__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [V: num,B: real,C: real] :
% 5.64/5.85 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.64/5.85 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % right_diff_distrib_numeral
% 5.64/5.85 thf(fact_1537_right__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [V: num,B: rat,C: rat] :
% 5.64/5.85 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.64/5.85 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % right_diff_distrib_numeral
% 5.64/5.85 thf(fact_1538_right__diff__distrib__numeral,axiom,
% 5.64/5.85 ! [V: num,B: int,C: int] :
% 5.64/5.85 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.64/5.85 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % right_diff_distrib_numeral
% 5.64/5.85 thf(fact_1539_diff__Suc__1,axiom,
% 5.64/5.85 ! [N: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.64/5.85 = N ) ).
% 5.64/5.85
% 5.64/5.85 % diff_Suc_1
% 5.64/5.85 thf(fact_1540_Nat_Oadd__diff__assoc,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.add_diff_assoc
% 5.64/5.85 thf(fact_1541_Nat_Oadd__diff__assoc2,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.add_diff_assoc2
% 5.64/5.85 thf(fact_1542_Nat_Odiff__diff__right,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.diff_diff_right
% 5.64/5.85 thf(fact_1543_num__double,axiom,
% 5.64/5.85 ! [N: num] :
% 5.64/5.85 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.64/5.85 = ( bit0 @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % num_double
% 5.64/5.85 thf(fact_1544_power__mult__numeral,axiom,
% 5.64/5.85 ! [A: nat,M: num,N: num] :
% 5.64/5.85 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.85 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult_numeral
% 5.64/5.85 thf(fact_1545_power__mult__numeral,axiom,
% 5.64/5.85 ! [A: real,M: num,N: num] :
% 5.64/5.85 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.85 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult_numeral
% 5.64/5.85 thf(fact_1546_power__mult__numeral,axiom,
% 5.64/5.85 ! [A: int,M: num,N: num] :
% 5.64/5.85 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.85 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult_numeral
% 5.64/5.85 thf(fact_1547_power__mult__numeral,axiom,
% 5.64/5.85 ! [A: complex,M: num,N: num] :
% 5.64/5.85 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.85 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power_mult_numeral
% 5.64/5.85 thf(fact_1548_option_Ocollapse,axiom,
% 5.64/5.85 ! [Option: option4927543243414619207at_nat] :
% 5.64/5.85 ( ( Option != none_P5556105721700978146at_nat )
% 5.64/5.85 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.64/5.85 = Option ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.collapse
% 5.64/5.85 thf(fact_1549_option_Ocollapse,axiom,
% 5.64/5.85 ! [Option: option_nat] :
% 5.64/5.85 ( ( Option != none_nat )
% 5.64/5.85 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.64/5.85 = Option ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.collapse
% 5.64/5.85 thf(fact_1550_option_Ocollapse,axiom,
% 5.64/5.85 ! [Option: option_num] :
% 5.64/5.85 ( ( Option != none_num )
% 5.64/5.85 => ( ( some_num @ ( the_num @ Option ) )
% 5.64/5.85 = Option ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.collapse
% 5.64/5.85 thf(fact_1551_diff__Suc__diff__eq1,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_Suc_diff_eq1
% 5.64/5.85 thf(fact_1552_diff__Suc__diff__eq2,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.64/5.85 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_Suc_diff_eq2
% 5.64/5.85 thf(fact_1553_diff__eq__diff__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.85 ( ( ( minus_minus_real @ A @ B )
% 5.64/5.85 = ( minus_minus_real @ C @ D ) )
% 5.64/5.85 => ( ( A = B )
% 5.64/5.85 = ( C = D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_eq
% 5.64/5.85 thf(fact_1554_diff__eq__diff__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.85 ( ( ( minus_minus_rat @ A @ B )
% 5.64/5.85 = ( minus_minus_rat @ C @ D ) )
% 5.64/5.85 => ( ( A = B )
% 5.64/5.85 = ( C = D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_eq
% 5.64/5.85 thf(fact_1555_diff__eq__diff__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.85 ( ( ( minus_minus_int @ A @ B )
% 5.64/5.85 = ( minus_minus_int @ C @ D ) )
% 5.64/5.85 => ( ( A = B )
% 5.64/5.85 = ( C = D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_eq
% 5.64/5.85 thf(fact_1556_diff__right__commute,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.64/5.85 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_commute
% 5.64/5.85 thf(fact_1557_diff__right__commute,axiom,
% 5.64/5.85 ! [A: rat,C: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.64/5.85 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_commute
% 5.64/5.85 thf(fact_1558_diff__right__commute,axiom,
% 5.64/5.85 ! [A: nat,C: nat,B: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.64/5.85 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_commute
% 5.64/5.85 thf(fact_1559_diff__right__commute,axiom,
% 5.64/5.85 ! [A: int,C: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.64/5.85 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_commute
% 5.64/5.85 thf(fact_1560_diff__commute,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.64/5.85 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_commute
% 5.64/5.85 thf(fact_1561_add__diff__add,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real,D: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.64/5.85 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_add
% 5.64/5.85 thf(fact_1562_add__diff__add,axiom,
% 5.64/5.85 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.64/5.85 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_add
% 5.64/5.85 thf(fact_1563_add__diff__add,axiom,
% 5.64/5.85 ! [A: int,C: int,B: int,D: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.64/5.85 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_add
% 5.64/5.85 thf(fact_1564_diff__mono,axiom,
% 5.64/5.85 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.85 => ( ( ord_less_eq_rat @ D @ C )
% 5.64/5.85 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_mono
% 5.64/5.85 thf(fact_1565_diff__mono,axiom,
% 5.64/5.85 ! [A: int,B: int,D: int,C: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.85 => ( ( ord_less_eq_int @ D @ C )
% 5.64/5.85 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_mono
% 5.64/5.85 thf(fact_1566_diff__mono,axiom,
% 5.64/5.85 ! [A: real,B: real,D: real,C: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.85 => ( ( ord_less_eq_real @ D @ C )
% 5.64/5.85 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_mono
% 5.64/5.85 thf(fact_1567_diff__left__mono,axiom,
% 5.64/5.85 ! [B: rat,A: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.85 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_left_mono
% 5.64/5.85 thf(fact_1568_diff__left__mono,axiom,
% 5.64/5.85 ! [B: int,A: int,C: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.85 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_left_mono
% 5.64/5.85 thf(fact_1569_diff__left__mono,axiom,
% 5.64/5.85 ! [B: real,A: real,C: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.85 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_left_mono
% 5.64/5.85 thf(fact_1570_diff__right__mono,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.85 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_mono
% 5.64/5.85 thf(fact_1571_diff__right__mono,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.85 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_mono
% 5.64/5.85 thf(fact_1572_diff__right__mono,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.85 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_right_mono
% 5.64/5.85 thf(fact_1573_diff__eq__diff__less__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.85 ( ( ( minus_minus_rat @ A @ B )
% 5.64/5.85 = ( minus_minus_rat @ C @ D ) )
% 5.64/5.85 => ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.85 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_less_eq
% 5.64/5.85 thf(fact_1574_diff__eq__diff__less__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.85 ( ( ( minus_minus_int @ A @ B )
% 5.64/5.85 = ( minus_minus_int @ C @ D ) )
% 5.64/5.85 => ( ( ord_less_eq_int @ A @ B )
% 5.64/5.85 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_less_eq
% 5.64/5.85 thf(fact_1575_diff__eq__diff__less__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.85 ( ( ( minus_minus_real @ A @ B )
% 5.64/5.85 = ( minus_minus_real @ C @ D ) )
% 5.64/5.85 => ( ( ord_less_eq_real @ A @ B )
% 5.64/5.85 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_less_eq
% 5.64/5.85 thf(fact_1576_diff__strict__mono,axiom,
% 5.64/5.85 ! [A: real,B: real,D: real,C: real] :
% 5.64/5.85 ( ( ord_less_real @ A @ B )
% 5.64/5.85 => ( ( ord_less_real @ D @ C )
% 5.64/5.85 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_mono
% 5.64/5.85 thf(fact_1577_diff__strict__mono,axiom,
% 5.64/5.85 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_rat @ A @ B )
% 5.64/5.85 => ( ( ord_less_rat @ D @ C )
% 5.64/5.85 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_mono
% 5.64/5.85 thf(fact_1578_diff__strict__mono,axiom,
% 5.64/5.85 ! [A: int,B: int,D: int,C: int] :
% 5.64/5.85 ( ( ord_less_int @ A @ B )
% 5.64/5.85 => ( ( ord_less_int @ D @ C )
% 5.64/5.85 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_mono
% 5.64/5.85 thf(fact_1579_diff__eq__diff__less,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.85 ( ( ( minus_minus_real @ A @ B )
% 5.64/5.85 = ( minus_minus_real @ C @ D ) )
% 5.64/5.85 => ( ( ord_less_real @ A @ B )
% 5.64/5.85 = ( ord_less_real @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_less
% 5.64/5.85 thf(fact_1580_diff__eq__diff__less,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.85 ( ( ( minus_minus_rat @ A @ B )
% 5.64/5.85 = ( minus_minus_rat @ C @ D ) )
% 5.64/5.85 => ( ( ord_less_rat @ A @ B )
% 5.64/5.85 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_less
% 5.64/5.85 thf(fact_1581_diff__eq__diff__less,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.85 ( ( ( minus_minus_int @ A @ B )
% 5.64/5.85 = ( minus_minus_int @ C @ D ) )
% 5.64/5.85 => ( ( ord_less_int @ A @ B )
% 5.64/5.85 = ( ord_less_int @ C @ D ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_diff_less
% 5.64/5.85 thf(fact_1582_diff__strict__left__mono,axiom,
% 5.64/5.85 ! [B: real,A: real,C: real] :
% 5.64/5.85 ( ( ord_less_real @ B @ A )
% 5.64/5.85 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_left_mono
% 5.64/5.85 thf(fact_1583_diff__strict__left__mono,axiom,
% 5.64/5.85 ! [B: rat,A: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_rat @ B @ A )
% 5.64/5.85 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_left_mono
% 5.64/5.85 thf(fact_1584_diff__strict__left__mono,axiom,
% 5.64/5.85 ! [B: int,A: int,C: int] :
% 5.64/5.85 ( ( ord_less_int @ B @ A )
% 5.64/5.85 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_left_mono
% 5.64/5.85 thf(fact_1585_diff__strict__right__mono,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( ord_less_real @ A @ B )
% 5.64/5.85 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_right_mono
% 5.64/5.85 thf(fact_1586_diff__strict__right__mono,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_rat @ A @ B )
% 5.64/5.85 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_right_mono
% 5.64/5.85 thf(fact_1587_diff__strict__right__mono,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( ord_less_int @ A @ B )
% 5.64/5.85 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_strict_right_mono
% 5.64/5.85 thf(fact_1588_group__cancel_Osub1,axiom,
% 5.64/5.85 ! [A4: real,K: real,A: real,B: real] :
% 5.64/5.85 ( ( A4
% 5.64/5.85 = ( plus_plus_real @ K @ A ) )
% 5.64/5.85 => ( ( minus_minus_real @ A4 @ B )
% 5.64/5.85 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % group_cancel.sub1
% 5.64/5.85 thf(fact_1589_group__cancel_Osub1,axiom,
% 5.64/5.85 ! [A4: rat,K: rat,A: rat,B: rat] :
% 5.64/5.85 ( ( A4
% 5.64/5.85 = ( plus_plus_rat @ K @ A ) )
% 5.64/5.85 => ( ( minus_minus_rat @ A4 @ B )
% 5.64/5.85 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % group_cancel.sub1
% 5.64/5.85 thf(fact_1590_group__cancel_Osub1,axiom,
% 5.64/5.85 ! [A4: int,K: int,A: int,B: int] :
% 5.64/5.85 ( ( A4
% 5.64/5.85 = ( plus_plus_int @ K @ A ) )
% 5.64/5.85 => ( ( minus_minus_int @ A4 @ B )
% 5.64/5.85 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % group_cancel.sub1
% 5.64/5.85 thf(fact_1591_diff__eq__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( ( minus_minus_real @ A @ B )
% 5.64/5.85 = C )
% 5.64/5.85 = ( A
% 5.64/5.85 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_eq
% 5.64/5.85 thf(fact_1592_diff__eq__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( ( minus_minus_rat @ A @ B )
% 5.64/5.85 = C )
% 5.64/5.85 = ( A
% 5.64/5.85 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_eq
% 5.64/5.85 thf(fact_1593_diff__eq__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( ( minus_minus_int @ A @ B )
% 5.64/5.85 = C )
% 5.64/5.85 = ( A
% 5.64/5.85 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_eq_eq
% 5.64/5.85 thf(fact_1594_eq__diff__eq,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real] :
% 5.64/5.85 ( ( A
% 5.64/5.85 = ( minus_minus_real @ C @ B ) )
% 5.64/5.85 = ( ( plus_plus_real @ A @ B )
% 5.64/5.85 = C ) ) ).
% 5.64/5.85
% 5.64/5.85 % eq_diff_eq
% 5.64/5.85 thf(fact_1595_eq__diff__eq,axiom,
% 5.64/5.85 ! [A: rat,C: rat,B: rat] :
% 5.64/5.85 ( ( A
% 5.64/5.85 = ( minus_minus_rat @ C @ B ) )
% 5.64/5.85 = ( ( plus_plus_rat @ A @ B )
% 5.64/5.85 = C ) ) ).
% 5.64/5.85
% 5.64/5.85 % eq_diff_eq
% 5.64/5.85 thf(fact_1596_eq__diff__eq,axiom,
% 5.64/5.85 ! [A: int,C: int,B: int] :
% 5.64/5.85 ( ( A
% 5.64/5.85 = ( minus_minus_int @ C @ B ) )
% 5.64/5.85 = ( ( plus_plus_int @ A @ B )
% 5.64/5.85 = C ) ) ).
% 5.64/5.85
% 5.64/5.85 % eq_diff_eq
% 5.64/5.85 thf(fact_1597_add__diff__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.64/5.85 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_eq
% 5.64/5.85 thf(fact_1598_add__diff__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.64/5.85 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_eq
% 5.64/5.85 thf(fact_1599_add__diff__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.64/5.85 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_eq
% 5.64/5.85 thf(fact_1600_diff__diff__eq2,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.64/5.85 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq2
% 5.64/5.85 thf(fact_1601_diff__diff__eq2,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.64/5.85 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq2
% 5.64/5.85 thf(fact_1602_diff__diff__eq2,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.64/5.85 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq2
% 5.64/5.85 thf(fact_1603_diff__add__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_eq
% 5.64/5.85 thf(fact_1604_diff__add__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_eq
% 5.64/5.85 thf(fact_1605_diff__add__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_eq
% 5.64/5.85 thf(fact_1606_diff__add__eq__diff__diff__swap,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.64/5.85 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_eq_diff_diff_swap
% 5.64/5.85 thf(fact_1607_diff__add__eq__diff__diff__swap,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.85 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_eq_diff_diff_swap
% 5.64/5.85 thf(fact_1608_diff__add__eq__diff__diff__swap,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.64/5.85 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_eq_diff_diff_swap
% 5.64/5.85 thf(fact_1609_add__implies__diff,axiom,
% 5.64/5.85 ! [C: real,B: real,A: real] :
% 5.64/5.85 ( ( ( plus_plus_real @ C @ B )
% 5.64/5.85 = A )
% 5.64/5.85 => ( C
% 5.64/5.85 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_implies_diff
% 5.64/5.85 thf(fact_1610_add__implies__diff,axiom,
% 5.64/5.85 ! [C: rat,B: rat,A: rat] :
% 5.64/5.85 ( ( ( plus_plus_rat @ C @ B )
% 5.64/5.85 = A )
% 5.64/5.85 => ( C
% 5.64/5.85 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_implies_diff
% 5.64/5.85 thf(fact_1611_add__implies__diff,axiom,
% 5.64/5.85 ! [C: nat,B: nat,A: nat] :
% 5.64/5.85 ( ( ( plus_plus_nat @ C @ B )
% 5.64/5.85 = A )
% 5.64/5.85 => ( C
% 5.64/5.85 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_implies_diff
% 5.64/5.85 thf(fact_1612_add__implies__diff,axiom,
% 5.64/5.85 ! [C: int,B: int,A: int] :
% 5.64/5.85 ( ( ( plus_plus_int @ C @ B )
% 5.64/5.85 = A )
% 5.64/5.85 => ( C
% 5.64/5.85 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_implies_diff
% 5.64/5.85 thf(fact_1613_diff__diff__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq
% 5.64/5.85 thf(fact_1614_diff__diff__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq
% 5.64/5.85 thf(fact_1615_diff__diff__eq,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq
% 5.64/5.85 thf(fact_1616_diff__diff__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.64/5.85 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_diff_eq
% 5.64/5.85 thf(fact_1617_zero__induct__lemma,axiom,
% 5.64/5.85 ! [P: nat > $o,K: nat,I: nat] :
% 5.64/5.85 ( ( P @ K )
% 5.64/5.85 => ( ! [N3: nat] :
% 5.64/5.85 ( ( P @ ( suc @ N3 ) )
% 5.64/5.85 => ( P @ N3 ) )
% 5.64/5.85 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % zero_induct_lemma
% 5.64/5.85 thf(fact_1618_diff__less__mono2,axiom,
% 5.64/5.85 ! [M: nat,N: nat,L: nat] :
% 5.64/5.85 ( ( ord_less_nat @ M @ N )
% 5.64/5.85 => ( ( ord_less_nat @ M @ L )
% 5.64/5.85 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_less_mono2
% 5.64/5.85 thf(fact_1619_less__imp__diff__less,axiom,
% 5.64/5.85 ! [J: nat,K: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_nat @ J @ K )
% 5.64/5.85 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_imp_diff_less
% 5.64/5.85 thf(fact_1620_eq__diff__iff,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.85 => ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.85 => ( ( ( minus_minus_nat @ M @ K )
% 5.64/5.85 = ( minus_minus_nat @ N @ K ) )
% 5.64/5.85 = ( M = N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % eq_diff_iff
% 5.64/5.85 thf(fact_1621_le__diff__iff,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.85 => ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.85 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.64/5.85 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_diff_iff
% 5.64/5.85 thf(fact_1622_Nat_Odiff__diff__eq,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.85 => ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.85 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.64/5.85 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.diff_diff_eq
% 5.64/5.85 thf(fact_1623_diff__le__mono,axiom,
% 5.64/5.85 ! [M: nat,N: nat,L: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.85 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_mono
% 5.64/5.85 thf(fact_1624_diff__le__self,axiom,
% 5.64/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_self
% 5.64/5.85 thf(fact_1625_le__diff__iff_H,axiom,
% 5.64/5.85 ! [A: nat,C: nat,B: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ C )
% 5.64/5.85 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.85 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.64/5.85 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_diff_iff'
% 5.64/5.85 thf(fact_1626_diff__le__mono2,axiom,
% 5.64/5.85 ! [M: nat,N: nat,L: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.85 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_mono2
% 5.64/5.85 thf(fact_1627_Nat_Odiff__cancel,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.64/5.85 = ( minus_minus_nat @ M @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.diff_cancel
% 5.64/5.85 thf(fact_1628_diff__cancel2,axiom,
% 5.64/5.85 ! [M: nat,K: nat,N: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.64/5.85 = ( minus_minus_nat @ M @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_cancel2
% 5.64/5.85 thf(fact_1629_diff__add__inverse,axiom,
% 5.64/5.85 ! [N: nat,M: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.64/5.85 = M ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_inverse
% 5.64/5.85 thf(fact_1630_diff__add__inverse2,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.64/5.85 = M ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add_inverse2
% 5.64/5.85 thf(fact_1631_diff__mult__distrib,axiom,
% 5.64/5.85 ! [M: nat,N: nat,K: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.64/5.85 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_mult_distrib
% 5.64/5.85 thf(fact_1632_diff__mult__distrib2,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.85 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_mult_distrib2
% 5.64/5.85 thf(fact_1633_mult__diff__mult,axiom,
% 5.64/5.85 ! [X2: real,Y4: real,A: real,B: real] :
% 5.64/5.85 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y4 ) @ ( times_times_real @ A @ B ) )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y4 @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_diff_mult
% 5.64/5.85 thf(fact_1634_mult__diff__mult,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat,A: rat,B: rat] :
% 5.64/5.85 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ Y4 ) @ ( times_times_rat @ A @ B ) )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ X2 @ ( minus_minus_rat @ Y4 @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X2 @ A ) @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_diff_mult
% 5.64/5.85 thf(fact_1635_mult__diff__mult,axiom,
% 5.64/5.85 ! [X2: int,Y4: int,A: int,B: int] :
% 5.64/5.85 ( ( minus_minus_int @ ( times_times_int @ X2 @ Y4 ) @ ( times_times_int @ A @ B ) )
% 5.64/5.85 = ( plus_plus_int @ ( times_times_int @ X2 @ ( minus_minus_int @ Y4 @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X2 @ A ) @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % mult_diff_mult
% 5.64/5.85 thf(fact_1636_div__mult2__numeral__eq,axiom,
% 5.64/5.85 ! [A: nat,K: num,L: num] :
% 5.64/5.85 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.64/5.85 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_mult2_numeral_eq
% 5.64/5.85 thf(fact_1637_div__mult2__numeral__eq,axiom,
% 5.64/5.85 ! [A: int,K: num,L: num] :
% 5.64/5.85 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.64/5.85 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_mult2_numeral_eq
% 5.64/5.85 thf(fact_1638_option_Osel,axiom,
% 5.64/5.85 ! [X22: product_prod_nat_nat] :
% 5.64/5.85 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.64/5.85 = X22 ) ).
% 5.64/5.85
% 5.64/5.85 % option.sel
% 5.64/5.85 thf(fact_1639_option_Osel,axiom,
% 5.64/5.85 ! [X22: nat] :
% 5.64/5.85 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.64/5.85 = X22 ) ).
% 5.64/5.85
% 5.64/5.85 % option.sel
% 5.64/5.85 thf(fact_1640_option_Osel,axiom,
% 5.64/5.85 ! [X22: num] :
% 5.64/5.85 ( ( the_num @ ( some_num @ X22 ) )
% 5.64/5.85 = X22 ) ).
% 5.64/5.85
% 5.64/5.85 % option.sel
% 5.64/5.85 thf(fact_1641_option_Oexpand,axiom,
% 5.64/5.85 ! [Option: option_nat,Option2: option_nat] :
% 5.64/5.85 ( ( ( Option = none_nat )
% 5.64/5.85 = ( Option2 = none_nat ) )
% 5.64/5.85 => ( ( ( Option != none_nat )
% 5.64/5.85 => ( ( Option2 != none_nat )
% 5.64/5.85 => ( ( the_nat @ Option )
% 5.64/5.85 = ( the_nat @ Option2 ) ) ) )
% 5.64/5.85 => ( Option = Option2 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.expand
% 5.64/5.85 thf(fact_1642_option_Oexpand,axiom,
% 5.64/5.85 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.64/5.85 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.64/5.85 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.64/5.85 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.64/5.85 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.64/5.85 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.64/5.85 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.64/5.85 => ( Option = Option2 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.expand
% 5.64/5.85 thf(fact_1643_option_Oexpand,axiom,
% 5.64/5.85 ! [Option: option_num,Option2: option_num] :
% 5.64/5.85 ( ( ( Option = none_num )
% 5.64/5.85 = ( Option2 = none_num ) )
% 5.64/5.85 => ( ( ( Option != none_num )
% 5.64/5.85 => ( ( Option2 != none_num )
% 5.64/5.85 => ( ( the_num @ Option )
% 5.64/5.85 = ( the_num @ Option2 ) ) ) )
% 5.64/5.85 => ( Option = Option2 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.expand
% 5.64/5.85 thf(fact_1644_diff__le__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.64/5.85 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_eq
% 5.64/5.85 thf(fact_1645_diff__le__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.64/5.85 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_eq
% 5.64/5.85 thf(fact_1646_diff__le__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.64/5.85 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_eq
% 5.64/5.85 thf(fact_1647_le__diff__eq,axiom,
% 5.64/5.85 ! [A: rat,C: rat,B: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.64/5.85 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_diff_eq
% 5.64/5.85 thf(fact_1648_le__diff__eq,axiom,
% 5.64/5.85 ! [A: int,C: int,B: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.64/5.85 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_diff_eq
% 5.64/5.85 thf(fact_1649_le__diff__eq,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.64/5.85 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_diff_eq
% 5.64/5.85 thf(fact_1650_diff__add,axiom,
% 5.64/5.85 ! [A: nat,B: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.64/5.85 = B ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_add
% 5.64/5.85 thf(fact_1651_le__add__diff,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff
% 5.64/5.85 thf(fact_1652_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.64/5.85 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.64/5.85 thf(fact_1653_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.64/5.85 thf(fact_1654_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.64/5.85 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.64/5.85 thf(fact_1655_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.64/5.85 thf(fact_1656_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.64/5.85 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.64/5.85 thf(fact_1657_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.64/5.85 thf(fact_1658_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.64/5.85 ! [A: nat,B: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.64/5.85 = B ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.64/5.85 thf(fact_1659_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.85 => ( ( ( minus_minus_nat @ B @ A )
% 5.64/5.85 = C )
% 5.64/5.85 = ( B
% 5.64/5.85 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.64/5.85 thf(fact_1660_less__diff__eq,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real] :
% 5.64/5.85 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.64/5.85 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_diff_eq
% 5.64/5.85 thf(fact_1661_less__diff__eq,axiom,
% 5.64/5.85 ! [A: rat,C: rat,B: rat] :
% 5.64/5.85 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.64/5.85 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_diff_eq
% 5.64/5.85 thf(fact_1662_less__diff__eq,axiom,
% 5.64/5.85 ! [A: int,C: int,B: int] :
% 5.64/5.85 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.64/5.85 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_diff_eq
% 5.64/5.85 thf(fact_1663_diff__less__eq,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.64/5.85 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_less_eq
% 5.64/5.85 thf(fact_1664_diff__less__eq,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.64/5.85 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_less_eq
% 5.64/5.85 thf(fact_1665_diff__less__eq,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.64/5.85 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_less_eq
% 5.64/5.85 thf(fact_1666_L2__set__mult__ineq__lemma,axiom,
% 5.64/5.85 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % L2_set_mult_ineq_lemma
% 5.64/5.85 thf(fact_1667_four__x__squared,axiom,
% 5.64/5.85 ! [X2: real] :
% 5.64/5.85 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % four_x_squared
% 5.64/5.85 thf(fact_1668_Suc__diff__Suc,axiom,
% 5.64/5.85 ! [N: nat,M: nat] :
% 5.64/5.85 ( ( ord_less_nat @ N @ M )
% 5.64/5.85 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.64/5.85 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_diff_Suc
% 5.64/5.85 thf(fact_1669_diff__less__Suc,axiom,
% 5.64/5.85 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_less_Suc
% 5.64/5.85 thf(fact_1670_Suc__diff__le,axiom,
% 5.64/5.85 ! [N: nat,M: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.85 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.64/5.85 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_diff_le
% 5.64/5.85 thf(fact_1671_diff__less__mono,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( ord_less_nat @ A @ B )
% 5.64/5.85 => ( ( ord_less_eq_nat @ C @ A )
% 5.64/5.85 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_less_mono
% 5.64/5.85 thf(fact_1672_less__diff__iff,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.85 => ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.85 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.64/5.85 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_diff_iff
% 5.64/5.85 thf(fact_1673_add__diff__inverse__nat,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ~ ( ord_less_nat @ M @ N )
% 5.64/5.85 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.85 = M ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_inverse_nat
% 5.64/5.85 thf(fact_1674_less__diff__conv,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.64/5.85 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_diff_conv
% 5.64/5.85 thf(fact_1675_diff__Suc__eq__diff__pred,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.64/5.85 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_Suc_eq_diff_pred
% 5.64/5.85 thf(fact_1676_le__diff__conv,axiom,
% 5.64/5.85 ! [J: nat,K: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.64/5.85 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_diff_conv
% 5.64/5.85 thf(fact_1677_Nat_Ole__diff__conv2,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.64/5.85 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.le_diff_conv2
% 5.64/5.85 thf(fact_1678_Nat_Odiff__add__assoc,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.64/5.85 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.diff_add_assoc
% 5.64/5.85 thf(fact_1679_Nat_Odiff__add__assoc2,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.64/5.85 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.diff_add_assoc2
% 5.64/5.85 thf(fact_1680_Nat_Ole__imp__diff__is__add,axiom,
% 5.64/5.85 ! [I: nat,J: nat,K: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ( ( minus_minus_nat @ J @ I )
% 5.64/5.85 = K )
% 5.64/5.85 = ( J
% 5.64/5.85 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % Nat.le_imp_diff_is_add
% 5.64/5.85 thf(fact_1681_option_Oexhaust__sel,axiom,
% 5.64/5.85 ! [Option: option4927543243414619207at_nat] :
% 5.64/5.85 ( ( Option != none_P5556105721700978146at_nat )
% 5.64/5.85 => ( Option
% 5.64/5.85 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.exhaust_sel
% 5.64/5.85 thf(fact_1682_option_Oexhaust__sel,axiom,
% 5.64/5.85 ! [Option: option_nat] :
% 5.64/5.85 ( ( Option != none_nat )
% 5.64/5.85 => ( Option
% 5.64/5.85 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.exhaust_sel
% 5.64/5.85 thf(fact_1683_option_Oexhaust__sel,axiom,
% 5.64/5.85 ! [Option: option_num] :
% 5.64/5.85 ( ( Option != none_num )
% 5.64/5.85 => ( Option
% 5.64/5.85 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % option.exhaust_sel
% 5.64/5.85 thf(fact_1684_less__diff__conv2,axiom,
% 5.64/5.85 ! [K: nat,J: nat,I: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ K @ J )
% 5.64/5.85 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.64/5.85 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_diff_conv2
% 5.64/5.85 thf(fact_1685_nat__eq__add__iff1,axiom,
% 5.64/5.85 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ J @ I )
% 5.64/5.85 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.64/5.85 = N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_eq_add_iff1
% 5.64/5.85 thf(fact_1686_nat__eq__add__iff2,axiom,
% 5.64/5.85 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( M
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_eq_add_iff2
% 5.64/5.85 thf(fact_1687_nat__le__add__iff1,axiom,
% 5.64/5.85 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ J @ I )
% 5.64/5.85 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_le_add_iff1
% 5.64/5.85 thf(fact_1688_nat__le__add__iff2,axiom,
% 5.64/5.85 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_le_add_iff2
% 5.64/5.85 thf(fact_1689_nat__diff__add__eq1,axiom,
% 5.64/5.85 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ J @ I )
% 5.64/5.85 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_diff_add_eq1
% 5.64/5.85 thf(fact_1690_nat__diff__add__eq2,axiom,
% 5.64/5.85 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_diff_add_eq2
% 5.64/5.85 thf(fact_1691_vebt__mint_Osimps_I2_J,axiom,
% 5.64/5.85 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.64/5.85 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.64/5.85 = none_nat ) ).
% 5.64/5.85
% 5.64/5.85 % vebt_mint.simps(2)
% 5.64/5.85 thf(fact_1692_vebt__maxt_Osimps_I2_J,axiom,
% 5.64/5.85 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.64/5.85 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.64/5.85 = none_nat ) ).
% 5.64/5.85
% 5.64/5.85 % vebt_maxt.simps(2)
% 5.64/5.85 thf(fact_1693_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I2_J,axiom,
% 5.64/5.85 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X2: nat] :
% 5.64/5.85 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X2 )
% 5.64/5.85 = one_one_nat ) ).
% 5.64/5.85
% 5.64/5.85 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(2)
% 5.64/5.85 thf(fact_1694_power2__commute,axiom,
% 5.64/5.85 ! [X2: complex,Y4: complex] :
% 5.64/5.85 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( power_power_complex @ ( minus_minus_complex @ Y4 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_commute
% 5.64/5.85 thf(fact_1695_power2__commute,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] :
% 5.64/5.85 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( power_power_real @ ( minus_minus_real @ Y4 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_commute
% 5.64/5.85 thf(fact_1696_power2__commute,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat] :
% 5.64/5.85 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( power_power_rat @ ( minus_minus_rat @ Y4 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_commute
% 5.64/5.85 thf(fact_1697_power2__commute,axiom,
% 5.64/5.85 ! [X2: int,Y4: int] :
% 5.64/5.85 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( power_power_int @ ( minus_minus_int @ Y4 @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_commute
% 5.64/5.85 thf(fact_1698_nat__less__add__iff1,axiom,
% 5.64/5.85 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ J @ I )
% 5.64/5.85 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_less_add_iff1
% 5.64/5.85 thf(fact_1699_nat__less__add__iff2,axiom,
% 5.64/5.85 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.85 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.64/5.85 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % nat_less_add_iff2
% 5.64/5.85 thf(fact_1700_diff__le__diff__pow,axiom,
% 5.64/5.85 ! [K: nat,M: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.64/5.85 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % diff_le_diff_pow
% 5.64/5.85 thf(fact_1701_two__realpow__ge__one,axiom,
% 5.64/5.85 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % two_realpow_ge_one
% 5.64/5.85 thf(fact_1702_power2__diff,axiom,
% 5.64/5.85 ! [X2: complex,Y4: complex] :
% 5.64/5.85 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_diff
% 5.64/5.85 thf(fact_1703_power2__diff,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] :
% 5.64/5.85 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_diff
% 5.64/5.85 thf(fact_1704_power2__diff,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat] :
% 5.64/5.85 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_diff
% 5.64/5.85 thf(fact_1705_power2__diff,axiom,
% 5.64/5.85 ! [X2: int,Y4: int] :
% 5.64/5.85 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % power2_diff
% 5.64/5.85 thf(fact_1706_div__le__mono,axiom,
% 5.64/5.85 ! [M: nat,N: nat,K: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.85 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_le_mono
% 5.64/5.85 thf(fact_1707_div__le__dividend,axiom,
% 5.64/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.64/5.85
% 5.64/5.85 % div_le_dividend
% 5.64/5.85 thf(fact_1708_div__mult2__eq,axiom,
% 5.64/5.85 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.85 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q3 ) )
% 5.64/5.85 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q3 ) ) ).
% 5.64/5.85
% 5.64/5.85 % div_mult2_eq
% 5.64/5.85 thf(fact_1709_Suc__div__le__mono,axiom,
% 5.64/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_div_le_mono
% 5.64/5.85 thf(fact_1710_invar__vebt_Ointros_I2_J,axiom,
% 5.64/5.85 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.64/5.85 ( ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.64/5.85 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.64/5.85 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.64/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( M = N )
% 5.64/5.85 => ( ( Deg
% 5.64/5.85 = ( plus_plus_nat @ N @ M ) )
% 5.64/5.85 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.64/5.85 => ( ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % invar_vebt.intros(2)
% 5.64/5.85 thf(fact_1711_less__mult__imp__div__less,axiom,
% 5.64/5.85 ! [M: nat,I: nat,N: nat] :
% 5.64/5.85 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.64/5.85 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_mult_imp_div_less
% 5.64/5.85 thf(fact_1712_times__div__less__eq__dividend,axiom,
% 5.64/5.85 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.64/5.85
% 5.64/5.85 % times_div_less_eq_dividend
% 5.64/5.85 thf(fact_1713_div__times__less__eq__dividend,axiom,
% 5.64/5.85 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.64/5.85
% 5.64/5.85 % div_times_less_eq_dividend
% 5.64/5.85 thf(fact_1714_invar__vebt_Ointros_I3_J,axiom,
% 5.64/5.85 ! [TreeList: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.64/5.85 ( ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.64/5.85 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.64/5.85 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.64/5.85 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 => ( ( M
% 5.64/5.85 = ( suc @ N ) )
% 5.64/5.85 => ( ( Deg
% 5.64/5.85 = ( plus_plus_nat @ N @ M ) )
% 5.64/5.85 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.64/5.85 => ( ! [X4: vEBT_VEBT] :
% 5.64/5.85 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/5.85 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 5.64/5.85 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % invar_vebt.intros(3)
% 5.64/5.85 thf(fact_1715_numeral__Bit0__div__2,axiom,
% 5.64/5.85 ! [N: num] :
% 5.64/5.85 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % numeral_Bit0_div_2
% 5.64/5.85 thf(fact_1716_numeral__Bit0__div__2,axiom,
% 5.64/5.85 ! [N: num] :
% 5.64/5.85 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.85 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % numeral_Bit0_div_2
% 5.64/5.85 thf(fact_1717_field__sum__of__halves,axiom,
% 5.64/5.85 ! [X2: real] :
% 5.64/5.85 ( ( plus_plus_real @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = X2 ) ).
% 5.64/5.85
% 5.64/5.85 % field_sum_of_halves
% 5.64/5.85 thf(fact_1718_field__sum__of__halves,axiom,
% 5.64/5.85 ! [X2: rat] :
% 5.64/5.85 ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.64/5.85 = X2 ) ).
% 5.64/5.85
% 5.64/5.85 % field_sum_of_halves
% 5.64/5.85 thf(fact_1719_le__add__diff__inverse,axiom,
% 5.64/5.85 ! [B: rat,A: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.85 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse
% 5.64/5.85 thf(fact_1720_le__add__diff__inverse,axiom,
% 5.64/5.85 ! [B: nat,A: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.85 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse
% 5.64/5.85 thf(fact_1721_le__add__diff__inverse,axiom,
% 5.64/5.85 ! [B: int,A: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.85 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse
% 5.64/5.85 thf(fact_1722_le__add__diff__inverse,axiom,
% 5.64/5.85 ! [B: real,A: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.85 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse
% 5.64/5.85 thf(fact_1723_le__add__diff__inverse2,axiom,
% 5.64/5.85 ! [B: rat,A: rat] :
% 5.64/5.85 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.85 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse2
% 5.64/5.85 thf(fact_1724_le__add__diff__inverse2,axiom,
% 5.64/5.85 ! [B: nat,A: nat] :
% 5.64/5.85 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.85 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse2
% 5.64/5.85 thf(fact_1725_le__add__diff__inverse2,axiom,
% 5.64/5.85 ! [B: int,A: int] :
% 5.64/5.85 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.85 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse2
% 5.64/5.85 thf(fact_1726_le__add__diff__inverse2,axiom,
% 5.64/5.85 ! [B: real,A: real] :
% 5.64/5.85 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.85 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.64/5.85 = A ) ) ).
% 5.64/5.85
% 5.64/5.85 % le_add_diff_inverse2
% 5.64/5.85 thf(fact_1727_vebt__insert_Osimps_I4_J,axiom,
% 5.64/5.85 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.85 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.85 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 5.64/5.85
% 5.64/5.85 % vebt_insert.simps(4)
% 5.64/5.85 thf(fact_1728_double__not__eq__Suc__double,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.64/5.85 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % double_not_eq_Suc_double
% 5.64/5.85 thf(fact_1729_Suc__double__not__eq__double,axiom,
% 5.64/5.85 ! [M: nat,N: nat] :
% 5.64/5.85 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.85 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.85
% 5.64/5.85 % Suc_double_not_eq_double
% 5.64/5.85 thf(fact_1730_div__by__1,axiom,
% 5.64/5.85 ! [A: complex] :
% 5.64/5.85 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % div_by_1
% 5.64/5.85 thf(fact_1731_div__by__1,axiom,
% 5.64/5.85 ! [A: real] :
% 5.64/5.85 ( ( divide_divide_real @ A @ one_one_real )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % div_by_1
% 5.64/5.85 thf(fact_1732_div__by__1,axiom,
% 5.64/5.85 ! [A: rat] :
% 5.64/5.85 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % div_by_1
% 5.64/5.85 thf(fact_1733_div__by__1,axiom,
% 5.64/5.85 ! [A: nat] :
% 5.64/5.85 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % div_by_1
% 5.64/5.85 thf(fact_1734_div__by__1,axiom,
% 5.64/5.85 ! [A: int] :
% 5.64/5.85 ( ( divide_divide_int @ A @ one_one_int )
% 5.64/5.85 = A ) ).
% 5.64/5.85
% 5.64/5.85 % div_by_1
% 5.64/5.85 thf(fact_1735_times__divide__eq__right,axiom,
% 5.64/5.85 ! [A: complex,B: complex,C: complex] :
% 5.64/5.85 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.85 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % times_divide_eq_right
% 5.64/5.85 thf(fact_1736_times__divide__eq__right,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.85 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % times_divide_eq_right
% 5.64/5.85 thf(fact_1737_times__divide__eq__right,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.85 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % times_divide_eq_right
% 5.64/5.85 thf(fact_1738_divide__divide__eq__right,axiom,
% 5.64/5.85 ! [A: complex,B: complex,C: complex] :
% 5.64/5.85 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.85 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % divide_divide_eq_right
% 5.64/5.85 thf(fact_1739_divide__divide__eq__right,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.85 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % divide_divide_eq_right
% 5.64/5.85 thf(fact_1740_divide__divide__eq__right,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.85 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.64/5.85
% 5.64/5.85 % divide_divide_eq_right
% 5.64/5.85 thf(fact_1741_divide__divide__eq__left,axiom,
% 5.64/5.85 ! [A: complex,B: complex,C: complex] :
% 5.64/5.85 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.64/5.85 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % divide_divide_eq_left
% 5.64/5.85 thf(fact_1742_divide__divide__eq__left,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.64/5.85 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % divide_divide_eq_left
% 5.64/5.85 thf(fact_1743_divide__divide__eq__left,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.64/5.85 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % divide_divide_eq_left
% 5.64/5.85 thf(fact_1744_times__divide__eq__left,axiom,
% 5.64/5.85 ! [B: complex,C: complex,A: complex] :
% 5.64/5.85 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.64/5.85 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % times_divide_eq_left
% 5.64/5.85 thf(fact_1745_times__divide__eq__left,axiom,
% 5.64/5.85 ! [B: real,C: real,A: real] :
% 5.64/5.85 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.85 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % times_divide_eq_left
% 5.64/5.85 thf(fact_1746_times__divide__eq__left,axiom,
% 5.64/5.85 ! [B: rat,C: rat,A: rat] :
% 5.64/5.85 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.85 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % times_divide_eq_left
% 5.64/5.85 thf(fact_1747_real__divide__square__eq,axiom,
% 5.64/5.85 ! [R2: real,A: real] :
% 5.64/5.85 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 5.64/5.85 = ( divide_divide_real @ A @ R2 ) ) ).
% 5.64/5.85
% 5.64/5.85 % real_divide_square_eq
% 5.64/5.85 thf(fact_1748_less__eq__real__def,axiom,
% 5.64/5.85 ( ord_less_eq_real
% 5.64/5.85 = ( ^ [X: real,Y: real] :
% 5.64/5.85 ( ( ord_less_real @ X @ Y )
% 5.64/5.85 | ( X = Y ) ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % less_eq_real_def
% 5.64/5.85 thf(fact_1749_real__arch__pow,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] :
% 5.64/5.85 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.85 => ? [N3: nat] : ( ord_less_real @ Y4 @ ( power_power_real @ X2 @ N3 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % real_arch_pow
% 5.64/5.85 thf(fact_1750_add__diff__assoc__enat,axiom,
% 5.64/5.85 ! [Z: extended_enat,Y4: extended_enat,X2: extended_enat] :
% 5.64/5.85 ( ( ord_le2932123472753598470d_enat @ Z @ Y4 )
% 5.64/5.85 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y4 @ Z ) )
% 5.64/5.85 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y4 ) @ Z ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % add_diff_assoc_enat
% 5.64/5.85 thf(fact_1751_linordered__field__no__lb,axiom,
% 5.64/5.85 ! [X3: real] :
% 5.64/5.85 ? [Y3: real] : ( ord_less_real @ Y3 @ X3 ) ).
% 5.64/5.85
% 5.64/5.85 % linordered_field_no_lb
% 5.64/5.85 thf(fact_1752_linordered__field__no__lb,axiom,
% 5.64/5.85 ! [X3: rat] :
% 5.64/5.85 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X3 ) ).
% 5.64/5.85
% 5.64/5.85 % linordered_field_no_lb
% 5.64/5.85 thf(fact_1753_linordered__field__no__ub,axiom,
% 5.64/5.85 ! [X3: real] :
% 5.64/5.85 ? [X_12: real] : ( ord_less_real @ X3 @ X_12 ) ).
% 5.64/5.85
% 5.64/5.85 % linordered_field_no_ub
% 5.64/5.85 thf(fact_1754_linordered__field__no__ub,axiom,
% 5.64/5.85 ! [X3: rat] :
% 5.64/5.85 ? [X_12: rat] : ( ord_less_rat @ X3 @ X_12 ) ).
% 5.64/5.85
% 5.64/5.85 % linordered_field_no_ub
% 5.64/5.85 thf(fact_1755_linorder__neqE__linordered__idom,axiom,
% 5.64/5.85 ! [X2: real,Y4: real] :
% 5.64/5.85 ( ( X2 != Y4 )
% 5.64/5.85 => ( ~ ( ord_less_real @ X2 @ Y4 )
% 5.64/5.85 => ( ord_less_real @ Y4 @ X2 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % linorder_neqE_linordered_idom
% 5.64/5.85 thf(fact_1756_linorder__neqE__linordered__idom,axiom,
% 5.64/5.85 ! [X2: rat,Y4: rat] :
% 5.64/5.85 ( ( X2 != Y4 )
% 5.64/5.85 => ( ~ ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.85 => ( ord_less_rat @ Y4 @ X2 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % linorder_neqE_linordered_idom
% 5.64/5.85 thf(fact_1757_linorder__neqE__linordered__idom,axiom,
% 5.64/5.85 ! [X2: int,Y4: int] :
% 5.64/5.85 ( ( X2 != Y4 )
% 5.64/5.85 => ( ~ ( ord_less_int @ X2 @ Y4 )
% 5.64/5.85 => ( ord_less_int @ Y4 @ X2 ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % linorder_neqE_linordered_idom
% 5.64/5.85 thf(fact_1758_combine__common__factor,axiom,
% 5.64/5.85 ! [A: real,E: real,B: real,C: real] :
% 5.64/5.85 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % combine_common_factor
% 5.64/5.85 thf(fact_1759_combine__common__factor,axiom,
% 5.64/5.85 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % combine_common_factor
% 5.64/5.85 thf(fact_1760_combine__common__factor,axiom,
% 5.64/5.85 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % combine_common_factor
% 5.64/5.85 thf(fact_1761_combine__common__factor,axiom,
% 5.64/5.85 ! [A: int,E: int,B: int,C: int] :
% 5.64/5.85 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.64/5.85 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.64/5.85
% 5.64/5.85 % combine_common_factor
% 5.64/5.85 thf(fact_1762_distrib__right,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_right
% 5.64/5.85 thf(fact_1763_distrib__right,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_right
% 5.64/5.85 thf(fact_1764_distrib__right,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_right
% 5.64/5.85 thf(fact_1765_distrib__right,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_right
% 5.64/5.85 thf(fact_1766_distrib__left,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_left
% 5.64/5.85 thf(fact_1767_distrib__left,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_left
% 5.64/5.85 thf(fact_1768_distrib__left,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_left
% 5.64/5.85 thf(fact_1769_distrib__left,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.64/5.85 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % distrib_left
% 5.64/5.85 thf(fact_1770_comm__semiring__class_Odistrib,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % comm_semiring_class.distrib
% 5.64/5.85 thf(fact_1771_comm__semiring__class_Odistrib,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % comm_semiring_class.distrib
% 5.64/5.85 thf(fact_1772_comm__semiring__class_Odistrib,axiom,
% 5.64/5.85 ! [A: nat,B: nat,C: nat] :
% 5.64/5.85 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % comm_semiring_class.distrib
% 5.64/5.85 thf(fact_1773_comm__semiring__class_Odistrib,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.85 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % comm_semiring_class.distrib
% 5.64/5.85 thf(fact_1774_ring__class_Oring__distribs_I1_J,axiom,
% 5.64/5.85 ! [A: real,B: real,C: real] :
% 5.64/5.85 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.64/5.85 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ring_class.ring_distribs(1)
% 5.64/5.85 thf(fact_1775_ring__class_Oring__distribs_I1_J,axiom,
% 5.64/5.85 ! [A: rat,B: rat,C: rat] :
% 5.64/5.85 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.85 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.64/5.85
% 5.64/5.85 % ring_class.ring_distribs(1)
% 5.64/5.85 thf(fact_1776_ring__class_Oring__distribs_I1_J,axiom,
% 5.64/5.85 ! [A: int,B: int,C: int] :
% 5.64/5.85 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.64/5.86 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ring_class.ring_distribs(1)
% 5.64/5.86 thf(fact_1777_ring__class_Oring__distribs_I2_J,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.86 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ring_class.ring_distribs(2)
% 5.64/5.86 thf(fact_1778_ring__class_Oring__distribs_I2_J,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.86 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ring_class.ring_distribs(2)
% 5.64/5.86 thf(fact_1779_ring__class_Oring__distribs_I2_J,axiom,
% 5.64/5.86 ! [A: int,B: int,C: int] :
% 5.64/5.86 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.86 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ring_class.ring_distribs(2)
% 5.64/5.86 thf(fact_1780_left__diff__distrib,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.64/5.86 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib
% 5.64/5.86 thf(fact_1781_left__diff__distrib,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.64/5.86 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib
% 5.64/5.86 thf(fact_1782_left__diff__distrib,axiom,
% 5.64/5.86 ! [A: int,B: int,C: int] :
% 5.64/5.86 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.64/5.86 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib
% 5.64/5.86 thf(fact_1783_right__diff__distrib,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.64/5.86 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib
% 5.64/5.86 thf(fact_1784_right__diff__distrib,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.64/5.86 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib
% 5.64/5.86 thf(fact_1785_right__diff__distrib,axiom,
% 5.64/5.86 ! [A: int,B: int,C: int] :
% 5.64/5.86 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.64/5.86 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib
% 5.64/5.86 thf(fact_1786_left__diff__distrib_H,axiom,
% 5.64/5.86 ! [B: real,C: real,A: real] :
% 5.64/5.86 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.64/5.86 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib'
% 5.64/5.86 thf(fact_1787_left__diff__distrib_H,axiom,
% 5.64/5.86 ! [B: rat,C: rat,A: rat] :
% 5.64/5.86 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.64/5.86 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib'
% 5.64/5.86 thf(fact_1788_left__diff__distrib_H,axiom,
% 5.64/5.86 ! [B: nat,C: nat,A: nat] :
% 5.64/5.86 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.64/5.86 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib'
% 5.64/5.86 thf(fact_1789_left__diff__distrib_H,axiom,
% 5.64/5.86 ! [B: int,C: int,A: int] :
% 5.64/5.86 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.64/5.86 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % left_diff_distrib'
% 5.64/5.86 thf(fact_1790_right__diff__distrib_H,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.64/5.86 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib'
% 5.64/5.86 thf(fact_1791_right__diff__distrib_H,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.64/5.86 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib'
% 5.64/5.86 thf(fact_1792_right__diff__distrib_H,axiom,
% 5.64/5.86 ! [A: nat,B: nat,C: nat] :
% 5.64/5.86 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.64/5.86 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib'
% 5.64/5.86 thf(fact_1793_right__diff__distrib_H,axiom,
% 5.64/5.86 ! [A: int,B: int,C: int] :
% 5.64/5.86 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.64/5.86 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % right_diff_distrib'
% 5.64/5.86 thf(fact_1794_times__divide__times__eq,axiom,
% 5.64/5.86 ! [X2: complex,Y4: complex,Z: complex,W: complex] :
% 5.64/5.86 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X2 @ Y4 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ Y4 @ W ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % times_divide_times_eq
% 5.64/5.86 thf(fact_1795_times__divide__times__eq,axiom,
% 5.64/5.86 ! [X2: real,Y4: real,Z: real,W: real] :
% 5.64/5.86 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y4 ) @ ( divide_divide_real @ Z @ W ) )
% 5.64/5.86 = ( divide_divide_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y4 @ W ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % times_divide_times_eq
% 5.64/5.86 thf(fact_1796_times__divide__times__eq,axiom,
% 5.64/5.86 ! [X2: rat,Y4: rat,Z: rat,W: rat] :
% 5.64/5.86 ( ( times_times_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.64/5.86 = ( divide_divide_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y4 @ W ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % times_divide_times_eq
% 5.64/5.86 thf(fact_1797_divide__divide__times__eq,axiom,
% 5.64/5.86 ! [X2: complex,Y4: complex,Z: complex,W: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X2 @ Y4 ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ W ) @ ( times_times_complex @ Y4 @ Z ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_divide_times_eq
% 5.64/5.86 thf(fact_1798_divide__divide__times__eq,axiom,
% 5.64/5.86 ! [X2: real,Y4: real,Z: real,W: real] :
% 5.64/5.86 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y4 ) @ ( divide_divide_real @ Z @ W ) )
% 5.64/5.86 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y4 @ Z ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_divide_times_eq
% 5.64/5.86 thf(fact_1799_divide__divide__times__eq,axiom,
% 5.64/5.86 ! [X2: rat,Y4: rat,Z: rat,W: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ ( divide_divide_rat @ Z @ W ) )
% 5.64/5.86 = ( divide_divide_rat @ ( times_times_rat @ X2 @ W ) @ ( times_times_rat @ Y4 @ Z ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_divide_times_eq
% 5.64/5.86 thf(fact_1800_divide__divide__eq__left_H,axiom,
% 5.64/5.86 ! [A: complex,B: complex,C: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_divide_eq_left'
% 5.64/5.86 thf(fact_1801_divide__divide__eq__left_H,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.64/5.86 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_divide_eq_left'
% 5.64/5.86 thf(fact_1802_divide__divide__eq__left_H,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.64/5.86 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_divide_eq_left'
% 5.64/5.86 thf(fact_1803_add__divide__distrib,axiom,
% 5.64/5.86 ! [A: complex,B: complex,C: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.64/5.86 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_divide_distrib
% 5.64/5.86 thf(fact_1804_add__divide__distrib,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.64/5.86 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_divide_distrib
% 5.64/5.86 thf(fact_1805_add__divide__distrib,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.64/5.86 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_divide_distrib
% 5.64/5.86 thf(fact_1806_diff__divide__distrib,axiom,
% 5.64/5.86 ! [A: complex,B: complex,C: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.64/5.86 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_divide_distrib
% 5.64/5.86 thf(fact_1807_diff__divide__distrib,axiom,
% 5.64/5.86 ! [A: real,B: real,C: real] :
% 5.64/5.86 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.64/5.86 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_divide_distrib
% 5.64/5.86 thf(fact_1808_diff__divide__distrib,axiom,
% 5.64/5.86 ! [A: rat,B: rat,C: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.64/5.86 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_divide_distrib
% 5.64/5.86 thf(fact_1809_less__1__mult,axiom,
% 5.64/5.86 ! [M: real,N: real] :
% 5.64/5.86 ( ( ord_less_real @ one_one_real @ M )
% 5.64/5.86 => ( ( ord_less_real @ one_one_real @ N )
% 5.64/5.86 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_1_mult
% 5.64/5.86 thf(fact_1810_less__1__mult,axiom,
% 5.64/5.86 ! [M: rat,N: rat] :
% 5.64/5.86 ( ( ord_less_rat @ one_one_rat @ M )
% 5.64/5.86 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.64/5.86 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_1_mult
% 5.64/5.86 thf(fact_1811_less__1__mult,axiom,
% 5.64/5.86 ! [M: nat,N: nat] :
% 5.64/5.86 ( ( ord_less_nat @ one_one_nat @ M )
% 5.64/5.86 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.64/5.86 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_1_mult
% 5.64/5.86 thf(fact_1812_less__1__mult,axiom,
% 5.64/5.86 ! [M: int,N: int] :
% 5.64/5.86 ( ( ord_less_int @ one_one_int @ M )
% 5.64/5.86 => ( ( ord_less_int @ one_one_int @ N )
% 5.64/5.86 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_1_mult
% 5.64/5.86 thf(fact_1813_add__mono1,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ A @ B )
% 5.64/5.86 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_mono1
% 5.64/5.86 thf(fact_1814_add__mono1,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ A @ B )
% 5.64/5.86 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_mono1
% 5.64/5.86 thf(fact_1815_add__mono1,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_nat @ A @ B )
% 5.64/5.86 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_mono1
% 5.64/5.86 thf(fact_1816_add__mono1,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_int @ A @ B )
% 5.64/5.86 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_mono1
% 5.64/5.86 thf(fact_1817_less__add__one,axiom,
% 5.64/5.86 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_one
% 5.64/5.86 thf(fact_1818_less__add__one,axiom,
% 5.64/5.86 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_one
% 5.64/5.86 thf(fact_1819_less__add__one,axiom,
% 5.64/5.86 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_one
% 5.64/5.86 thf(fact_1820_less__add__one,axiom,
% 5.64/5.86 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_one
% 5.64/5.86 thf(fact_1821_add__le__add__imp__diff__le,axiom,
% 5.64/5.86 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.64/5.86 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.64/5.86 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_add_imp_diff_le
% 5.64/5.86 thf(fact_1822_add__le__add__imp__diff__le,axiom,
% 5.64/5.86 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.64/5.86 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.64/5.86 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_add_imp_diff_le
% 5.64/5.86 thf(fact_1823_add__le__add__imp__diff__le,axiom,
% 5.64/5.86 ! [I: int,K: int,N: int,J: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.64/5.86 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.64/5.86 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_add_imp_diff_le
% 5.64/5.86 thf(fact_1824_add__le__add__imp__diff__le,axiom,
% 5.64/5.86 ! [I: real,K: real,N: real,J: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.64/5.86 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.64/5.86 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.64/5.86 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_add_imp_diff_le
% 5.64/5.86 thf(fact_1825_add__le__imp__le__diff,axiom,
% 5.64/5.86 ! [I: rat,K: rat,N: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.64/5.86 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_imp_le_diff
% 5.64/5.86 thf(fact_1826_add__le__imp__le__diff,axiom,
% 5.64/5.86 ! [I: nat,K: nat,N: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.64/5.86 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_imp_le_diff
% 5.64/5.86 thf(fact_1827_add__le__imp__le__diff,axiom,
% 5.64/5.86 ! [I: int,K: int,N: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.64/5.86 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_imp_le_diff
% 5.64/5.86 thf(fact_1828_add__le__imp__le__diff,axiom,
% 5.64/5.86 ! [I: real,K: real,N: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.64/5.86 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_imp_le_diff
% 5.64/5.86 thf(fact_1829_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ~ ( ord_less_real @ A @ B )
% 5.64/5.86 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % linordered_semidom_class.add_diff_inverse
% 5.64/5.86 thf(fact_1830_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ~ ( ord_less_rat @ A @ B )
% 5.64/5.86 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % linordered_semidom_class.add_diff_inverse
% 5.64/5.86 thf(fact_1831_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ~ ( ord_less_nat @ A @ B )
% 5.64/5.86 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % linordered_semidom_class.add_diff_inverse
% 5.64/5.86 thf(fact_1832_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ~ ( ord_less_int @ A @ B )
% 5.64/5.86 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % linordered_semidom_class.add_diff_inverse
% 5.64/5.86 thf(fact_1833_eq__add__iff1,axiom,
% 5.64/5.86 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.64/5.86 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.64/5.86 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.64/5.86 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.64/5.86 = D ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_add_iff1
% 5.64/5.86 thf(fact_1834_eq__add__iff1,axiom,
% 5.64/5.86 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.64/5.86 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.64/5.86 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.64/5.86 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.64/5.86 = D ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_add_iff1
% 5.64/5.86 thf(fact_1835_eq__add__iff1,axiom,
% 5.64/5.86 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.64/5.86 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.64/5.86 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.64/5.86 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.64/5.86 = D ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_add_iff1
% 5.64/5.86 thf(fact_1836_eq__add__iff2,axiom,
% 5.64/5.86 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.64/5.86 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.64/5.86 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.64/5.86 = ( C
% 5.64/5.86 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_add_iff2
% 5.64/5.86 thf(fact_1837_eq__add__iff2,axiom,
% 5.64/5.86 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.64/5.86 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.64/5.86 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.64/5.86 = ( C
% 5.64/5.86 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_add_iff2
% 5.64/5.86 thf(fact_1838_eq__add__iff2,axiom,
% 5.64/5.86 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.64/5.86 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.64/5.86 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.64/5.86 = ( C
% 5.64/5.86 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_add_iff2
% 5.64/5.86 thf(fact_1839_square__diff__square__factored,axiom,
% 5.64/5.86 ! [X2: real,Y4: real] :
% 5.64/5.86 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) )
% 5.64/5.86 = ( times_times_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( minus_minus_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_square_factored
% 5.64/5.86 thf(fact_1840_square__diff__square__factored,axiom,
% 5.64/5.86 ! [X2: rat,Y4: rat] :
% 5.64/5.86 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y4 @ Y4 ) )
% 5.64/5.86 = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y4 ) @ ( minus_minus_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_square_factored
% 5.64/5.86 thf(fact_1841_square__diff__square__factored,axiom,
% 5.64/5.86 ! [X2: int,Y4: int] :
% 5.64/5.86 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y4 @ Y4 ) )
% 5.64/5.86 = ( times_times_int @ ( plus_plus_int @ X2 @ Y4 ) @ ( minus_minus_int @ X2 @ Y4 ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_square_factored
% 5.64/5.86 thf(fact_1842_ordered__ring__class_Ole__add__iff2,axiom,
% 5.64/5.86 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ordered_ring_class.le_add_iff2
% 5.64/5.86 thf(fact_1843_ordered__ring__class_Ole__add__iff2,axiom,
% 5.64/5.86 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ordered_ring_class.le_add_iff2
% 5.64/5.86 thf(fact_1844_ordered__ring__class_Ole__add__iff2,axiom,
% 5.64/5.86 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % ordered_ring_class.le_add_iff2
% 5.64/5.86 thf(fact_1845_ordered__ring__class_Ole__add__iff1,axiom,
% 5.64/5.86 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.64/5.86
% 5.64/5.86 % ordered_ring_class.le_add_iff1
% 5.64/5.86 thf(fact_1846_ordered__ring__class_Ole__add__iff1,axiom,
% 5.64/5.86 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.64/5.86
% 5.64/5.86 % ordered_ring_class.le_add_iff1
% 5.64/5.86 thf(fact_1847_ordered__ring__class_Ole__add__iff1,axiom,
% 5.64/5.86 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.64/5.86
% 5.64/5.86 % ordered_ring_class.le_add_iff1
% 5.64/5.86 thf(fact_1848_less__add__iff1,axiom,
% 5.64/5.86 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.64/5.86 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_iff1
% 5.64/5.86 thf(fact_1849_less__add__iff1,axiom,
% 5.64/5.86 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.64/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_iff1
% 5.64/5.86 thf(fact_1850_less__add__iff1,axiom,
% 5.64/5.86 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.64/5.86 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_iff1
% 5.64/5.86 thf(fact_1851_less__add__iff2,axiom,
% 5.64/5.86 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.64/5.86 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_iff2
% 5.64/5.86 thf(fact_1852_less__add__iff2,axiom,
% 5.64/5.86 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.64/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_iff2
% 5.64/5.86 thf(fact_1853_less__add__iff2,axiom,
% 5.64/5.86 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.64/5.86 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.64/5.86 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_iff2
% 5.64/5.86 thf(fact_1854_less__half__sum,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ A @ B )
% 5.64/5.86 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_half_sum
% 5.64/5.86 thf(fact_1855_less__half__sum,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ A @ B )
% 5.64/5.86 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_half_sum
% 5.64/5.86 thf(fact_1856_gt__half__sum,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ A @ B )
% 5.64/5.86 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % gt_half_sum
% 5.64/5.86 thf(fact_1857_gt__half__sum,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ A @ B )
% 5.64/5.86 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % gt_half_sum
% 5.64/5.86 thf(fact_1858_square__diff__one__factored,axiom,
% 5.64/5.86 ! [X2: complex] :
% 5.64/5.86 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ one_one_complex )
% 5.64/5.86 = ( times_times_complex @ ( plus_plus_complex @ X2 @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_one_factored
% 5.64/5.86 thf(fact_1859_square__diff__one__factored,axiom,
% 5.64/5.86 ! [X2: real] :
% 5.64/5.86 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 5.64/5.86 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_one_factored
% 5.64/5.86 thf(fact_1860_square__diff__one__factored,axiom,
% 5.64/5.86 ! [X2: rat] :
% 5.64/5.86 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 5.64/5.86 = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_one_factored
% 5.64/5.86 thf(fact_1861_square__diff__one__factored,axiom,
% 5.64/5.86 ! [X2: int] :
% 5.64/5.86 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 5.64/5.86 = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % square_diff_one_factored
% 5.64/5.86 thf(fact_1862_real__average__minus__first,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.64/5.86 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % real_average_minus_first
% 5.64/5.86 thf(fact_1863_real__average__minus__second,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.64/5.86 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % real_average_minus_second
% 5.64/5.86 thf(fact_1864_pred__less__length__list,axiom,
% 5.64/5.86 ! [Deg: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.86 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.64/5.86 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % pred_less_length_list
% 5.64/5.86 thf(fact_1865_pred__lesseq__max,axiom,
% 5.64/5.86 ! [Deg: nat,X2: nat,Ma: nat,Mi: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.86 => ( ( ord_less_eq_nat @ X2 @ Ma )
% 5.64/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.86 @ none_nat ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % pred_lesseq_max
% 5.64/5.86 thf(fact_1866_succ__greatereq__min,axiom,
% 5.64/5.86 ! [Deg: nat,Mi: nat,X2: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.86 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.64/5.86 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ none_nat
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( 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 @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.86 @ none_nat ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % succ_greatereq_min
% 5.64/5.86 thf(fact_1867_succ__less__length__list,axiom,
% 5.64/5.86 ! [Deg: nat,Mi: nat,X2: nat,TreeList: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.86 => ( ( ord_less_eq_nat @ Mi @ X2 )
% 5.64/5.86 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ none_nat
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( 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 @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % succ_less_length_list
% 5.64/5.86 thf(fact_1868_vebt__pred_Osimps_I4_J,axiom,
% 5.64/5.86 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.64/5.86 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.64/5.86 = none_nat ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_pred.simps(4)
% 5.64/5.86 thf(fact_1869_vebt__succ_Osimps_I3_J,axiom,
% 5.64/5.86 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.64/5.86 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.64/5.86 = none_nat ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_succ.simps(3)
% 5.64/5.86 thf(fact_1870_divmod__step__eq,axiom,
% 5.64/5.86 ! [L: num,R2: nat,Q3: nat] :
% 5.64/5.86 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.64/5.86 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.64/5.86 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.64/5.86 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.64/5.86 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.64/5.86 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divmod_step_eq
% 5.64/5.86 thf(fact_1871_divmod__step__eq,axiom,
% 5.64/5.86 ! [L: num,R2: int,Q3: int] :
% 5.64/5.86 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.64/5.86 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.86 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.64/5.86 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.64/5.86 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.86 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divmod_step_eq
% 5.64/5.86 thf(fact_1872_divmod__step__eq,axiom,
% 5.64/5.86 ! [L: num,R2: code_integer,Q3: code_integer] :
% 5.64/5.86 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.64/5.86 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.64/5.86 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.64/5.86 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.64/5.86 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R2 ) )
% 5.64/5.86 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divmod_step_eq
% 5.64/5.86 thf(fact_1873_maxt__corr__help__empty,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.86 => ( ( ( vEBT_vebt_maxt @ T )
% 5.64/5.86 = none_nat )
% 5.64/5.86 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.64/5.86 = bot_bot_set_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % maxt_corr_help_empty
% 5.64/5.86 thf(fact_1874_set__vebt_H__def,axiom,
% 5.64/5.86 ( vEBT_VEBT_set_vebt
% 5.64/5.86 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % set_vebt'_def
% 5.64/5.86 thf(fact_1875_zdiv__numeral__Bit0,axiom,
% 5.64/5.86 ! [V: num,W: num] :
% 5.64/5.86 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.64/5.86 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % zdiv_numeral_Bit0
% 5.64/5.86 thf(fact_1876_mint__corr__help__empty,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.86 => ( ( ( vEBT_vebt_mint @ T )
% 5.64/5.86 = none_nat )
% 5.64/5.86 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.64/5.86 = bot_bot_set_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mint_corr_help_empty
% 5.64/5.86 thf(fact_1877_pred__empty,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.86 => ( ( ( vEBT_vebt_pred @ T @ X2 )
% 5.64/5.86 = none_nat )
% 5.64/5.86 = ( ( collect_nat
% 5.64/5.86 @ ^ [Y: nat] :
% 5.64/5.86 ( ( vEBT_vebt_member @ T @ Y )
% 5.64/5.86 & ( ord_less_nat @ Y @ X2 ) ) )
% 5.64/5.86 = bot_bot_set_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % pred_empty
% 5.64/5.86 thf(fact_1878_succ__empty,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.86 => ( ( ( vEBT_vebt_succ @ T @ X2 )
% 5.64/5.86 = none_nat )
% 5.64/5.86 = ( ( collect_nat
% 5.64/5.86 @ ^ [Y: nat] :
% 5.64/5.86 ( ( vEBT_vebt_member @ T @ Y )
% 5.64/5.86 & ( ord_less_nat @ X2 @ Y ) ) )
% 5.64/5.86 = bot_bot_set_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % succ_empty
% 5.64/5.86 thf(fact_1879_mult__commute__abs,axiom,
% 5.64/5.86 ! [C: real] :
% 5.64/5.86 ( ( ^ [X: real] : ( times_times_real @ X @ C ) )
% 5.64/5.86 = ( times_times_real @ C ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_commute_abs
% 5.64/5.86 thf(fact_1880_mult__commute__abs,axiom,
% 5.64/5.86 ! [C: rat] :
% 5.64/5.86 ( ( ^ [X: rat] : ( times_times_rat @ X @ C ) )
% 5.64/5.86 = ( times_times_rat @ C ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_commute_abs
% 5.64/5.86 thf(fact_1881_mult__commute__abs,axiom,
% 5.64/5.86 ! [C: nat] :
% 5.64/5.86 ( ( ^ [X: nat] : ( times_times_nat @ X @ C ) )
% 5.64/5.86 = ( times_times_nat @ C ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_commute_abs
% 5.64/5.86 thf(fact_1882_mult__commute__abs,axiom,
% 5.64/5.86 ! [C: int] :
% 5.64/5.86 ( ( ^ [X: int] : ( times_times_int @ X @ C ) )
% 5.64/5.86 = ( times_times_int @ C ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_commute_abs
% 5.64/5.86 thf(fact_1883_lambda__one,axiom,
% 5.64/5.86 ( ( ^ [X: complex] : X )
% 5.64/5.86 = ( times_times_complex @ one_one_complex ) ) ).
% 5.64/5.86
% 5.64/5.86 % lambda_one
% 5.64/5.86 thf(fact_1884_lambda__one,axiom,
% 5.64/5.86 ( ( ^ [X: real] : X )
% 5.64/5.86 = ( times_times_real @ one_one_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % lambda_one
% 5.64/5.86 thf(fact_1885_lambda__one,axiom,
% 5.64/5.86 ( ( ^ [X: rat] : X )
% 5.64/5.86 = ( times_times_rat @ one_one_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % lambda_one
% 5.64/5.86 thf(fact_1886_lambda__one,axiom,
% 5.64/5.86 ( ( ^ [X: nat] : X )
% 5.64/5.86 = ( times_times_nat @ one_one_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % lambda_one
% 5.64/5.86 thf(fact_1887_lambda__one,axiom,
% 5.64/5.86 ( ( ^ [X: int] : X )
% 5.64/5.86 = ( times_times_int @ one_one_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % lambda_one
% 5.64/5.86 thf(fact_1888_bot_Oextremum,axiom,
% 5.64/5.86 ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum
% 5.64/5.86 thf(fact_1889_bot_Oextremum,axiom,
% 5.64/5.86 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum
% 5.64/5.86 thf(fact_1890_bot_Oextremum,axiom,
% 5.64/5.86 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum
% 5.64/5.86 thf(fact_1891_bot_Oextremum,axiom,
% 5.64/5.86 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum
% 5.64/5.86 thf(fact_1892_bot_Oextremum,axiom,
% 5.64/5.86 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum
% 5.64/5.86 thf(fact_1893_bot_Oextremum__unique,axiom,
% 5.64/5.86 ! [A: extended_enat] :
% 5.64/5.86 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.64/5.86 = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_unique
% 5.64/5.86 thf(fact_1894_bot_Oextremum__unique,axiom,
% 5.64/5.86 ! [A: set_int] :
% 5.64/5.86 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.64/5.86 = ( A = bot_bot_set_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_unique
% 5.64/5.86 thf(fact_1895_bot_Oextremum__unique,axiom,
% 5.64/5.86 ! [A: set_real] :
% 5.64/5.86 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.64/5.86 = ( A = bot_bot_set_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_unique
% 5.64/5.86 thf(fact_1896_bot_Oextremum__unique,axiom,
% 5.64/5.86 ! [A: set_nat] :
% 5.64/5.86 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.64/5.86 = ( A = bot_bot_set_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_unique
% 5.64/5.86 thf(fact_1897_bot_Oextremum__unique,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.64/5.86 = ( A = bot_bot_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_unique
% 5.64/5.86 thf(fact_1898_bot_Oextremum__uniqueI,axiom,
% 5.64/5.86 ! [A: extended_enat] :
% 5.64/5.86 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.64/5.86 => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_uniqueI
% 5.64/5.86 thf(fact_1899_bot_Oextremum__uniqueI,axiom,
% 5.64/5.86 ! [A: set_int] :
% 5.64/5.86 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.64/5.86 => ( A = bot_bot_set_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_uniqueI
% 5.64/5.86 thf(fact_1900_bot_Oextremum__uniqueI,axiom,
% 5.64/5.86 ! [A: set_real] :
% 5.64/5.86 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.64/5.86 => ( A = bot_bot_set_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_uniqueI
% 5.64/5.86 thf(fact_1901_bot_Oextremum__uniqueI,axiom,
% 5.64/5.86 ! [A: set_nat] :
% 5.64/5.86 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.64/5.86 => ( A = bot_bot_set_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_uniqueI
% 5.64/5.86 thf(fact_1902_bot_Oextremum__uniqueI,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.64/5.86 => ( A = bot_bot_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_uniqueI
% 5.64/5.86 thf(fact_1903_bot_Onot__eq__extremum,axiom,
% 5.64/5.86 ! [A: set_nat] :
% 5.64/5.86 ( ( A != bot_bot_set_nat )
% 5.64/5.86 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.not_eq_extremum
% 5.64/5.86 thf(fact_1904_bot_Onot__eq__extremum,axiom,
% 5.64/5.86 ! [A: extended_enat] :
% 5.64/5.86 ( ( A != bot_bo4199563552545308370d_enat )
% 5.64/5.86 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.not_eq_extremum
% 5.64/5.86 thf(fact_1905_bot_Onot__eq__extremum,axiom,
% 5.64/5.86 ! [A: set_int] :
% 5.64/5.86 ( ( A != bot_bot_set_int )
% 5.64/5.86 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.not_eq_extremum
% 5.64/5.86 thf(fact_1906_bot_Onot__eq__extremum,axiom,
% 5.64/5.86 ! [A: set_real] :
% 5.64/5.86 ( ( A != bot_bot_set_real )
% 5.64/5.86 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.not_eq_extremum
% 5.64/5.86 thf(fact_1907_bot_Onot__eq__extremum,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( A != bot_bot_nat )
% 5.64/5.86 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot.not_eq_extremum
% 5.64/5.86 thf(fact_1908_bot_Oextremum__strict,axiom,
% 5.64/5.86 ! [A: set_nat] :
% 5.64/5.86 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_strict
% 5.64/5.86 thf(fact_1909_bot_Oextremum__strict,axiom,
% 5.64/5.86 ! [A: extended_enat] :
% 5.64/5.86 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_strict
% 5.64/5.86 thf(fact_1910_bot_Oextremum__strict,axiom,
% 5.64/5.86 ! [A: set_int] :
% 5.64/5.86 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_strict
% 5.64/5.86 thf(fact_1911_bot_Oextremum__strict,axiom,
% 5.64/5.86 ! [A: set_real] :
% 5.64/5.86 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_strict
% 5.64/5.86 thf(fact_1912_bot_Oextremum__strict,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.64/5.86
% 5.64/5.86 % bot.extremum_strict
% 5.64/5.86 thf(fact_1913_set__vebt__def,axiom,
% 5.64/5.86 ( vEBT_set_vebt
% 5.64/5.86 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % set_vebt_def
% 5.64/5.86 thf(fact_1914_numeral__code_I2_J,axiom,
% 5.64/5.86 ! [N: num] :
% 5.64/5.86 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.64/5.86 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % numeral_code(2)
% 5.64/5.86 thf(fact_1915_numeral__code_I2_J,axiom,
% 5.64/5.86 ! [N: num] :
% 5.64/5.86 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.64/5.86 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % numeral_code(2)
% 5.64/5.86 thf(fact_1916_numeral__code_I2_J,axiom,
% 5.64/5.86 ! [N: num] :
% 5.64/5.86 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.64/5.86 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % numeral_code(2)
% 5.64/5.86 thf(fact_1917_numeral__code_I2_J,axiom,
% 5.64/5.86 ! [N: num] :
% 5.64/5.86 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.64/5.86 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % numeral_code(2)
% 5.64/5.86 thf(fact_1918_numeral__code_I2_J,axiom,
% 5.64/5.86 ! [N: num] :
% 5.64/5.86 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.64/5.86 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % numeral_code(2)
% 5.64/5.86 thf(fact_1919_power__numeral__even,axiom,
% 5.64/5.86 ! [Z: complex,W: num] :
% 5.64/5.86 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.64/5.86 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % power_numeral_even
% 5.64/5.86 thf(fact_1920_power__numeral__even,axiom,
% 5.64/5.86 ! [Z: real,W: num] :
% 5.64/5.86 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.64/5.86 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % power_numeral_even
% 5.64/5.86 thf(fact_1921_power__numeral__even,axiom,
% 5.64/5.86 ! [Z: rat,W: num] :
% 5.64/5.86 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.64/5.86 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % power_numeral_even
% 5.64/5.86 thf(fact_1922_power__numeral__even,axiom,
% 5.64/5.86 ! [Z: nat,W: num] :
% 5.64/5.86 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.64/5.86 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % power_numeral_even
% 5.64/5.86 thf(fact_1923_power__numeral__even,axiom,
% 5.64/5.86 ! [Z: int,W: num] :
% 5.64/5.86 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.64/5.86 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % power_numeral_even
% 5.64/5.86 thf(fact_1924_vebt__succ_Osimps_I6_J,axiom,
% 5.64/5.86 ! [X2: nat,Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.86 ( ( ( ord_less_nat @ X2 @ Mi )
% 5.64/5.86 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( some_nat @ Mi ) ) )
% 5.64/5.86 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.64/5.86 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( 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 @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ none_nat
% 5.64/5.86 @ ( 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 @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.86 @ none_nat ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_succ.simps(6)
% 5.64/5.86 thf(fact_1925_vebt__pred_Osimps_I7_J,axiom,
% 5.64/5.86 ! [Ma: nat,X2: nat,Mi: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/5.86 ( ( ( ord_less_nat @ Ma @ X2 )
% 5.64/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( some_nat @ Ma ) ) )
% 5.64/5.86 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.64/5.86 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( 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 @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X2 ) @ ( some_nat @ Mi ) @ none_nat )
% 5.64/5.86 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.86 @ none_nat ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_pred.simps(7)
% 5.64/5.86 thf(fact_1926_is__succ__in__set__def,axiom,
% 5.64/5.86 ( vEBT_is_succ_in_set
% 5.64/5.86 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.64/5.86 ( ( member_nat @ Y @ Xs )
% 5.64/5.86 & ( ord_less_nat @ X @ Y )
% 5.64/5.86 & ! [Z4: nat] :
% 5.64/5.86 ( ( member_nat @ Z4 @ Xs )
% 5.64/5.86 => ( ( ord_less_nat @ X @ Z4 )
% 5.64/5.86 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % is_succ_in_set_def
% 5.64/5.86 thf(fact_1927_is__pred__in__set__def,axiom,
% 5.64/5.86 ( vEBT_is_pred_in_set
% 5.64/5.86 = ( ^ [Xs: set_nat,X: nat,Y: nat] :
% 5.64/5.86 ( ( member_nat @ Y @ Xs )
% 5.64/5.86 & ( ord_less_nat @ Y @ X )
% 5.64/5.86 & ! [Z4: nat] :
% 5.64/5.86 ( ( member_nat @ Z4 @ Xs )
% 5.64/5.86 => ( ( ord_less_nat @ Z4 @ X )
% 5.64/5.86 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % is_pred_in_set_def
% 5.64/5.86 thf(fact_1928_discrete,axiom,
% 5.64/5.86 ( ord_less_nat
% 5.64/5.86 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % discrete
% 5.64/5.86 thf(fact_1929_discrete,axiom,
% 5.64/5.86 ( ord_less_int
% 5.64/5.86 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % discrete
% 5.64/5.86 thf(fact_1930_vebt__member_Osimps_I5_J,axiom,
% 5.64/5.86 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.86 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( ( X2 != Mi )
% 5.64/5.86 => ( ( X2 != Ma )
% 5.64/5.86 => ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.64/5.86 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.64/5.86 => ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.64/5.86 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.64/5.86 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_member.simps(5)
% 5.64/5.86 thf(fact_1931_buildup__gives__empty,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.64/5.86 = bot_bot_set_nat ) ).
% 5.64/5.86
% 5.64/5.86 % buildup_gives_empty
% 5.64/5.86 thf(fact_1932_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I5_J,axiom,
% 5.64/5.86 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.86 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.86 = ( plus_plus_nat @ one_one_nat
% 5.64/5.86 @ ( if_nat @ ( X2 = Mi ) @ zero_zero_nat
% 5.64/5.86 @ ( if_nat @ ( X2 = Ma ) @ zero_zero_nat
% 5.64/5.86 @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ zero_zero_nat
% 5.64/5.86 @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ zero_zero_nat
% 5.64/5.86 @ ( if_nat
% 5.64/5.86 @ ( ( ord_less_nat @ Mi @ X2 )
% 5.64/5.86 & ( ord_less_nat @ X2 @ Ma ) )
% 5.64/5.86 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.64/5.86 @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(5)
% 5.64/5.86 thf(fact_1933_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.64/5.86 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.64/5.86 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X2 )
% 5.64/5.86 = ( ( X2 = Mi )
% 5.64/5.86 | ( X2 = Ma )
% 5.64/5.86 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % VEBT_internal.membermima.simps(4)
% 5.64/5.86 thf(fact_1934_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.64/5.86 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.64/5.86 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S2 ) @ X2 )
% 5.64/5.86 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % VEBT_internal.naive_member.simps(3)
% 5.64/5.86 thf(fact_1935_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.64/5.86 ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X2: nat] :
% 5.64/5.86 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X2 )
% 5.64/5.86 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.86 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % VEBT_internal.membermima.simps(5)
% 5.64/5.86 thf(fact_1936_vebt__succ_Oelims,axiom,
% 5.64/5.86 ! [X2: vEBT_VEBT,Xa2: nat,Y4: option_nat] :
% 5.64/5.86 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.64/5.86 = Y4 )
% 5.64/5.86 => ( ! [Uu: $o,B5: $o] :
% 5.64/5.86 ( ( X2
% 5.64/5.86 = ( vEBT_Leaf @ Uu @ B5 ) )
% 5.64/5.86 => ( ( Xa2 = zero_zero_nat )
% 5.64/5.86 => ~ ( ( B5
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.86 & ( ~ B5
% 5.64/5.86 => ( Y4 = none_nat ) ) ) ) )
% 5.64/5.86 => ( ( ? [Uv: $o,Uw: $o] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Leaf @ Uv @ Uw ) )
% 5.64/5.86 => ( ? [N3: nat] :
% 5.64/5.86 ( Xa2
% 5.64/5.86 = ( suc @ N3 ) )
% 5.64/5.86 => ( Y4 != none_nat ) ) )
% 5.64/5.86 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.64/5.86 => ( Y4 != none_nat ) )
% 5.64/5.86 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.64/5.86 => ( Y4 != none_nat ) )
% 5.64/5.86 => ( ( ? [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.64/5.86 => ( Y4 != none_nat ) )
% 5.64/5.86 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.86 ( ( X2
% 5.64/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.86 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( some_nat @ Mi2 ) ) )
% 5.64/5.86 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ none_nat
% 5.64/5.86 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.86 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_succ.elims
% 5.64/5.86 thf(fact_1937_vebt__pred_Oelims,axiom,
% 5.64/5.86 ! [X2: vEBT_VEBT,Xa2: nat,Y4: option_nat] :
% 5.64/5.86 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.64/5.86 = Y4 )
% 5.64/5.86 => ( ( ? [Uu: $o,Uv: $o] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/5.86 => ( ( Xa2 = zero_zero_nat )
% 5.64/5.86 => ( Y4 != none_nat ) ) )
% 5.64/5.86 => ( ! [A5: $o] :
% 5.64/5.86 ( ? [Uw: $o] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Leaf @ A5 @ Uw ) )
% 5.64/5.86 => ( ( Xa2
% 5.64/5.86 = ( suc @ zero_zero_nat ) )
% 5.64/5.86 => ~ ( ( A5
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.86 & ( ~ A5
% 5.64/5.86 => ( Y4 = none_nat ) ) ) ) )
% 5.64/5.86 => ( ! [A5: $o,B5: $o] :
% 5.64/5.86 ( ( X2
% 5.64/5.86 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.86 => ( ? [Va2: nat] :
% 5.64/5.86 ( Xa2
% 5.64/5.86 = ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.86 => ~ ( ( B5
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.86 & ( ~ B5
% 5.64/5.86 => ( ( A5
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.86 & ( ~ A5
% 5.64/5.86 => ( Y4 = none_nat ) ) ) ) ) ) )
% 5.64/5.86 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.64/5.86 => ( Y4 != none_nat ) )
% 5.64/5.86 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.64/5.86 => ( Y4 != none_nat ) )
% 5.64/5.86 => ( ( ? [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.64/5.86 ( X2
% 5.64/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.64/5.86 => ( Y4 != none_nat ) )
% 5.64/5.86 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.86 ( ( X2
% 5.64/5.86 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.86 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( some_nat @ Ma2 ) ) )
% 5.64/5.86 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.86 => ( Y4
% 5.64/5.86 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 != none_nat )
% 5.64/5.86 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.86 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.86 @ ( if_option_nat
% 5.64/5.86 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.86 = none_nat )
% 5.64/5.86 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.64/5.86 @ ( 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_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.86 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % vebt_pred.elims
% 5.64/5.86 thf(fact_1938_low__def,axiom,
% 5.64/5.86 ( vEBT_VEBT_low
% 5.64/5.86 = ( ^ [X: nat,N2: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % low_def
% 5.64/5.86 thf(fact_1939_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.64/5.86 ! [Uw2: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux @ Uy ) ) ).
% 5.64/5.86
% 5.64/5.86 % VEBT_internal.minNull.simps(4)
% 5.64/5.86 thf(fact_1940_valid__0__not,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT] :
% 5.64/5.86 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % valid_0_not
% 5.64/5.86 thf(fact_1941_valid__tree__deg__neq__0,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT] :
% 5.64/5.86 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % valid_tree_deg_neq_0
% 5.64/5.86 thf(fact_1942_buildup__nothing__in__min__max,axiom,
% 5.64/5.86 ! [N: nat,X2: nat] :
% 5.64/5.86 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.64/5.86
% 5.64/5.86 % buildup_nothing_in_min_max
% 5.64/5.86 thf(fact_1943_buildup__nothing__in__leaf,axiom,
% 5.64/5.86 ! [N: nat,X2: nat] :
% 5.64/5.86 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X2 ) ).
% 5.64/5.86
% 5.64/5.86 % buildup_nothing_in_leaf
% 5.64/5.86 thf(fact_1944_deg__not__0,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.86 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.86
% 5.64/5.86 % deg_not_0
% 5.64/5.86 thf(fact_1945_Leaf__0__not,axiom,
% 5.64/5.86 ! [A: $o,B: $o] :
% 5.64/5.86 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % Leaf_0_not
% 5.64/5.86 thf(fact_1946_deg__1__Leafy,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.86 => ( ( N = one_one_nat )
% 5.64/5.86 => ? [A5: $o,B5: $o] :
% 5.64/5.86 ( T
% 5.64/5.86 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % deg_1_Leafy
% 5.64/5.86 thf(fact_1947_deg__1__Leaf,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.64/5.86 => ? [A5: $o,B5: $o] :
% 5.64/5.86 ( T
% 5.64/5.86 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % deg_1_Leaf
% 5.64/5.86 thf(fact_1948_deg1Leaf,axiom,
% 5.64/5.86 ! [T: vEBT_VEBT] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.64/5.86 = ( ? [A3: $o,B3: $o] :
% 5.64/5.86 ( T
% 5.64/5.86 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % deg1Leaf
% 5.64/5.86 thf(fact_1949_both__member__options__def,axiom,
% 5.64/5.86 ( vEBT_V8194947554948674370ptions
% 5.64/5.86 = ( ^ [T2: vEBT_VEBT,X: nat] :
% 5.64/5.86 ( ( vEBT_V5719532721284313246member @ T2 @ X )
% 5.64/5.86 | ( vEBT_VEBT_membermima @ T2 @ X ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % both_member_options_def
% 5.64/5.86 thf(fact_1950_buildup__gives__valid,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.86 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.64/5.86
% 5.64/5.86 % buildup_gives_valid
% 5.64/5.86 thf(fact_1951_member__valid__both__member__options,axiom,
% 5.64/5.86 ! [Tree: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.86 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.64/5.86 => ( ( vEBT_vebt_member @ Tree @ X2 )
% 5.64/5.86 => ( ( vEBT_V5719532721284313246member @ Tree @ X2 )
% 5.64/5.86 | ( vEBT_VEBT_membermima @ Tree @ X2 ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % member_valid_both_member_options
% 5.64/5.86 thf(fact_1952_VEBT_Oinject_I2_J,axiom,
% 5.64/5.86 ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 5.64/5.86 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.64/5.86 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 5.64/5.86 = ( ( X21 = Y21 )
% 5.64/5.86 & ( X222 = Y22 ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % VEBT.inject(2)
% 5.64/5.86 thf(fact_1953_le__zero__eq,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.64/5.86 = ( N = zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_zero_eq
% 5.64/5.86 thf(fact_1954_not__gr__zero,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.64/5.86 = ( N = zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % not_gr_zero
% 5.64/5.86 thf(fact_1955_mult__zero__left,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_left
% 5.64/5.86 thf(fact_1956_mult__zero__left,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( times_times_real @ zero_zero_real @ A )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_left
% 5.64/5.86 thf(fact_1957_mult__zero__left,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_left
% 5.64/5.86 thf(fact_1958_mult__zero__left,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_left
% 5.64/5.86 thf(fact_1959_mult__zero__left,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( times_times_int @ zero_zero_int @ A )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_left
% 5.64/5.86 thf(fact_1960_mult__zero__right,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_right
% 5.64/5.86 thf(fact_1961_mult__zero__right,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( times_times_real @ A @ zero_zero_real )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_right
% 5.64/5.86 thf(fact_1962_mult__zero__right,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_right
% 5.64/5.86 thf(fact_1963_mult__zero__right,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_right
% 5.64/5.86 thf(fact_1964_mult__zero__right,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( times_times_int @ A @ zero_zero_int )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % mult_zero_right
% 5.64/5.86 thf(fact_1965_mult__eq__0__iff,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( ( times_times_complex @ A @ B )
% 5.64/5.86 = zero_zero_complex )
% 5.64/5.86 = ( ( A = zero_zero_complex )
% 5.64/5.86 | ( B = zero_zero_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_eq_0_iff
% 5.64/5.86 thf(fact_1966_mult__eq__0__iff,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ( times_times_real @ A @ B )
% 5.64/5.86 = zero_zero_real )
% 5.64/5.86 = ( ( A = zero_zero_real )
% 5.64/5.86 | ( B = zero_zero_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_eq_0_iff
% 5.64/5.86 thf(fact_1967_mult__eq__0__iff,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ( times_times_rat @ A @ B )
% 5.64/5.86 = zero_zero_rat )
% 5.64/5.86 = ( ( A = zero_zero_rat )
% 5.64/5.86 | ( B = zero_zero_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_eq_0_iff
% 5.64/5.86 thf(fact_1968_mult__eq__0__iff,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ( times_times_nat @ A @ B )
% 5.64/5.86 = zero_zero_nat )
% 5.64/5.86 = ( ( A = zero_zero_nat )
% 5.64/5.86 | ( B = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_eq_0_iff
% 5.64/5.86 thf(fact_1969_mult__eq__0__iff,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ( times_times_int @ A @ B )
% 5.64/5.86 = zero_zero_int )
% 5.64/5.86 = ( ( A = zero_zero_int )
% 5.64/5.86 | ( B = zero_zero_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_eq_0_iff
% 5.64/5.86 thf(fact_1970_mult__cancel__left,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( ( times_times_complex @ C @ A )
% 5.64/5.86 = ( times_times_complex @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left
% 5.64/5.86 thf(fact_1971_mult__cancel__left,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( ( times_times_real @ C @ A )
% 5.64/5.86 = ( times_times_real @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left
% 5.64/5.86 thf(fact_1972_mult__cancel__left,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( ( times_times_rat @ C @ A )
% 5.64/5.86 = ( times_times_rat @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left
% 5.64/5.86 thf(fact_1973_mult__cancel__left,axiom,
% 5.64/5.86 ! [C: nat,A: nat,B: nat] :
% 5.64/5.86 ( ( ( times_times_nat @ C @ A )
% 5.64/5.86 = ( times_times_nat @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_nat )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left
% 5.64/5.86 thf(fact_1974_mult__cancel__left,axiom,
% 5.64/5.86 ! [C: int,A: int,B: int] :
% 5.64/5.86 ( ( ( times_times_int @ C @ A )
% 5.64/5.86 = ( times_times_int @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_int )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left
% 5.64/5.86 thf(fact_1975_mult__cancel__right,axiom,
% 5.64/5.86 ! [A: complex,C: complex,B: complex] :
% 5.64/5.86 ( ( ( times_times_complex @ A @ C )
% 5.64/5.86 = ( times_times_complex @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right
% 5.64/5.86 thf(fact_1976_mult__cancel__right,axiom,
% 5.64/5.86 ! [A: real,C: real,B: real] :
% 5.64/5.86 ( ( ( times_times_real @ A @ C )
% 5.64/5.86 = ( times_times_real @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right
% 5.64/5.86 thf(fact_1977_mult__cancel__right,axiom,
% 5.64/5.86 ! [A: rat,C: rat,B: rat] :
% 5.64/5.86 ( ( ( times_times_rat @ A @ C )
% 5.64/5.86 = ( times_times_rat @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right
% 5.64/5.86 thf(fact_1978_mult__cancel__right,axiom,
% 5.64/5.86 ! [A: nat,C: nat,B: nat] :
% 5.64/5.86 ( ( ( times_times_nat @ A @ C )
% 5.64/5.86 = ( times_times_nat @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_nat )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right
% 5.64/5.86 thf(fact_1979_mult__cancel__right,axiom,
% 5.64/5.86 ! [A: int,C: int,B: int] :
% 5.64/5.86 ( ( ( times_times_int @ A @ C )
% 5.64/5.86 = ( times_times_int @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_int )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right
% 5.64/5.86 thf(fact_1980_add__0,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add_0
% 5.64/5.86 thf(fact_1981_add__0,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add_0
% 5.64/5.86 thf(fact_1982_add__0,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add_0
% 5.64/5.86 thf(fact_1983_add__0,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add_0
% 5.64/5.86 thf(fact_1984_add__0,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add_0
% 5.64/5.86 thf(fact_1985_zero__eq__add__iff__both__eq__0,axiom,
% 5.64/5.86 ! [X2: nat,Y4: nat] :
% 5.64/5.86 ( ( zero_zero_nat
% 5.64/5.86 = ( plus_plus_nat @ X2 @ Y4 ) )
% 5.64/5.86 = ( ( X2 = zero_zero_nat )
% 5.64/5.86 & ( Y4 = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_eq_add_iff_both_eq_0
% 5.64/5.86 thf(fact_1986_add__eq__0__iff__both__eq__0,axiom,
% 5.64/5.86 ! [X2: nat,Y4: nat] :
% 5.64/5.86 ( ( ( plus_plus_nat @ X2 @ Y4 )
% 5.64/5.86 = zero_zero_nat )
% 5.64/5.86 = ( ( X2 = zero_zero_nat )
% 5.64/5.86 & ( Y4 = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_eq_0_iff_both_eq_0
% 5.64/5.86 thf(fact_1987_add__cancel__right__right,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_complex @ A @ B ) )
% 5.64/5.86 = ( B = zero_zero_complex ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_right
% 5.64/5.86 thf(fact_1988_add__cancel__right__right,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_real @ A @ B ) )
% 5.64/5.86 = ( B = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_right
% 5.64/5.86 thf(fact_1989_add__cancel__right__right,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_rat @ A @ B ) )
% 5.64/5.86 = ( B = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_right
% 5.64/5.86 thf(fact_1990_add__cancel__right__right,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_nat @ A @ B ) )
% 5.64/5.86 = ( B = zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_right
% 5.64/5.86 thf(fact_1991_add__cancel__right__right,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_int @ A @ B ) )
% 5.64/5.86 = ( B = zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_right
% 5.64/5.86 thf(fact_1992_add__cancel__right__left,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_complex @ B @ A ) )
% 5.64/5.86 = ( B = zero_zero_complex ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_left
% 5.64/5.86 thf(fact_1993_add__cancel__right__left,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_real @ B @ A ) )
% 5.64/5.86 = ( B = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_left
% 5.64/5.86 thf(fact_1994_add__cancel__right__left,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_rat @ B @ A ) )
% 5.64/5.86 = ( B = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_left
% 5.64/5.86 thf(fact_1995_add__cancel__right__left,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_nat @ B @ A ) )
% 5.64/5.86 = ( B = zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_left
% 5.64/5.86 thf(fact_1996_add__cancel__right__left,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( A
% 5.64/5.86 = ( plus_plus_int @ B @ A ) )
% 5.64/5.86 = ( B = zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_right_left
% 5.64/5.86 thf(fact_1997_add__cancel__left__right,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( ( plus_plus_complex @ A @ B )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_complex ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_right
% 5.64/5.86 thf(fact_1998_add__cancel__left__right,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ( plus_plus_real @ A @ B )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_right
% 5.64/5.86 thf(fact_1999_add__cancel__left__right,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ( plus_plus_rat @ A @ B )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_right
% 5.64/5.86 thf(fact_2000_add__cancel__left__right,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ( plus_plus_nat @ A @ B )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_right
% 5.64/5.86 thf(fact_2001_add__cancel__left__right,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ( plus_plus_int @ A @ B )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_right
% 5.64/5.86 thf(fact_2002_add__cancel__left__left,axiom,
% 5.64/5.86 ! [B: complex,A: complex] :
% 5.64/5.86 ( ( ( plus_plus_complex @ B @ A )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_complex ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_left
% 5.64/5.86 thf(fact_2003_add__cancel__left__left,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( ( plus_plus_real @ B @ A )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_left
% 5.64/5.86 thf(fact_2004_add__cancel__left__left,axiom,
% 5.64/5.86 ! [B: rat,A: rat] :
% 5.64/5.86 ( ( ( plus_plus_rat @ B @ A )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_left
% 5.64/5.86 thf(fact_2005_add__cancel__left__left,axiom,
% 5.64/5.86 ! [B: nat,A: nat] :
% 5.64/5.86 ( ( ( plus_plus_nat @ B @ A )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_left
% 5.64/5.86 thf(fact_2006_add__cancel__left__left,axiom,
% 5.64/5.86 ! [B: int,A: int] :
% 5.64/5.86 ( ( ( plus_plus_int @ B @ A )
% 5.64/5.86 = A )
% 5.64/5.86 = ( B = zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_cancel_left_left
% 5.64/5.86 thf(fact_2007_double__zero__sym,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( zero_zero_real
% 5.64/5.86 = ( plus_plus_real @ A @ A ) )
% 5.64/5.86 = ( A = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_zero_sym
% 5.64/5.86 thf(fact_2008_double__zero__sym,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( zero_zero_rat
% 5.64/5.86 = ( plus_plus_rat @ A @ A ) )
% 5.64/5.86 = ( A = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_zero_sym
% 5.64/5.86 thf(fact_2009_double__zero__sym,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( zero_zero_int
% 5.64/5.86 = ( plus_plus_int @ A @ A ) )
% 5.64/5.86 = ( A = zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_zero_sym
% 5.64/5.86 thf(fact_2010_add_Oright__neutral,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add.right_neutral
% 5.64/5.86 thf(fact_2011_add_Oright__neutral,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add.right_neutral
% 5.64/5.86 thf(fact_2012_add_Oright__neutral,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add.right_neutral
% 5.64/5.86 thf(fact_2013_add_Oright__neutral,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add.right_neutral
% 5.64/5.86 thf(fact_2014_add_Oright__neutral,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % add.right_neutral
% 5.64/5.86 thf(fact_2015_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( minus_minus_complex @ A @ A )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % cancel_comm_monoid_add_class.diff_cancel
% 5.64/5.86 thf(fact_2016_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( minus_minus_real @ A @ A )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % cancel_comm_monoid_add_class.diff_cancel
% 5.64/5.86 thf(fact_2017_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( minus_minus_rat @ A @ A )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % cancel_comm_monoid_add_class.diff_cancel
% 5.64/5.86 thf(fact_2018_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( minus_minus_nat @ A @ A )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % cancel_comm_monoid_add_class.diff_cancel
% 5.64/5.86 thf(fact_2019_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( minus_minus_int @ A @ A )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % cancel_comm_monoid_add_class.diff_cancel
% 5.64/5.86 thf(fact_2020_diff__zero,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_zero
% 5.64/5.86 thf(fact_2021_diff__zero,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_zero
% 5.64/5.86 thf(fact_2022_diff__zero,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_zero
% 5.64/5.86 thf(fact_2023_diff__zero,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_zero
% 5.64/5.86 thf(fact_2024_diff__zero,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_zero
% 5.64/5.86 thf(fact_2025_zero__diff,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % zero_diff
% 5.64/5.86 thf(fact_2026_diff__0__right,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_0_right
% 5.64/5.86 thf(fact_2027_diff__0__right,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_0_right
% 5.64/5.86 thf(fact_2028_diff__0__right,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_0_right
% 5.64/5.86 thf(fact_2029_diff__0__right,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.64/5.86 = A ) ).
% 5.64/5.86
% 5.64/5.86 % diff_0_right
% 5.64/5.86 thf(fact_2030_diff__self,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( minus_minus_complex @ A @ A )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % diff_self
% 5.64/5.86 thf(fact_2031_diff__self,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( minus_minus_real @ A @ A )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % diff_self
% 5.64/5.86 thf(fact_2032_diff__self,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( minus_minus_rat @ A @ A )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % diff_self
% 5.64/5.86 thf(fact_2033_diff__self,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( minus_minus_int @ A @ A )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % diff_self
% 5.64/5.86 thf(fact_2034_div__0,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % div_0
% 5.64/5.86 thf(fact_2035_div__0,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % div_0
% 5.64/5.86 thf(fact_2036_div__0,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % div_0
% 5.64/5.86 thf(fact_2037_div__0,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % div_0
% 5.64/5.86 thf(fact_2038_div__0,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % div_0
% 5.64/5.86 thf(fact_2039_divide__eq__0__iff,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.64/5.86 = zero_zero_complex )
% 5.64/5.86 = ( ( A = zero_zero_complex )
% 5.64/5.86 | ( B = zero_zero_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_eq_0_iff
% 5.64/5.86 thf(fact_2040_divide__eq__0__iff,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ( divide_divide_real @ A @ B )
% 5.64/5.86 = zero_zero_real )
% 5.64/5.86 = ( ( A = zero_zero_real )
% 5.64/5.86 | ( B = zero_zero_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_eq_0_iff
% 5.64/5.86 thf(fact_2041_divide__eq__0__iff,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ( divide_divide_rat @ A @ B )
% 5.64/5.86 = zero_zero_rat )
% 5.64/5.86 = ( ( A = zero_zero_rat )
% 5.64/5.86 | ( B = zero_zero_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_eq_0_iff
% 5.64/5.86 thf(fact_2042_div__by__0,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % div_by_0
% 5.64/5.86 thf(fact_2043_div__by__0,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % div_by_0
% 5.64/5.86 thf(fact_2044_div__by__0,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % div_by_0
% 5.64/5.86 thf(fact_2045_div__by__0,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % div_by_0
% 5.64/5.86 thf(fact_2046_div__by__0,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % div_by_0
% 5.64/5.86 thf(fact_2047_divide__cancel__left,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.64/5.86 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_cancel_left
% 5.64/5.86 thf(fact_2048_divide__cancel__left,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( ( divide_divide_real @ C @ A )
% 5.64/5.86 = ( divide_divide_real @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_cancel_left
% 5.64/5.86 thf(fact_2049_divide__cancel__left,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( ( divide_divide_rat @ C @ A )
% 5.64/5.86 = ( divide_divide_rat @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_cancel_left
% 5.64/5.86 thf(fact_2050_divide__cancel__right,axiom,
% 5.64/5.86 ! [A: complex,C: complex,B: complex] :
% 5.64/5.86 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.64/5.86 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_cancel_right
% 5.64/5.86 thf(fact_2051_divide__cancel__right,axiom,
% 5.64/5.86 ! [A: real,C: real,B: real] :
% 5.64/5.86 ( ( ( divide_divide_real @ A @ C )
% 5.64/5.86 = ( divide_divide_real @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_cancel_right
% 5.64/5.86 thf(fact_2052_divide__cancel__right,axiom,
% 5.64/5.86 ! [A: rat,C: rat,B: rat] :
% 5.64/5.86 ( ( ( divide_divide_rat @ A @ C )
% 5.64/5.86 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_cancel_right
% 5.64/5.86 thf(fact_2053_division__ring__divide__zero,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % division_ring_divide_zero
% 5.64/5.86 thf(fact_2054_division__ring__divide__zero,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % division_ring_divide_zero
% 5.64/5.86 thf(fact_2055_division__ring__divide__zero,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % division_ring_divide_zero
% 5.64/5.86 thf(fact_2056_bits__div__0,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % bits_div_0
% 5.64/5.86 thf(fact_2057_bits__div__0,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % bits_div_0
% 5.64/5.86 thf(fact_2058_bits__div__by__0,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % bits_div_by_0
% 5.64/5.86 thf(fact_2059_bits__div__by__0,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % bits_div_by_0
% 5.64/5.86 thf(fact_2060_less__nat__zero__code,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % less_nat_zero_code
% 5.64/5.86 thf(fact_2061_neq0__conv,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ( ( N != zero_zero_nat )
% 5.64/5.86 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.86
% 5.64/5.86 % neq0_conv
% 5.64/5.86 thf(fact_2062_bot__nat__0_Onot__eq__extremum,axiom,
% 5.64/5.86 ! [A: nat] :
% 5.64/5.86 ( ( A != zero_zero_nat )
% 5.64/5.86 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % bot_nat_0.not_eq_extremum
% 5.64/5.86 thf(fact_2063_le0,axiom,
% 5.64/5.86 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.64/5.86
% 5.64/5.86 % le0
% 5.64/5.86 thf(fact_2064_bot__nat__0_Oextremum,axiom,
% 5.64/5.86 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.64/5.86
% 5.64/5.86 % bot_nat_0.extremum
% 5.64/5.86 thf(fact_2065_mod__add__self2,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.64/5.86 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_add_self2
% 5.64/5.86 thf(fact_2066_mod__add__self2,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.64/5.86 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_add_self2
% 5.64/5.86 thf(fact_2067_mod__add__self2,axiom,
% 5.64/5.86 ! [A: code_integer,B: code_integer] :
% 5.64/5.86 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.64/5.86 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_add_self2
% 5.64/5.86 thf(fact_2068_mod__add__self1,axiom,
% 5.64/5.86 ! [B: nat,A: nat] :
% 5.64/5.86 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.64/5.86 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_add_self1
% 5.64/5.86 thf(fact_2069_mod__add__self1,axiom,
% 5.64/5.86 ! [B: int,A: int] :
% 5.64/5.86 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.64/5.86 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_add_self1
% 5.64/5.86 thf(fact_2070_mod__add__self1,axiom,
% 5.64/5.86 ! [B: code_integer,A: code_integer] :
% 5.64/5.86 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.64/5.86 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_add_self1
% 5.64/5.86 thf(fact_2071_Nat_Oadd__0__right,axiom,
% 5.64/5.86 ! [M: nat] :
% 5.64/5.86 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.64/5.86 = M ) ).
% 5.64/5.86
% 5.64/5.86 % Nat.add_0_right
% 5.64/5.86 thf(fact_2072_add__is__0,axiom,
% 5.64/5.86 ! [M: nat,N: nat] :
% 5.64/5.86 ( ( ( plus_plus_nat @ M @ N )
% 5.64/5.86 = zero_zero_nat )
% 5.64/5.86 = ( ( M = zero_zero_nat )
% 5.64/5.86 & ( N = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_is_0
% 5.64/5.86 thf(fact_2073_diff__self__eq__0,axiom,
% 5.64/5.86 ! [M: nat] :
% 5.64/5.86 ( ( minus_minus_nat @ M @ M )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % diff_self_eq_0
% 5.64/5.86 thf(fact_2074_diff__0__eq__0,axiom,
% 5.64/5.86 ! [N: nat] :
% 5.64/5.86 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % diff_0_eq_0
% 5.64/5.86 thf(fact_2075_mult__cancel2,axiom,
% 5.64/5.86 ! [M: nat,K: nat,N: nat] :
% 5.64/5.86 ( ( ( times_times_nat @ M @ K )
% 5.64/5.86 = ( times_times_nat @ N @ K ) )
% 5.64/5.86 = ( ( M = N )
% 5.64/5.86 | ( K = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel2
% 5.64/5.86 thf(fact_2076_mult__cancel1,axiom,
% 5.64/5.86 ! [K: nat,M: nat,N: nat] :
% 5.64/5.86 ( ( ( times_times_nat @ K @ M )
% 5.64/5.86 = ( times_times_nat @ K @ N ) )
% 5.64/5.86 = ( ( M = N )
% 5.64/5.86 | ( K = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel1
% 5.64/5.86 thf(fact_2077_mult__0__right,axiom,
% 5.64/5.86 ! [M: nat] :
% 5.64/5.86 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % mult_0_right
% 5.64/5.86 thf(fact_2078_mult__is__0,axiom,
% 5.64/5.86 ! [M: nat,N: nat] :
% 5.64/5.86 ( ( ( times_times_nat @ M @ N )
% 5.64/5.86 = zero_zero_nat )
% 5.64/5.86 = ( ( M = zero_zero_nat )
% 5.64/5.86 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_is_0
% 5.64/5.86 thf(fact_2079_mod__less,axiom,
% 5.64/5.86 ! [M: nat,N: nat] :
% 5.64/5.86 ( ( ord_less_nat @ M @ N )
% 5.64/5.86 => ( ( modulo_modulo_nat @ M @ N )
% 5.64/5.86 = M ) ) ).
% 5.64/5.86
% 5.64/5.86 % mod_less
% 5.64/5.86 thf(fact_2080_dbl__simps_I2_J,axiom,
% 5.64/5.86 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % dbl_simps(2)
% 5.64/5.86 thf(fact_2081_dbl__simps_I2_J,axiom,
% 5.64/5.86 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % dbl_simps(2)
% 5.64/5.86 thf(fact_2082_dbl__simps_I2_J,axiom,
% 5.64/5.86 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % dbl_simps(2)
% 5.64/5.86 thf(fact_2083_dbl__simps_I2_J,axiom,
% 5.64/5.86 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % dbl_simps(2)
% 5.64/5.86 thf(fact_2084_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.64/5.86 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_le_double_add_iff_zero_le_single_add
% 5.64/5.86 thf(fact_2085_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.64/5.86 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_le_double_add_iff_zero_le_single_add
% 5.64/5.86 thf(fact_2086_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.64/5.86 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_le_double_add_iff_zero_le_single_add
% 5.64/5.86 thf(fact_2087_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.64/5.86 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_add_le_zero_iff_single_add_le_zero
% 5.64/5.86 thf(fact_2088_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.64/5.86 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_add_le_zero_iff_single_add_le_zero
% 5.64/5.86 thf(fact_2089_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.64/5.86 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_add_le_zero_iff_single_add_le_zero
% 5.64/5.86 thf(fact_2090_le__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.64/5.86 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel2
% 5.64/5.86 thf(fact_2091_le__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.64/5.86 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel2
% 5.64/5.86 thf(fact_2092_le__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.64/5.86 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel2
% 5.64/5.86 thf(fact_2093_le__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.64/5.86 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel2
% 5.64/5.86 thf(fact_2094_le__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel1
% 5.64/5.86 thf(fact_2095_le__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel1
% 5.64/5.86 thf(fact_2096_le__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel1
% 5.64/5.86 thf(fact_2097_le__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % le_add_same_cancel1
% 5.64/5.86 thf(fact_2098_add__le__same__cancel2,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel2
% 5.64/5.86 thf(fact_2099_add__le__same__cancel2,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel2
% 5.64/5.86 thf(fact_2100_add__le__same__cancel2,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel2
% 5.64/5.86 thf(fact_2101_add__le__same__cancel2,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel2
% 5.64/5.86 thf(fact_2102_add__le__same__cancel1,axiom,
% 5.64/5.86 ! [B: rat,A: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel1
% 5.64/5.86 thf(fact_2103_add__le__same__cancel1,axiom,
% 5.64/5.86 ! [B: nat,A: nat] :
% 5.64/5.86 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel1
% 5.64/5.86 thf(fact_2104_add__le__same__cancel1,axiom,
% 5.64/5.86 ! [B: int,A: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel1
% 5.64/5.86 thf(fact_2105_add__le__same__cancel1,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_le_same_cancel1
% 5.64/5.86 thf(fact_2106_add__less__same__cancel1,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel1
% 5.64/5.86 thf(fact_2107_add__less__same__cancel1,axiom,
% 5.64/5.86 ! [B: rat,A: rat] :
% 5.64/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel1
% 5.64/5.86 thf(fact_2108_add__less__same__cancel1,axiom,
% 5.64/5.86 ! [B: nat,A: nat] :
% 5.64/5.86 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel1
% 5.64/5.86 thf(fact_2109_add__less__same__cancel1,axiom,
% 5.64/5.86 ! [B: int,A: int] :
% 5.64/5.86 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.64/5.86 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel1
% 5.64/5.86 thf(fact_2110_add__less__same__cancel2,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel2
% 5.64/5.86 thf(fact_2111_add__less__same__cancel2,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel2
% 5.64/5.86 thf(fact_2112_add__less__same__cancel2,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel2
% 5.64/5.86 thf(fact_2113_add__less__same__cancel2,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.64/5.86 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % add_less_same_cancel2
% 5.64/5.86 thf(fact_2114_less__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.64/5.86 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel1
% 5.64/5.86 thf(fact_2115_less__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.86 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel1
% 5.64/5.86 thf(fact_2116_less__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.86 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel1
% 5.64/5.86 thf(fact_2117_less__add__same__cancel1,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.64/5.86 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel1
% 5.64/5.86 thf(fact_2118_less__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.64/5.86 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel2
% 5.64/5.86 thf(fact_2119_less__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.64/5.86 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel2
% 5.64/5.86 thf(fact_2120_less__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.64/5.86 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel2
% 5.64/5.86 thf(fact_2121_less__add__same__cancel2,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.64/5.86 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.64/5.86
% 5.64/5.86 % less_add_same_cancel2
% 5.64/5.86 thf(fact_2122_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.64/5.86 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_add_less_zero_iff_single_add_less_zero
% 5.64/5.86 thf(fact_2123_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.64/5.86 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_add_less_zero_iff_single_add_less_zero
% 5.64/5.86 thf(fact_2124_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.64/5.86 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.64/5.86
% 5.64/5.86 % double_add_less_zero_iff_single_add_less_zero
% 5.64/5.86 thf(fact_2125_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.64/5.86 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_less_double_add_iff_zero_less_single_add
% 5.64/5.86 thf(fact_2126_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.64/5.86 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_less_double_add_iff_zero_less_single_add
% 5.64/5.86 thf(fact_2127_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.64/5.86 ! [A: int] :
% 5.64/5.86 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.64/5.86 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_less_double_add_iff_zero_less_single_add
% 5.64/5.86 thf(fact_2128_diff__ge__0__iff__ge,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_ge_0_iff_ge
% 5.64/5.86 thf(fact_2129_diff__ge__0__iff__ge,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_ge_0_iff_ge
% 5.64/5.86 thf(fact_2130_diff__ge__0__iff__ge,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.64/5.86 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_ge_0_iff_ge
% 5.64/5.86 thf(fact_2131_diff__gt__0__iff__gt,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.64/5.86 = ( ord_less_real @ B @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_gt_0_iff_gt
% 5.64/5.86 thf(fact_2132_diff__gt__0__iff__gt,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.64/5.86 = ( ord_less_rat @ B @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_gt_0_iff_gt
% 5.64/5.86 thf(fact_2133_diff__gt__0__iff__gt,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.64/5.86 = ( ord_less_int @ B @ A ) ) ).
% 5.64/5.86
% 5.64/5.86 % diff_gt_0_iff_gt
% 5.64/5.86 thf(fact_2134_mult__cancel__right2,axiom,
% 5.64/5.86 ! [A: complex,C: complex] :
% 5.64/5.86 ( ( ( times_times_complex @ A @ C )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( A = one_one_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right2
% 5.64/5.86 thf(fact_2135_mult__cancel__right2,axiom,
% 5.64/5.86 ! [A: real,C: real] :
% 5.64/5.86 ( ( ( times_times_real @ A @ C )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( A = one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right2
% 5.64/5.86 thf(fact_2136_mult__cancel__right2,axiom,
% 5.64/5.86 ! [A: rat,C: rat] :
% 5.64/5.86 ( ( ( times_times_rat @ A @ C )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( A = one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right2
% 5.64/5.86 thf(fact_2137_mult__cancel__right2,axiom,
% 5.64/5.86 ! [A: int,C: int] :
% 5.64/5.86 ( ( ( times_times_int @ A @ C )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_int )
% 5.64/5.86 | ( A = one_one_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right2
% 5.64/5.86 thf(fact_2138_mult__cancel__right1,axiom,
% 5.64/5.86 ! [C: complex,B: complex] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_complex @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( B = one_one_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right1
% 5.64/5.86 thf(fact_2139_mult__cancel__right1,axiom,
% 5.64/5.86 ! [C: real,B: real] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_real @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( B = one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right1
% 5.64/5.86 thf(fact_2140_mult__cancel__right1,axiom,
% 5.64/5.86 ! [C: rat,B: rat] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_rat @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( B = one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right1
% 5.64/5.86 thf(fact_2141_mult__cancel__right1,axiom,
% 5.64/5.86 ! [C: int,B: int] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_int @ B @ C ) )
% 5.64/5.86 = ( ( C = zero_zero_int )
% 5.64/5.86 | ( B = one_one_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_right1
% 5.64/5.86 thf(fact_2142_mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: complex,A: complex] :
% 5.64/5.86 ( ( ( times_times_complex @ C @ A )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( A = one_one_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left2
% 5.64/5.86 thf(fact_2143_mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: real,A: real] :
% 5.64/5.86 ( ( ( times_times_real @ C @ A )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( A = one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left2
% 5.64/5.86 thf(fact_2144_mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: rat,A: rat] :
% 5.64/5.86 ( ( ( times_times_rat @ C @ A )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( A = one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left2
% 5.64/5.86 thf(fact_2145_mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: int,A: int] :
% 5.64/5.86 ( ( ( times_times_int @ C @ A )
% 5.64/5.86 = C )
% 5.64/5.86 = ( ( C = zero_zero_int )
% 5.64/5.86 | ( A = one_one_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left2
% 5.64/5.86 thf(fact_2146_mult__cancel__left1,axiom,
% 5.64/5.86 ! [C: complex,B: complex] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_complex @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_complex )
% 5.64/5.86 | ( B = one_one_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left1
% 5.64/5.86 thf(fact_2147_mult__cancel__left1,axiom,
% 5.64/5.86 ! [C: real,B: real] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_real @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_real )
% 5.64/5.86 | ( B = one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left1
% 5.64/5.86 thf(fact_2148_mult__cancel__left1,axiom,
% 5.64/5.86 ! [C: rat,B: rat] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_rat @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_rat )
% 5.64/5.86 | ( B = one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left1
% 5.64/5.86 thf(fact_2149_mult__cancel__left1,axiom,
% 5.64/5.86 ! [C: int,B: int] :
% 5.64/5.86 ( ( C
% 5.64/5.86 = ( times_times_int @ C @ B ) )
% 5.64/5.86 = ( ( C = zero_zero_int )
% 5.64/5.86 | ( B = one_one_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_cancel_left1
% 5.64/5.86 thf(fact_2150_sum__squares__eq__zero__iff,axiom,
% 5.64/5.86 ! [X2: real,Y4: real] :
% 5.64/5.86 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) )
% 5.64/5.86 = zero_zero_real )
% 5.64/5.86 = ( ( X2 = zero_zero_real )
% 5.64/5.86 & ( Y4 = zero_zero_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % sum_squares_eq_zero_iff
% 5.64/5.86 thf(fact_2151_sum__squares__eq__zero__iff,axiom,
% 5.64/5.86 ! [X2: rat,Y4: rat] :
% 5.64/5.86 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y4 @ Y4 ) )
% 5.64/5.86 = zero_zero_rat )
% 5.64/5.86 = ( ( X2 = zero_zero_rat )
% 5.64/5.86 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % sum_squares_eq_zero_iff
% 5.64/5.86 thf(fact_2152_sum__squares__eq__zero__iff,axiom,
% 5.64/5.86 ! [X2: int,Y4: int] :
% 5.64/5.86 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y4 @ Y4 ) )
% 5.64/5.86 = zero_zero_int )
% 5.64/5.86 = ( ( X2 = zero_zero_int )
% 5.64/5.86 & ( Y4 = zero_zero_int ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % sum_squares_eq_zero_iff
% 5.64/5.86 thf(fact_2153_diff__numeral__special_I9_J,axiom,
% 5.64/5.86 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.64/5.86 = zero_zero_complex ) ).
% 5.64/5.86
% 5.64/5.86 % diff_numeral_special(9)
% 5.64/5.86 thf(fact_2154_diff__numeral__special_I9_J,axiom,
% 5.64/5.86 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.64/5.86 = zero_zero_real ) ).
% 5.64/5.86
% 5.64/5.86 % diff_numeral_special(9)
% 5.64/5.86 thf(fact_2155_diff__numeral__special_I9_J,axiom,
% 5.64/5.86 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.64/5.86 = zero_zero_rat ) ).
% 5.64/5.86
% 5.64/5.86 % diff_numeral_special(9)
% 5.64/5.86 thf(fact_2156_diff__numeral__special_I9_J,axiom,
% 5.64/5.86 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.64/5.86 = zero_zero_int ) ).
% 5.64/5.86
% 5.64/5.86 % diff_numeral_special(9)
% 5.64/5.86 thf(fact_2157_mult__divide__mult__cancel__left__if,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( ( C = zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.64/5.86 = zero_zero_complex ) )
% 5.64/5.86 & ( ( C != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_divide_mult_cancel_left_if
% 5.64/5.86 thf(fact_2158_mult__divide__mult__cancel__left__if,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( ( C = zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.86 = zero_zero_real ) )
% 5.64/5.86 & ( ( C != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.86 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_divide_mult_cancel_left_if
% 5.64/5.86 thf(fact_2159_mult__divide__mult__cancel__left__if,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( ( C = zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.86 = zero_zero_rat ) )
% 5.64/5.86 & ( ( C != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.86 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % mult_divide_mult_cancel_left_if
% 5.64/5.86 thf(fact_2160_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( C != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_left
% 5.64/5.86 thf(fact_2161_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( C != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.86 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_left
% 5.64/5.86 thf(fact_2162_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( C != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.86 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_left
% 5.64/5.86 thf(fact_2163_nonzero__mult__div__cancel__left,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( A != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.64/5.86 = B ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_left
% 5.64/5.86 thf(fact_2164_nonzero__mult__div__cancel__left,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( A != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.64/5.86 = B ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_left
% 5.64/5.86 thf(fact_2165_nonzero__mult__div__cancel__left,axiom,
% 5.64/5.86 ! [A: rat,B: rat] :
% 5.64/5.86 ( ( A != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.64/5.86 = B ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_left
% 5.64/5.86 thf(fact_2166_nonzero__mult__div__cancel__left,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( A != zero_zero_nat )
% 5.64/5.86 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.64/5.86 = B ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_left
% 5.64/5.86 thf(fact_2167_nonzero__mult__div__cancel__left,axiom,
% 5.64/5.86 ! [A: int,B: int] :
% 5.64/5.86 ( ( A != zero_zero_int )
% 5.64/5.86 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.64/5.86 = B ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_left
% 5.64/5.86 thf(fact_2168_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( C != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_left2
% 5.64/5.86 thf(fact_2169_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( C != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.64/5.86 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_left2
% 5.64/5.86 thf(fact_2170_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( C != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.86 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_left2
% 5.64/5.86 thf(fact_2171_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( C != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_right
% 5.64/5.86 thf(fact_2172_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( C != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.86 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_right
% 5.64/5.86 thf(fact_2173_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( C != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.86 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_right
% 5.64/5.86 thf(fact_2174_nonzero__mult__div__cancel__right,axiom,
% 5.64/5.86 ! [B: complex,A: complex] :
% 5.64/5.86 ( ( B != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_right
% 5.64/5.86 thf(fact_2175_nonzero__mult__div__cancel__right,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( B != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_right
% 5.64/5.86 thf(fact_2176_nonzero__mult__div__cancel__right,axiom,
% 5.64/5.86 ! [B: rat,A: rat] :
% 5.64/5.86 ( ( B != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_right
% 5.64/5.86 thf(fact_2177_nonzero__mult__div__cancel__right,axiom,
% 5.64/5.86 ! [B: nat,A: nat] :
% 5.64/5.86 ( ( B != zero_zero_nat )
% 5.64/5.86 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_right
% 5.64/5.86 thf(fact_2178_nonzero__mult__div__cancel__right,axiom,
% 5.64/5.86 ! [B: int,A: int] :
% 5.64/5.86 ( ( B != zero_zero_int )
% 5.64/5.86 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.64/5.86 = A ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_div_cancel_right
% 5.64/5.86 thf(fact_2179_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.64/5.86 ! [C: complex,A: complex,B: complex] :
% 5.64/5.86 ( ( C != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_right2
% 5.64/5.86 thf(fact_2180_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.64/5.86 ! [C: real,A: real,B: real] :
% 5.64/5.86 ( ( C != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.64/5.86 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_right2
% 5.64/5.86 thf(fact_2181_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.64/5.86 ! [C: rat,A: rat,B: rat] :
% 5.64/5.86 ( ( C != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.86 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % nonzero_mult_divide_mult_cancel_right2
% 5.64/5.86 thf(fact_2182_div__mult__mult1,axiom,
% 5.64/5.86 ! [C: nat,A: nat,B: nat] :
% 5.64/5.86 ( ( C != zero_zero_nat )
% 5.64/5.86 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.64/5.86 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % div_mult_mult1
% 5.64/5.86 thf(fact_2183_div__mult__mult1,axiom,
% 5.64/5.86 ! [C: int,A: int,B: int] :
% 5.64/5.86 ( ( C != zero_zero_int )
% 5.64/5.86 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.86 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % div_mult_mult1
% 5.64/5.86 thf(fact_2184_div__mult__mult2,axiom,
% 5.64/5.86 ! [C: nat,A: nat,B: nat] :
% 5.64/5.86 ( ( C != zero_zero_nat )
% 5.64/5.86 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.64/5.86 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % div_mult_mult2
% 5.64/5.86 thf(fact_2185_div__mult__mult2,axiom,
% 5.64/5.86 ! [C: int,A: int,B: int] :
% 5.64/5.86 ( ( C != zero_zero_int )
% 5.64/5.86 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.86 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % div_mult_mult2
% 5.64/5.86 thf(fact_2186_div__mult__mult1__if,axiom,
% 5.64/5.86 ! [C: nat,A: nat,B: nat] :
% 5.64/5.86 ( ( ( C = zero_zero_nat )
% 5.64/5.86 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.64/5.86 = zero_zero_nat ) )
% 5.64/5.86 & ( ( C != zero_zero_nat )
% 5.64/5.86 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.64/5.86 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % div_mult_mult1_if
% 5.64/5.86 thf(fact_2187_div__mult__mult1__if,axiom,
% 5.64/5.86 ! [C: int,A: int,B: int] :
% 5.64/5.86 ( ( ( C = zero_zero_int )
% 5.64/5.86 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.86 = zero_zero_int ) )
% 5.64/5.86 & ( ( C != zero_zero_int )
% 5.64/5.86 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.86 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % div_mult_mult1_if
% 5.64/5.86 thf(fact_2188_diff__add__zero,axiom,
% 5.64/5.86 ! [A: nat,B: nat] :
% 5.64/5.86 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.86 = zero_zero_nat ) ).
% 5.64/5.86
% 5.64/5.86 % diff_add_zero
% 5.64/5.86 thf(fact_2189_zero__eq__1__divide__iff,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( zero_zero_real
% 5.64/5.86 = ( divide_divide_real @ one_one_real @ A ) )
% 5.64/5.86 = ( A = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_eq_1_divide_iff
% 5.64/5.86 thf(fact_2190_zero__eq__1__divide__iff,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( zero_zero_rat
% 5.64/5.86 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.64/5.86 = ( A = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % zero_eq_1_divide_iff
% 5.64/5.86 thf(fact_2191_one__divide__eq__0__iff,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.64/5.86 = zero_zero_real )
% 5.64/5.86 = ( A = zero_zero_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % one_divide_eq_0_iff
% 5.64/5.86 thf(fact_2192_one__divide__eq__0__iff,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.64/5.86 = zero_zero_rat )
% 5.64/5.86 = ( A = zero_zero_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % one_divide_eq_0_iff
% 5.64/5.86 thf(fact_2193_eq__divide__eq__1,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( one_one_real
% 5.64/5.86 = ( divide_divide_real @ B @ A ) )
% 5.64/5.86 = ( ( A != zero_zero_real )
% 5.64/5.86 & ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_divide_eq_1
% 5.64/5.86 thf(fact_2194_eq__divide__eq__1,axiom,
% 5.64/5.86 ! [B: rat,A: rat] :
% 5.64/5.86 ( ( one_one_rat
% 5.64/5.86 = ( divide_divide_rat @ B @ A ) )
% 5.64/5.86 = ( ( A != zero_zero_rat )
% 5.64/5.86 & ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % eq_divide_eq_1
% 5.64/5.86 thf(fact_2195_divide__eq__eq__1,axiom,
% 5.64/5.86 ! [B: real,A: real] :
% 5.64/5.86 ( ( ( divide_divide_real @ B @ A )
% 5.64/5.86 = one_one_real )
% 5.64/5.86 = ( ( A != zero_zero_real )
% 5.64/5.86 & ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_eq_eq_1
% 5.64/5.86 thf(fact_2196_divide__eq__eq__1,axiom,
% 5.64/5.86 ! [B: rat,A: rat] :
% 5.64/5.86 ( ( ( divide_divide_rat @ B @ A )
% 5.64/5.86 = one_one_rat )
% 5.64/5.86 = ( ( A != zero_zero_rat )
% 5.64/5.86 & ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_eq_eq_1
% 5.64/5.86 thf(fact_2197_divide__self__if,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( ( A = zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.64/5.86 = zero_zero_complex ) )
% 5.64/5.86 & ( ( A != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.64/5.86 = one_one_complex ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_self_if
% 5.64/5.86 thf(fact_2198_divide__self__if,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( ( A = zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ A @ A )
% 5.64/5.86 = zero_zero_real ) )
% 5.64/5.86 & ( ( A != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ A @ A )
% 5.64/5.86 = one_one_real ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_self_if
% 5.64/5.86 thf(fact_2199_divide__self__if,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( ( A = zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ A @ A )
% 5.64/5.86 = zero_zero_rat ) )
% 5.64/5.86 & ( ( A != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ A @ A )
% 5.64/5.86 = one_one_rat ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_self_if
% 5.64/5.86 thf(fact_2200_divide__self,axiom,
% 5.64/5.86 ! [A: complex] :
% 5.64/5.86 ( ( A != zero_zero_complex )
% 5.64/5.86 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.64/5.86 = one_one_complex ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_self
% 5.64/5.86 thf(fact_2201_divide__self,axiom,
% 5.64/5.86 ! [A: real] :
% 5.64/5.86 ( ( A != zero_zero_real )
% 5.64/5.86 => ( ( divide_divide_real @ A @ A )
% 5.64/5.86 = one_one_real ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_self
% 5.64/5.86 thf(fact_2202_divide__self,axiom,
% 5.64/5.86 ! [A: rat] :
% 5.64/5.86 ( ( A != zero_zero_rat )
% 5.64/5.86 => ( ( divide_divide_rat @ A @ A )
% 5.64/5.86 = one_one_rat ) ) ).
% 5.64/5.86
% 5.64/5.86 % divide_self
% 5.64/5.86 thf(fact_2203_one__eq__divide__iff,axiom,
% 5.64/5.86 ! [A: complex,B: complex] :
% 5.64/5.86 ( ( one_one_complex
% 5.64/5.86 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.86 = ( ( B != zero_zero_complex )
% 5.64/5.86 & ( A = B ) ) ) ).
% 5.64/5.86
% 5.64/5.86 % one_eq_divide_iff
% 5.64/5.86 thf(fact_2204_one__eq__divide__iff,axiom,
% 5.64/5.86 ! [A: real,B: real] :
% 5.64/5.86 ( ( one_one_real
% 5.64/5.86 = ( divide_divide_real @ A @ B ) )
% 5.64/5.87 = ( ( B != zero_zero_real )
% 5.64/5.87 & ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % one_eq_divide_iff
% 5.64/5.87 thf(fact_2205_one__eq__divide__iff,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( one_one_rat
% 5.64/5.87 = ( divide_divide_rat @ A @ B ) )
% 5.64/5.87 = ( ( B != zero_zero_rat )
% 5.64/5.87 & ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % one_eq_divide_iff
% 5.64/5.87 thf(fact_2206_div__self,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( A != zero_zero_complex )
% 5.64/5.87 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.64/5.87 = one_one_complex ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_self
% 5.64/5.87 thf(fact_2207_div__self,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( A != zero_zero_real )
% 5.64/5.87 => ( ( divide_divide_real @ A @ A )
% 5.64/5.87 = one_one_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_self
% 5.64/5.87 thf(fact_2208_div__self,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( A != zero_zero_rat )
% 5.64/5.87 => ( ( divide_divide_rat @ A @ A )
% 5.64/5.87 = one_one_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_self
% 5.64/5.87 thf(fact_2209_div__self,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( A != zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ A @ A )
% 5.64/5.87 = one_one_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_self
% 5.64/5.87 thf(fact_2210_div__self,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( A != zero_zero_int )
% 5.64/5.87 => ( ( divide_divide_int @ A @ A )
% 5.64/5.87 = one_one_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_self
% 5.64/5.87 thf(fact_2211_divide__eq__1__iff,axiom,
% 5.64/5.87 ! [A: complex,B: complex] :
% 5.64/5.87 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.64/5.87 = one_one_complex )
% 5.64/5.87 = ( ( B != zero_zero_complex )
% 5.64/5.87 & ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_eq_1_iff
% 5.64/5.87 thf(fact_2212_divide__eq__1__iff,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ( divide_divide_real @ A @ B )
% 5.64/5.87 = one_one_real )
% 5.64/5.87 = ( ( B != zero_zero_real )
% 5.64/5.87 & ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_eq_1_iff
% 5.64/5.87 thf(fact_2213_divide__eq__1__iff,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ( divide_divide_rat @ A @ B )
% 5.64/5.87 = one_one_rat )
% 5.64/5.87 = ( ( B != zero_zero_rat )
% 5.64/5.87 & ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_eq_1_iff
% 5.64/5.87 thf(fact_2214_power__0__Suc,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.64/5.87 = zero_zero_rat ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_Suc
% 5.64/5.87 thf(fact_2215_power__0__Suc,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_Suc
% 5.64/5.87 thf(fact_2216_power__0__Suc,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.64/5.87 = zero_zero_real ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_Suc
% 5.64/5.87 thf(fact_2217_power__0__Suc,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_Suc
% 5.64/5.87 thf(fact_2218_power__0__Suc,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.64/5.87 = zero_zero_complex ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_Suc
% 5.64/5.87 thf(fact_2219_power__zero__numeral,axiom,
% 5.64/5.87 ! [K: num] :
% 5.64/5.87 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.64/5.87 = zero_zero_rat ) ).
% 5.64/5.87
% 5.64/5.87 % power_zero_numeral
% 5.64/5.87 thf(fact_2220_power__zero__numeral,axiom,
% 5.64/5.87 ! [K: num] :
% 5.64/5.87 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % power_zero_numeral
% 5.64/5.87 thf(fact_2221_power__zero__numeral,axiom,
% 5.64/5.87 ! [K: num] :
% 5.64/5.87 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.64/5.87 = zero_zero_real ) ).
% 5.64/5.87
% 5.64/5.87 % power_zero_numeral
% 5.64/5.87 thf(fact_2222_power__zero__numeral,axiom,
% 5.64/5.87 ! [K: num] :
% 5.64/5.87 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % power_zero_numeral
% 5.64/5.87 thf(fact_2223_power__zero__numeral,axiom,
% 5.64/5.87 ! [K: num] :
% 5.64/5.87 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.64/5.87 = zero_zero_complex ) ).
% 5.64/5.87
% 5.64/5.87 % power_zero_numeral
% 5.64/5.87 thf(fact_2224_mod__mult__self2__is__0,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self2_is_0
% 5.64/5.87 thf(fact_2225_mod__mult__self2__is__0,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self2_is_0
% 5.64/5.87 thf(fact_2226_mod__mult__self2__is__0,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self2_is_0
% 5.64/5.87 thf(fact_2227_mod__mult__self1__is__0,axiom,
% 5.64/5.87 ! [B: nat,A: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self1_is_0
% 5.64/5.87 thf(fact_2228_mod__mult__self1__is__0,axiom,
% 5.64/5.87 ! [B: int,A: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self1_is_0
% 5.64/5.87 thf(fact_2229_mod__mult__self1__is__0,axiom,
% 5.64/5.87 ! [B: code_integer,A: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self1_is_0
% 5.64/5.87 thf(fact_2230_mod__by__1,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % mod_by_1
% 5.64/5.87 thf(fact_2231_mod__by__1,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % mod_by_1
% 5.64/5.87 thf(fact_2232_mod__by__1,axiom,
% 5.64/5.87 ! [A: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % mod_by_1
% 5.64/5.87 thf(fact_2233_bits__mod__by__1,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % bits_mod_by_1
% 5.64/5.87 thf(fact_2234_bits__mod__by__1,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % bits_mod_by_1
% 5.64/5.87 thf(fact_2235_bits__mod__by__1,axiom,
% 5.64/5.87 ! [A: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % bits_mod_by_1
% 5.64/5.87 thf(fact_2236_mod__div__trivial,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % mod_div_trivial
% 5.64/5.87 thf(fact_2237_mod__div__trivial,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % mod_div_trivial
% 5.64/5.87 thf(fact_2238_mod__div__trivial,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % mod_div_trivial
% 5.64/5.87 thf(fact_2239_bits__mod__div__trivial,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % bits_mod_div_trivial
% 5.64/5.87 thf(fact_2240_bits__mod__div__trivial,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % bits_mod_div_trivial
% 5.64/5.87 thf(fact_2241_bits__mod__div__trivial,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % bits_mod_div_trivial
% 5.64/5.87 thf(fact_2242_power__Suc0__right,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % power_Suc0_right
% 5.64/5.87 thf(fact_2243_power__Suc0__right,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % power_Suc0_right
% 5.64/5.87 thf(fact_2244_power__Suc0__right,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % power_Suc0_right
% 5.64/5.87 thf(fact_2245_power__Suc0__right,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % power_Suc0_right
% 5.64/5.87 thf(fact_2246_mod__mult__self1,axiom,
% 5.64/5.87 ! [A: nat,C: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.64/5.87 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self1
% 5.64/5.87 thf(fact_2247_mod__mult__self1,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.64/5.87 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self1
% 5.64/5.87 thf(fact_2248_mod__mult__self1,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.64/5.87 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self1
% 5.64/5.87 thf(fact_2249_mod__mult__self2,axiom,
% 5.64/5.87 ! [A: nat,B: nat,C: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.64/5.87 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self2
% 5.64/5.87 thf(fact_2250_mod__mult__self2,axiom,
% 5.64/5.87 ! [A: int,B: int,C: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.64/5.87 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self2
% 5.64/5.87 thf(fact_2251_mod__mult__self2,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.64/5.87 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self2
% 5.64/5.87 thf(fact_2252_mod__mult__self3,axiom,
% 5.64/5.87 ! [C: nat,B: nat,A: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.64/5.87 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self3
% 5.64/5.87 thf(fact_2253_mod__mult__self3,axiom,
% 5.64/5.87 ! [C: int,B: int,A: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.64/5.87 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self3
% 5.64/5.87 thf(fact_2254_mod__mult__self3,axiom,
% 5.64/5.87 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.64/5.87 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self3
% 5.64/5.87 thf(fact_2255_mod__mult__self4,axiom,
% 5.64/5.87 ! [B: nat,C: nat,A: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.64/5.87 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self4
% 5.64/5.87 thf(fact_2256_mod__mult__self4,axiom,
% 5.64/5.87 ! [B: int,C: int,A: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.64/5.87 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self4
% 5.64/5.87 thf(fact_2257_mod__mult__self4,axiom,
% 5.64/5.87 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.64/5.87 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_self4
% 5.64/5.87 thf(fact_2258_zero__less__Suc,axiom,
% 5.64/5.87 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_Suc
% 5.64/5.87 thf(fact_2259_less__Suc0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = ( N = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % less_Suc0
% 5.64/5.87 thf(fact_2260_add__gr__0,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.87 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % add_gr_0
% 5.64/5.87 thf(fact_2261_one__eq__mult__iff,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ( suc @ zero_zero_nat )
% 5.64/5.87 = ( times_times_nat @ M @ N ) )
% 5.64/5.87 = ( ( M
% 5.64/5.87 = ( suc @ zero_zero_nat ) )
% 5.64/5.87 & ( N
% 5.64/5.87 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % one_eq_mult_iff
% 5.64/5.87 thf(fact_2262_mult__eq__1__iff,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ( times_times_nat @ M @ N )
% 5.64/5.87 = ( suc @ zero_zero_nat ) )
% 5.64/5.87 = ( ( M
% 5.64/5.87 = ( suc @ zero_zero_nat ) )
% 5.64/5.87 & ( N
% 5.64/5.87 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_eq_1_iff
% 5.64/5.87 thf(fact_2263_zero__less__diff,axiom,
% 5.64/5.87 ! [N: nat,M: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.64/5.87 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_diff
% 5.64/5.87 thf(fact_2264_div__by__Suc__0,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = M ) ).
% 5.64/5.87
% 5.64/5.87 % div_by_Suc_0
% 5.64/5.87 thf(fact_2265_nat__mult__less__cancel__disj,axiom,
% 5.64/5.87 ! [K: nat,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.87 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_mult_less_cancel_disj
% 5.64/5.87 thf(fact_2266_nat__0__less__mult__iff,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.87 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_0_less_mult_iff
% 5.64/5.87 thf(fact_2267_mult__less__cancel2,axiom,
% 5.64/5.87 ! [M: nat,K: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.87 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_less_cancel2
% 5.64/5.87 thf(fact_2268_less__one,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ N @ one_one_nat )
% 5.64/5.87 = ( N = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % less_one
% 5.64/5.87 thf(fact_2269_diff__is__0__eq,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ( minus_minus_nat @ M @ N )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % diff_is_0_eq
% 5.64/5.87 thf(fact_2270_diff__is__0__eq_H,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.87 => ( ( minus_minus_nat @ M @ N )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % diff_is_0_eq'
% 5.64/5.87 thf(fact_2271_div__less,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ M @ N )
% 5.64/5.87 => ( ( divide_divide_nat @ M @ N )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_less
% 5.64/5.87 thf(fact_2272_nat__power__eq__Suc__0__iff,axiom,
% 5.64/5.87 ! [X2: nat,M: nat] :
% 5.64/5.87 ( ( ( power_power_nat @ X2 @ M )
% 5.64/5.87 = ( suc @ zero_zero_nat ) )
% 5.64/5.87 = ( ( M = zero_zero_nat )
% 5.64/5.87 | ( X2
% 5.64/5.87 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_power_eq_Suc_0_iff
% 5.64/5.87 thf(fact_2273_power__Suc__0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.87 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_Suc_0
% 5.64/5.87 thf(fact_2274_nat__zero__less__power__iff,axiom,
% 5.64/5.87 ! [X2: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.87 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_zero_less_power_iff
% 5.64/5.87 thf(fact_2275_nat__mult__div__cancel__disj,axiom,
% 5.64/5.87 ! [K: nat,M: nat,N: nat] :
% 5.64/5.87 ( ( ( K = zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.87 = zero_zero_nat ) )
% 5.64/5.87 & ( ( K != zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.87 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_mult_div_cancel_disj
% 5.64/5.87 thf(fact_2276_mod__by__Suc__0,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % mod_by_Suc_0
% 5.64/5.87 thf(fact_2277_zero__le__divide__1__iff,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.64/5.87 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_le_divide_1_iff
% 5.64/5.87 thf(fact_2278_zero__le__divide__1__iff,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.64/5.87 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_le_divide_1_iff
% 5.64/5.87 thf(fact_2279_divide__le__0__1__iff,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.64/5.87 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_le_0_1_iff
% 5.64/5.87 thf(fact_2280_divide__le__0__1__iff,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.64/5.87 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_le_0_1_iff
% 5.64/5.87 thf(fact_2281_zero__less__divide__1__iff,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.64/5.87 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_divide_1_iff
% 5.64/5.87 thf(fact_2282_zero__less__divide__1__iff,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.64/5.87 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_divide_1_iff
% 5.64/5.87 thf(fact_2283_less__divide__eq__1__pos,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.64/5.87 = ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % less_divide_eq_1_pos
% 5.64/5.87 thf(fact_2284_less__divide__eq__1__pos,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.64/5.87 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % less_divide_eq_1_pos
% 5.64/5.87 thf(fact_2285_less__divide__eq__1__neg,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.87 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.64/5.87 = ( ord_less_real @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % less_divide_eq_1_neg
% 5.64/5.87 thf(fact_2286_less__divide__eq__1__neg,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.87 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.64/5.87 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % less_divide_eq_1_neg
% 5.64/5.87 thf(fact_2287_divide__less__eq__1__pos,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.64/5.87 = ( ord_less_real @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_less_eq_1_pos
% 5.64/5.87 thf(fact_2288_divide__less__eq__1__pos,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.64/5.87 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_less_eq_1_pos
% 5.64/5.87 thf(fact_2289_divide__less__eq__1__neg,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.87 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.64/5.87 = ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_less_eq_1_neg
% 5.64/5.87 thf(fact_2290_divide__less__eq__1__neg,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.87 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.64/5.87 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_less_eq_1_neg
% 5.64/5.87 thf(fact_2291_divide__less__0__1__iff,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.64/5.87 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_less_0_1_iff
% 5.64/5.87 thf(fact_2292_divide__less__0__1__iff,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.64/5.87 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_less_0_1_iff
% 5.64/5.87 thf(fact_2293_eq__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.87 ! [A: complex,B: complex,W: num] :
% 5.64/5.87 ( ( A
% 5.64/5.87 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.87 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.64/5.87 != zero_zero_complex )
% 5.64/5.87 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.87 = B ) )
% 5.64/5.87 & ( ( ( numera6690914467698888265omplex @ W )
% 5.64/5.87 = zero_zero_complex )
% 5.64/5.87 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_divide_eq_numeral1(1)
% 5.64/5.87 thf(fact_2294_eq__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.87 ! [A: real,B: real,W: num] :
% 5.64/5.87 ( ( A
% 5.64/5.87 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.87 = ( ( ( ( numeral_numeral_real @ W )
% 5.64/5.87 != zero_zero_real )
% 5.64/5.87 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.64/5.87 = B ) )
% 5.64/5.87 & ( ( ( numeral_numeral_real @ W )
% 5.64/5.87 = zero_zero_real )
% 5.64/5.87 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_divide_eq_numeral1(1)
% 5.64/5.87 thf(fact_2295_eq__divide__eq__numeral1_I1_J,axiom,
% 5.64/5.87 ! [A: rat,B: rat,W: num] :
% 5.64/5.87 ( ( A
% 5.64/5.87 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.87 = ( ( ( ( numeral_numeral_rat @ W )
% 5.64/5.87 != zero_zero_rat )
% 5.64/5.87 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.64/5.87 = B ) )
% 5.64/5.87 & ( ( ( numeral_numeral_rat @ W )
% 5.64/5.87 = zero_zero_rat )
% 5.64/5.87 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_divide_eq_numeral1(1)
% 5.64/5.87 thf(fact_2296_divide__eq__eq__numeral1_I1_J,axiom,
% 5.64/5.87 ! [B: complex,W: num,A: complex] :
% 5.64/5.87 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.87 = A )
% 5.64/5.87 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.64/5.87 != zero_zero_complex )
% 5.64/5.87 => ( B
% 5.64/5.87 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.64/5.87 & ( ( ( numera6690914467698888265omplex @ W )
% 5.64/5.87 = zero_zero_complex )
% 5.64/5.87 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_eq_eq_numeral1(1)
% 5.64/5.87 thf(fact_2297_divide__eq__eq__numeral1_I1_J,axiom,
% 5.64/5.87 ! [B: real,W: num,A: real] :
% 5.64/5.87 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.64/5.87 = A )
% 5.64/5.87 = ( ( ( ( numeral_numeral_real @ W )
% 5.64/5.87 != zero_zero_real )
% 5.64/5.87 => ( B
% 5.64/5.87 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.64/5.87 & ( ( ( numeral_numeral_real @ W )
% 5.64/5.87 = zero_zero_real )
% 5.64/5.87 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_eq_eq_numeral1(1)
% 5.64/5.87 thf(fact_2298_divide__eq__eq__numeral1_I1_J,axiom,
% 5.64/5.87 ! [B: rat,W: num,A: rat] :
% 5.64/5.87 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.64/5.87 = A )
% 5.64/5.87 = ( ( ( ( numeral_numeral_rat @ W )
% 5.64/5.87 != zero_zero_rat )
% 5.64/5.87 => ( B
% 5.64/5.87 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.64/5.87 & ( ( ( numeral_numeral_rat @ W )
% 5.64/5.87 = zero_zero_rat )
% 5.64/5.87 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_eq_eq_numeral1(1)
% 5.64/5.87 thf(fact_2299_nonzero__divide__mult__cancel__right,axiom,
% 5.64/5.87 ! [B: complex,A: complex] :
% 5.64/5.87 ( ( B != zero_zero_complex )
% 5.64/5.87 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.64/5.87 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nonzero_divide_mult_cancel_right
% 5.64/5.87 thf(fact_2300_nonzero__divide__mult__cancel__right,axiom,
% 5.64/5.87 ! [B: real,A: real] :
% 5.64/5.87 ( ( B != zero_zero_real )
% 5.64/5.87 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.64/5.87 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nonzero_divide_mult_cancel_right
% 5.64/5.87 thf(fact_2301_nonzero__divide__mult__cancel__right,axiom,
% 5.64/5.87 ! [B: rat,A: rat] :
% 5.64/5.87 ( ( B != zero_zero_rat )
% 5.64/5.87 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.64/5.87 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nonzero_divide_mult_cancel_right
% 5.64/5.87 thf(fact_2302_nonzero__divide__mult__cancel__left,axiom,
% 5.64/5.87 ! [A: complex,B: complex] :
% 5.64/5.87 ( ( A != zero_zero_complex )
% 5.64/5.87 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.64/5.87 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nonzero_divide_mult_cancel_left
% 5.64/5.87 thf(fact_2303_nonzero__divide__mult__cancel__left,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( A != zero_zero_real )
% 5.64/5.87 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.64/5.87 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nonzero_divide_mult_cancel_left
% 5.64/5.87 thf(fact_2304_nonzero__divide__mult__cancel__left,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( A != zero_zero_rat )
% 5.64/5.87 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.64/5.87 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nonzero_divide_mult_cancel_left
% 5.64/5.87 thf(fact_2305_div__mult__self1,axiom,
% 5.64/5.87 ! [B: nat,A: nat,C: nat] :
% 5.64/5.87 ( ( B != zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.64/5.87 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self1
% 5.64/5.87 thf(fact_2306_div__mult__self1,axiom,
% 5.64/5.87 ! [B: int,A: int,C: int] :
% 5.64/5.87 ( ( B != zero_zero_int )
% 5.64/5.87 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.64/5.87 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self1
% 5.64/5.87 thf(fact_2307_div__mult__self2,axiom,
% 5.64/5.87 ! [B: nat,A: nat,C: nat] :
% 5.64/5.87 ( ( B != zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.64/5.87 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self2
% 5.64/5.87 thf(fact_2308_div__mult__self2,axiom,
% 5.64/5.87 ! [B: int,A: int,C: int] :
% 5.64/5.87 ( ( B != zero_zero_int )
% 5.64/5.87 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.64/5.87 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self2
% 5.64/5.87 thf(fact_2309_div__mult__self3,axiom,
% 5.64/5.87 ! [B: nat,C: nat,A: nat] :
% 5.64/5.87 ( ( B != zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.64/5.87 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self3
% 5.64/5.87 thf(fact_2310_div__mult__self3,axiom,
% 5.64/5.87 ! [B: int,C: int,A: int] :
% 5.64/5.87 ( ( B != zero_zero_int )
% 5.64/5.87 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.64/5.87 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self3
% 5.64/5.87 thf(fact_2311_div__mult__self4,axiom,
% 5.64/5.87 ! [B: nat,C: nat,A: nat] :
% 5.64/5.87 ( ( B != zero_zero_nat )
% 5.64/5.87 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.64/5.87 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self4
% 5.64/5.87 thf(fact_2312_div__mult__self4,axiom,
% 5.64/5.87 ! [B: int,C: int,A: int] :
% 5.64/5.87 ( ( B != zero_zero_int )
% 5.64/5.87 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.64/5.87 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self4
% 5.64/5.87 thf(fact_2313_power__eq__0__iff,axiom,
% 5.64/5.87 ! [A: rat,N: nat] :
% 5.64/5.87 ( ( ( power_power_rat @ A @ N )
% 5.64/5.87 = zero_zero_rat )
% 5.64/5.87 = ( ( A = zero_zero_rat )
% 5.64/5.87 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_0_iff
% 5.64/5.87 thf(fact_2314_power__eq__0__iff,axiom,
% 5.64/5.87 ! [A: nat,N: nat] :
% 5.64/5.87 ( ( ( power_power_nat @ A @ N )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 = ( ( A = zero_zero_nat )
% 5.64/5.87 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_0_iff
% 5.64/5.87 thf(fact_2315_power__eq__0__iff,axiom,
% 5.64/5.87 ! [A: real,N: nat] :
% 5.64/5.87 ( ( ( power_power_real @ A @ N )
% 5.64/5.87 = zero_zero_real )
% 5.64/5.87 = ( ( A = zero_zero_real )
% 5.64/5.87 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_0_iff
% 5.64/5.87 thf(fact_2316_power__eq__0__iff,axiom,
% 5.64/5.87 ! [A: int,N: nat] :
% 5.64/5.87 ( ( ( power_power_int @ A @ N )
% 5.64/5.87 = zero_zero_int )
% 5.64/5.87 = ( ( A = zero_zero_int )
% 5.64/5.87 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_0_iff
% 5.64/5.87 thf(fact_2317_power__eq__0__iff,axiom,
% 5.64/5.87 ! [A: complex,N: nat] :
% 5.64/5.87 ( ( ( power_power_complex @ A @ N )
% 5.64/5.87 = zero_zero_complex )
% 5.64/5.87 = ( ( A = zero_zero_complex )
% 5.64/5.87 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_0_iff
% 5.64/5.87 thf(fact_2318_Suc__pred,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.64/5.87 = N ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_pred
% 5.64/5.87 thf(fact_2319_one__le__mult__iff,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.64/5.87 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.64/5.87 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % one_le_mult_iff
% 5.64/5.87 thf(fact_2320_mult__le__cancel2,axiom,
% 5.64/5.87 ! [M: nat,K: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.87 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_le_cancel2
% 5.64/5.87 thf(fact_2321_nat__mult__le__cancel__disj,axiom,
% 5.64/5.87 ! [K: nat,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.87 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.87 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_mult_le_cancel_disj
% 5.64/5.87 thf(fact_2322_div__mult__self__is__m,axiom,
% 5.64/5.87 ! [N: nat,M: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.64/5.87 = M ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self_is_m
% 5.64/5.87 thf(fact_2323_div__mult__self1__is__m,axiom,
% 5.64/5.87 ! [N: nat,M: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.64/5.87 = M ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_mult_self1_is_m
% 5.64/5.87 thf(fact_2324_Suc__mod__mult__self4,axiom,
% 5.64/5.87 ! [N: nat,K: nat,M: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_mod_mult_self4
% 5.64/5.87 thf(fact_2325_Suc__mod__mult__self3,axiom,
% 5.64/5.87 ! [K: nat,N: nat,M: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_mod_mult_self3
% 5.64/5.87 thf(fact_2326_Suc__mod__mult__self2,axiom,
% 5.64/5.87 ! [M: nat,N: nat,K: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_mod_mult_self2
% 5.64/5.87 thf(fact_2327_Suc__mod__mult__self1,axiom,
% 5.64/5.87 ! [M: nat,K: nat,N: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_mod_mult_self1
% 5.64/5.87 thf(fact_2328_le__divide__eq__1__pos,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.64/5.87 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % le_divide_eq_1_pos
% 5.64/5.87 thf(fact_2329_le__divide__eq__1__pos,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.64/5.87 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % le_divide_eq_1_pos
% 5.64/5.87 thf(fact_2330_le__divide__eq__1__neg,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.87 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.64/5.87 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % le_divide_eq_1_neg
% 5.64/5.87 thf(fact_2331_le__divide__eq__1__neg,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.87 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.64/5.87 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % le_divide_eq_1_neg
% 5.64/5.87 thf(fact_2332_divide__le__eq__1__pos,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.64/5.87 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_le_eq_1_pos
% 5.64/5.87 thf(fact_2333_divide__le__eq__1__pos,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.64/5.87 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_le_eq_1_pos
% 5.64/5.87 thf(fact_2334_divide__le__eq__1__neg,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.87 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.64/5.87 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_le_eq_1_neg
% 5.64/5.87 thf(fact_2335_divide__le__eq__1__neg,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.87 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.64/5.87 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divide_le_eq_1_neg
% 5.64/5.87 thf(fact_2336_power__strict__decreasing__iff,axiom,
% 5.64/5.87 ! [B: real,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.87 => ( ( ord_less_real @ B @ one_one_real )
% 5.64/5.87 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.64/5.87 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_decreasing_iff
% 5.64/5.87 thf(fact_2337_power__strict__decreasing__iff,axiom,
% 5.64/5.87 ! [B: rat,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.87 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.64/5.87 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.64/5.87 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_decreasing_iff
% 5.64/5.87 thf(fact_2338_power__strict__decreasing__iff,axiom,
% 5.64/5.87 ! [B: nat,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.64/5.87 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.64/5.87 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_decreasing_iff
% 5.64/5.87 thf(fact_2339_power__strict__decreasing__iff,axiom,
% 5.64/5.87 ! [B: int,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ( ord_less_int @ B @ one_one_int )
% 5.64/5.87 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.64/5.87 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_decreasing_iff
% 5.64/5.87 thf(fact_2340_power__mono__iff,axiom,
% 5.64/5.87 ! [A: rat,B: rat,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mono_iff
% 5.64/5.87 thf(fact_2341_power__mono__iff,axiom,
% 5.64/5.87 ! [A: nat,B: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mono_iff
% 5.64/5.87 thf(fact_2342_power__mono__iff,axiom,
% 5.64/5.87 ! [A: int,B: int,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mono_iff
% 5.64/5.87 thf(fact_2343_power__mono__iff,axiom,
% 5.64/5.87 ! [A: real,B: real,N: nat] :
% 5.64/5.87 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mono_iff
% 5.64/5.87 thf(fact_2344_zero__eq__power2,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_rat )
% 5.64/5.87 = ( A = zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_eq_power2
% 5.64/5.87 thf(fact_2345_zero__eq__power2,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 = ( A = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_eq_power2
% 5.64/5.87 thf(fact_2346_zero__eq__power2,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_real )
% 5.64/5.87 = ( A = zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_eq_power2
% 5.64/5.87 thf(fact_2347_zero__eq__power2,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_int )
% 5.64/5.87 = ( A = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_eq_power2
% 5.64/5.87 thf(fact_2348_zero__eq__power2,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_complex )
% 5.64/5.87 = ( A = zero_zero_complex ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_eq_power2
% 5.64/5.87 thf(fact_2349_bits__one__mod__two__eq__one,axiom,
% 5.64/5.87 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_nat ) ).
% 5.64/5.87
% 5.64/5.87 % bits_one_mod_two_eq_one
% 5.64/5.87 thf(fact_2350_bits__one__mod__two__eq__one,axiom,
% 5.64/5.87 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_int ) ).
% 5.64/5.87
% 5.64/5.87 % bits_one_mod_two_eq_one
% 5.64/5.87 thf(fact_2351_bits__one__mod__two__eq__one,axiom,
% 5.64/5.87 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_Code_integer ) ).
% 5.64/5.87
% 5.64/5.87 % bits_one_mod_two_eq_one
% 5.64/5.87 thf(fact_2352_one__mod__two__eq__one,axiom,
% 5.64/5.87 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_nat ) ).
% 5.64/5.87
% 5.64/5.87 % one_mod_two_eq_one
% 5.64/5.87 thf(fact_2353_one__mod__two__eq__one,axiom,
% 5.64/5.87 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_int ) ).
% 5.64/5.87
% 5.64/5.87 % one_mod_two_eq_one
% 5.64/5.87 thf(fact_2354_one__mod__two__eq__one,axiom,
% 5.64/5.87 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_Code_integer ) ).
% 5.64/5.87
% 5.64/5.87 % one_mod_two_eq_one
% 5.64/5.87 thf(fact_2355_mod2__Suc__Suc,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod2_Suc_Suc
% 5.64/5.87 thf(fact_2356_Suc__diff__1,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.64/5.87 = N ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_diff_1
% 5.64/5.87 thf(fact_2357_Suc__times__numeral__mod__eq,axiom,
% 5.64/5.87 ! [K: num,N: nat] :
% 5.64/5.87 ( ( ( numeral_numeral_nat @ K )
% 5.64/5.87 != one_one_nat )
% 5.64/5.87 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.64/5.87 = one_one_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_times_numeral_mod_eq
% 5.64/5.87 thf(fact_2358_bits__1__div__2,axiom,
% 5.64/5.87 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % bits_1_div_2
% 5.64/5.87 thf(fact_2359_bits__1__div__2,axiom,
% 5.64/5.87 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % bits_1_div_2
% 5.64/5.87 thf(fact_2360_one__div__two__eq__zero,axiom,
% 5.64/5.87 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % one_div_two_eq_zero
% 5.64/5.87 thf(fact_2361_one__div__two__eq__zero,axiom,
% 5.64/5.87 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % one_div_two_eq_zero
% 5.64/5.87 thf(fact_2362_power__decreasing__iff,axiom,
% 5.64/5.87 ! [B: rat,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.87 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.64/5.87 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_decreasing_iff
% 5.64/5.87 thf(fact_2363_power__decreasing__iff,axiom,
% 5.64/5.87 ! [B: nat,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.64/5.87 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_decreasing_iff
% 5.64/5.87 thf(fact_2364_power__decreasing__iff,axiom,
% 5.64/5.87 ! [B: int,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ( ord_less_int @ B @ one_one_int )
% 5.64/5.87 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_decreasing_iff
% 5.64/5.87 thf(fact_2365_power__decreasing__iff,axiom,
% 5.64/5.87 ! [B: real,M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.87 => ( ( ord_less_real @ B @ one_one_real )
% 5.64/5.87 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.64/5.87 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_decreasing_iff
% 5.64/5.87 thf(fact_2366_power2__less__eq__zero__iff,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.64/5.87 = ( A = zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_less_eq_zero_iff
% 5.64/5.87 thf(fact_2367_power2__less__eq__zero__iff,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.64/5.87 = ( A = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_less_eq_zero_iff
% 5.64/5.87 thf(fact_2368_power2__less__eq__zero__iff,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.64/5.87 = ( A = zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_less_eq_zero_iff
% 5.64/5.87 thf(fact_2369_power2__eq__iff__nonneg,axiom,
% 5.64/5.87 ! [X2: rat,Y4: rat] :
% 5.64/5.87 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.87 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( X2 = Y4 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_eq_iff_nonneg
% 5.64/5.87 thf(fact_2370_power2__eq__iff__nonneg,axiom,
% 5.64/5.87 ! [X2: nat,Y4: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.64/5.87 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( X2 = Y4 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_eq_iff_nonneg
% 5.64/5.87 thf(fact_2371_power2__eq__iff__nonneg,axiom,
% 5.64/5.87 ! [X2: int,Y4: int] :
% 5.64/5.87 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.87 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( X2 = Y4 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_eq_iff_nonneg
% 5.64/5.87 thf(fact_2372_power2__eq__iff__nonneg,axiom,
% 5.64/5.87 ! [X2: real,Y4: real] :
% 5.64/5.87 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.87 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( X2 = Y4 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power2_eq_iff_nonneg
% 5.64/5.87 thf(fact_2373_zero__less__power2,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( A != zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_power2
% 5.64/5.87 thf(fact_2374_zero__less__power2,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( A != zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_power2
% 5.64/5.87 thf(fact_2375_zero__less__power2,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( A != zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_power2
% 5.64/5.87 thf(fact_2376_sum__power2__eq__zero__iff,axiom,
% 5.64/5.87 ! [X2: rat,Y4: rat] :
% 5.64/5.87 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = zero_zero_rat )
% 5.64/5.87 = ( ( X2 = zero_zero_rat )
% 5.64/5.87 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % sum_power2_eq_zero_iff
% 5.64/5.87 thf(fact_2377_sum__power2__eq__zero__iff,axiom,
% 5.64/5.87 ! [X2: real,Y4: real] :
% 5.64/5.87 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = zero_zero_real )
% 5.64/5.87 = ( ( X2 = zero_zero_real )
% 5.64/5.87 & ( Y4 = zero_zero_real ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % sum_power2_eq_zero_iff
% 5.64/5.87 thf(fact_2378_sum__power2__eq__zero__iff,axiom,
% 5.64/5.87 ! [X2: int,Y4: int] :
% 5.64/5.87 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = zero_zero_int )
% 5.64/5.87 = ( ( X2 = zero_zero_int )
% 5.64/5.87 & ( Y4 = zero_zero_int ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % sum_power2_eq_zero_iff
% 5.64/5.87 thf(fact_2379_not__mod__2__eq__0__eq__1,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 != zero_zero_nat )
% 5.64/5.87 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod_2_eq_0_eq_1
% 5.64/5.87 thf(fact_2380_not__mod__2__eq__0__eq__1,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 != zero_zero_int )
% 5.64/5.87 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod_2_eq_0_eq_1
% 5.64/5.87 thf(fact_2381_not__mod__2__eq__0__eq__1,axiom,
% 5.64/5.87 ! [A: code_integer] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.87 != zero_z3403309356797280102nteger )
% 5.64/5.87 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_Code_integer ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod_2_eq_0_eq_1
% 5.64/5.87 thf(fact_2382_not__mod__2__eq__1__eq__0,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 != one_one_nat )
% 5.64/5.87 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod_2_eq_1_eq_0
% 5.64/5.87 thf(fact_2383_not__mod__2__eq__1__eq__0,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 != one_one_int )
% 5.64/5.87 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod_2_eq_1_eq_0
% 5.64/5.87 thf(fact_2384_not__mod__2__eq__1__eq__0,axiom,
% 5.64/5.87 ! [A: code_integer] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.87 != one_one_Code_integer )
% 5.64/5.87 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod_2_eq_1_eq_0
% 5.64/5.87 thf(fact_2385_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 != ( suc @ zero_zero_nat ) )
% 5.64/5.87 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_mod2_eq_Suc_0_eq_0
% 5.64/5.87 thf(fact_2386_add__self__mod__2,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % add_self_mod_2
% 5.64/5.87 thf(fact_2387_mod2__gr__0,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.87 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.87 = one_one_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod2_gr_0
% 5.64/5.87 thf(fact_2388_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.87 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.64/5.87 thf(fact_2389_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.87 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.64/5.87 thf(fact_2390_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.87 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.64/5.87 thf(fact_2391_mod__eq__self__iff__div__eq__0,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ A @ B )
% 5.64/5.87 = A )
% 5.64/5.87 = ( ( divide_divide_nat @ A @ B )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_eq_self_iff_div_eq_0
% 5.64/5.87 thf(fact_2392_mod__eq__self__iff__div__eq__0,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ A @ B )
% 5.64/5.87 = A )
% 5.64/5.87 = ( ( divide_divide_int @ A @ B )
% 5.64/5.87 = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_eq_self_iff_div_eq_0
% 5.64/5.87 thf(fact_2393_mod__eq__self__iff__div__eq__0,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.64/5.87 = A )
% 5.64/5.87 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_eq_self_iff_div_eq_0
% 5.64/5.87 thf(fact_2394_mod__less__divisor,axiom,
% 5.64/5.87 ! [N: nat,M: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_less_divisor
% 5.64/5.87 thf(fact_2395_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.64/5.87 ! [B: nat,A: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.64/5.87 thf(fact_2396_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.64/5.87 ! [B: int,A: int] :
% 5.64/5.87 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.64/5.87 thf(fact_2397_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.64/5.87 ! [B: code_integer,A: code_integer] :
% 5.64/5.87 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.87 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.64/5.87 thf(fact_2398_bot__nat__def,axiom,
% 5.64/5.87 bot_bot_nat = zero_zero_nat ).
% 5.64/5.87
% 5.64/5.87 % bot_nat_def
% 5.64/5.87 thf(fact_2399_vebt__buildup_Osimps_I2_J,axiom,
% 5.64/5.87 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_buildup.simps(2)
% 5.64/5.87 thf(fact_2400_zero__reorient,axiom,
% 5.64/5.87 ! [X2: complex] :
% 5.64/5.87 ( ( zero_zero_complex = X2 )
% 5.64/5.87 = ( X2 = zero_zero_complex ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_reorient
% 5.64/5.87 thf(fact_2401_zero__reorient,axiom,
% 5.64/5.87 ! [X2: real] :
% 5.64/5.87 ( ( zero_zero_real = X2 )
% 5.64/5.87 = ( X2 = zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_reorient
% 5.64/5.87 thf(fact_2402_zero__reorient,axiom,
% 5.64/5.87 ! [X2: rat] :
% 5.64/5.87 ( ( zero_zero_rat = X2 )
% 5.64/5.87 = ( X2 = zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_reorient
% 5.64/5.87 thf(fact_2403_zero__reorient,axiom,
% 5.64/5.87 ! [X2: nat] :
% 5.64/5.87 ( ( zero_zero_nat = X2 )
% 5.64/5.87 = ( X2 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_reorient
% 5.64/5.87 thf(fact_2404_zero__reorient,axiom,
% 5.64/5.87 ! [X2: int] :
% 5.64/5.87 ( ( zero_zero_int = X2 )
% 5.64/5.87 = ( X2 = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_reorient
% 5.64/5.87 thf(fact_2405_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.64/5.87 ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.64/5.87 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.membermima.simps(1)
% 5.64/5.87 thf(fact_2406_vebt__buildup_Osimps_I1_J,axiom,
% 5.64/5.87 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.64/5.87 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_buildup.simps(1)
% 5.64/5.87 thf(fact_2407_VEBT_Osize_I4_J,axiom,
% 5.64/5.87 ! [X21: $o,X222: $o] :
% 5.64/5.87 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT.size(4)
% 5.64/5.87 thf(fact_2408_mod__Suc,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.64/5.87 = N )
% 5.64/5.87 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.64/5.87 = zero_zero_nat ) )
% 5.64/5.87 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.64/5.87 != N )
% 5.64/5.87 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.64/5.87 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_Suc
% 5.64/5.87 thf(fact_2409_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.64/5.87 ! [A: $o,B: $o,X2: nat] :
% 5.64/5.87 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.87 = ( ( ( X2 = zero_zero_nat )
% 5.64/5.87 => A )
% 5.64/5.87 & ( ( X2 != zero_zero_nat )
% 5.64/5.87 => ( ( ( X2 = one_one_nat )
% 5.64/5.87 => B )
% 5.64/5.87 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.naive_member.simps(1)
% 5.64/5.87 thf(fact_2410_mod__eq__0D,axiom,
% 5.64/5.87 ! [M: nat,D: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ M @ D )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 => ? [Q2: nat] :
% 5.64/5.87 ( M
% 5.64/5.87 = ( times_times_nat @ D @ Q2 ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_eq_0D
% 5.64/5.87 thf(fact_2411_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.64/5.87 ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux: nat] :
% 5.64/5.87 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.naive_member.simps(2)
% 5.64/5.87 thf(fact_2412_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.64/5.87 ! [Uu2: $o] :
% 5.64/5.87 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu2 @ $true ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.minNull.simps(3)
% 5.64/5.87 thf(fact_2413_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.64/5.87 ! [Uv2: $o] :
% 5.64/5.87 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv2 ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.minNull.simps(2)
% 5.64/5.87 thf(fact_2414_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.64/5.87 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.minNull.simps(1)
% 5.64/5.87 thf(fact_2415_vebt__member_Osimps_I1_J,axiom,
% 5.64/5.87 ! [A: $o,B: $o,X2: nat] :
% 5.64/5.87 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.87 = ( ( ( X2 = zero_zero_nat )
% 5.64/5.87 => A )
% 5.64/5.87 & ( ( X2 != zero_zero_nat )
% 5.64/5.87 => ( ( ( X2 = one_one_nat )
% 5.64/5.87 => B )
% 5.64/5.87 & ( X2 = one_one_nat ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_member.simps(1)
% 5.64/5.87 thf(fact_2416_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.87 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.64/5.87 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.64/5.87 = A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_less
% 5.64/5.87 thf(fact_2417_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.87 => ( ( ord_less_nat @ A @ B )
% 5.64/5.87 => ( ( modulo_modulo_nat @ A @ B )
% 5.64/5.87 = A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_less
% 5.64/5.87 thf(fact_2418_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.87 => ( ( ord_less_int @ A @ B )
% 5.64/5.87 => ( ( modulo_modulo_int @ A @ B )
% 5.64/5.87 = A ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_less
% 5.64/5.87 thf(fact_2419_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.64/5.87 ! [B: code_integer,A: code_integer] :
% 5.64/5.87 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.87 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.64/5.87 thf(fact_2420_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.64/5.87 ! [B: nat,A: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.64/5.87 thf(fact_2421_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.64/5.87 ! [B: int,A: int] :
% 5.64/5.87 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.64/5.87 thf(fact_2422_cong__exp__iff__simps_I2_J,axiom,
% 5.64/5.87 ! [N: num,Q3: num] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(2)
% 5.64/5.87 thf(fact_2423_cong__exp__iff__simps_I2_J,axiom,
% 5.64/5.87 ! [N: num,Q3: num] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.87 = zero_zero_int )
% 5.64/5.87 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 5.64/5.87 = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(2)
% 5.64/5.87 thf(fact_2424_cong__exp__iff__simps_I2_J,axiom,
% 5.64/5.87 ! [N: num,Q3: num] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.87 = zero_z3403309356797280102nteger )
% 5.64/5.87 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(2)
% 5.64/5.87 thf(fact_2425_cong__exp__iff__simps_I1_J,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(1)
% 5.64/5.87 thf(fact_2426_cong__exp__iff__simps_I1_J,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.64/5.87 = zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(1)
% 5.64/5.87 thf(fact_2427_cong__exp__iff__simps_I1_J,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.64/5.87 = zero_z3403309356797280102nteger ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(1)
% 5.64/5.87 thf(fact_2428_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.64/5.87 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.87 ( ! [A5: $o,B5: $o,X4: nat] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X4 ) )
% 5.64/5.87 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux2: nat] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux2 ) )
% 5.64/5.87 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ X4 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.naive_member.cases
% 5.64/5.87 thf(fact_2429_mod__le__divisor,axiom,
% 5.64/5.87 ! [N: nat,M: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_le_divisor
% 5.64/5.87 thf(fact_2430_div__less__mono,axiom,
% 5.64/5.87 ! [A4: nat,B4: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ A4 @ B4 )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ( modulo_modulo_nat @ A4 @ N )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 => ( ( ( modulo_modulo_nat @ B4 @ N )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B4 @ N ) ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_less_mono
% 5.64/5.87 thf(fact_2431_invar__vebt_Ointros_I1_J,axiom,
% 5.64/5.87 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % invar_vebt.intros(1)
% 5.64/5.87 thf(fact_2432_power__0__left,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ( N = zero_zero_nat )
% 5.64/5.87 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.64/5.87 = one_one_rat ) )
% 5.64/5.87 & ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.64/5.87 = zero_zero_rat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_left
% 5.64/5.87 thf(fact_2433_power__0__left,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ( N = zero_zero_nat )
% 5.64/5.87 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.64/5.87 = one_one_nat ) )
% 5.64/5.87 & ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.64/5.87 = zero_zero_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_left
% 5.64/5.87 thf(fact_2434_power__0__left,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ( N = zero_zero_nat )
% 5.64/5.87 => ( ( power_power_real @ zero_zero_real @ N )
% 5.64/5.87 = one_one_real ) )
% 5.64/5.87 & ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ( power_power_real @ zero_zero_real @ N )
% 5.64/5.87 = zero_zero_real ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_left
% 5.64/5.87 thf(fact_2435_power__0__left,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ( N = zero_zero_nat )
% 5.64/5.87 => ( ( power_power_int @ zero_zero_int @ N )
% 5.64/5.87 = one_one_int ) )
% 5.64/5.87 & ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ( power_power_int @ zero_zero_int @ N )
% 5.64/5.87 = zero_zero_int ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_left
% 5.64/5.87 thf(fact_2436_power__0__left,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ( N = zero_zero_nat )
% 5.64/5.87 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.64/5.87 = one_one_complex ) )
% 5.64/5.87 & ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.64/5.87 = zero_zero_complex ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_0_left
% 5.64/5.87 thf(fact_2437_zero__power,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.64/5.87 = zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_power
% 5.64/5.87 thf(fact_2438_zero__power,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.64/5.87 = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_power
% 5.64/5.87 thf(fact_2439_zero__power,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( power_power_real @ zero_zero_real @ N )
% 5.64/5.87 = zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_power
% 5.64/5.87 thf(fact_2440_zero__power,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( power_power_int @ zero_zero_int @ N )
% 5.64/5.87 = zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_power
% 5.64/5.87 thf(fact_2441_zero__power,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.64/5.87 = zero_zero_complex ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_power
% 5.64/5.87 thf(fact_2442_mod__mult__eq,axiom,
% 5.64/5.87 ! [A: nat,C: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_eq
% 5.64/5.87 thf(fact_2443_mod__mult__eq,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_eq
% 5.64/5.87 thf(fact_2444_mod__mult__eq,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_eq
% 5.64/5.87 thf(fact_2445_mod__mult__cong,axiom,
% 5.64/5.87 ! [A: nat,C: nat,A2: nat,B: nat,B2: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ A @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ A2 @ C ) )
% 5.64/5.87 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ B2 @ C ) )
% 5.64/5.87 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_cong
% 5.64/5.87 thf(fact_2446_mod__mult__cong,axiom,
% 5.64/5.87 ! [A: int,C: int,A2: int,B: int,B2: int] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ A @ C )
% 5.64/5.87 = ( modulo_modulo_int @ A2 @ C ) )
% 5.64/5.87 => ( ( ( modulo_modulo_int @ B @ C )
% 5.64/5.87 = ( modulo_modulo_int @ B2 @ C ) )
% 5.64/5.87 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_cong
% 5.64/5.87 thf(fact_2447_mod__mult__cong,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,A2: code_integer,B: code_integer,B2: code_integer] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ A2 @ C ) )
% 5.64/5.87 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ B2 @ C ) )
% 5.64/5.87 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_cong
% 5.64/5.87 thf(fact_2448_mod__mult__mult2,axiom,
% 5.64/5.87 ! [A: nat,C: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.64/5.87 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_mult2
% 5.64/5.87 thf(fact_2449_mod__mult__mult2,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.87 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_mult2
% 5.64/5.87 thf(fact_2450_mod__mult__mult2,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.87 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_mult2
% 5.64/5.87 thf(fact_2451_mult__mod__right,axiom,
% 5.64/5.87 ! [C: nat,A: nat,B: nat] :
% 5.64/5.87 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.64/5.87 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_mod_right
% 5.64/5.87 thf(fact_2452_mult__mod__right,axiom,
% 5.64/5.87 ! [C: int,A: int,B: int] :
% 5.64/5.87 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.64/5.87 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_mod_right
% 5.64/5.87 thf(fact_2453_mult__mod__right,axiom,
% 5.64/5.87 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_mod_right
% 5.64/5.87 thf(fact_2454_mod__mult__left__eq,axiom,
% 5.64/5.87 ! [A: nat,C: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_left_eq
% 5.64/5.87 thf(fact_2455_mod__mult__left__eq,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_left_eq
% 5.64/5.87 thf(fact_2456_mod__mult__left__eq,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_left_eq
% 5.64/5.87 thf(fact_2457_mod__mult__right__eq,axiom,
% 5.64/5.87 ! [A: nat,B: nat,C: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_right_eq
% 5.64/5.87 thf(fact_2458_mod__mult__right__eq,axiom,
% 5.64/5.87 ! [A: int,B: int,C: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_right_eq
% 5.64/5.87 thf(fact_2459_mod__mult__right__eq,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_mult_right_eq
% 5.64/5.87 thf(fact_2460_mod__add__right__eq,axiom,
% 5.64/5.87 ! [A: nat,B: nat,C: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_right_eq
% 5.64/5.87 thf(fact_2461_mod__add__right__eq,axiom,
% 5.64/5.87 ! [A: int,B: int,C: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_right_eq
% 5.64/5.87 thf(fact_2462_mod__add__right__eq,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_right_eq
% 5.64/5.87 thf(fact_2463_mod__add__left__eq,axiom,
% 5.64/5.87 ! [A: nat,C: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_left_eq
% 5.64/5.87 thf(fact_2464_mod__add__left__eq,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_left_eq
% 5.64/5.87 thf(fact_2465_mod__add__left__eq,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_left_eq
% 5.64/5.87 thf(fact_2466_mod__add__cong,axiom,
% 5.64/5.87 ! [A: nat,C: nat,A2: nat,B: nat,B2: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ A @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ A2 @ C ) )
% 5.64/5.87 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ B2 @ C ) )
% 5.64/5.87 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_cong
% 5.64/5.87 thf(fact_2467_mod__add__cong,axiom,
% 5.64/5.87 ! [A: int,C: int,A2: int,B: int,B2: int] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ A @ C )
% 5.64/5.87 = ( modulo_modulo_int @ A2 @ C ) )
% 5.64/5.87 => ( ( ( modulo_modulo_int @ B @ C )
% 5.64/5.87 = ( modulo_modulo_int @ B2 @ C ) )
% 5.64/5.87 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_cong
% 5.64/5.87 thf(fact_2468_mod__add__cong,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,A2: code_integer,B: code_integer,B2: code_integer] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ A2 @ C ) )
% 5.64/5.87 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ B2 @ C ) )
% 5.64/5.87 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_cong
% 5.64/5.87 thf(fact_2469_mod__add__eq,axiom,
% 5.64/5.87 ! [A: nat,C: nat,B: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_eq
% 5.64/5.87 thf(fact_2470_mod__add__eq,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_eq
% 5.64/5.87 thf(fact_2471_mod__add__eq,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_add_eq
% 5.64/5.87 thf(fact_2472_power__mod,axiom,
% 5.64/5.87 ! [A: nat,B: nat,N: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.64/5.87 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mod
% 5.64/5.87 thf(fact_2473_power__mod,axiom,
% 5.64/5.87 ! [A: int,B: int,N: nat] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.64/5.87 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mod
% 5.64/5.87 thf(fact_2474_power__mod,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer,N: nat] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_mod
% 5.64/5.87 thf(fact_2475_mod__Suc__eq,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_Suc_eq
% 5.64/5.87 thf(fact_2476_mod__Suc__Suc__eq,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_Suc_Suc_eq
% 5.64/5.87 thf(fact_2477_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.64/5.87 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.87 ( ! [Uu: $o,Uv: $o,D3: nat] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ D3 ) )
% 5.64/5.87 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.valid'.cases
% 5.64/5.87 thf(fact_2478_VEBT_Oexhaust,axiom,
% 5.64/5.87 ! [Y4: vEBT_VEBT] :
% 5.64/5.87 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.64/5.87 ( Y4
% 5.64/5.87 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.64/5.87 => ~ ! [X212: $o,X223: $o] :
% 5.64/5.87 ( Y4
% 5.64/5.87 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT.exhaust
% 5.64/5.87 thf(fact_2479_VEBT_Odistinct_I1_J,axiom,
% 5.64/5.87 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.64/5.87 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.64/5.87 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT.distinct(1)
% 5.64/5.87 thf(fact_2480_mod__less__eq__dividend,axiom,
% 5.64/5.87 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.64/5.87
% 5.64/5.87 % mod_less_eq_dividend
% 5.64/5.87 thf(fact_2481_vebt__insert_Osimps_I1_J,axiom,
% 5.64/5.87 ! [X2: nat,A: $o,B: $o] :
% 5.64/5.87 ( ( ( X2 = zero_zero_nat )
% 5.64/5.87 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.87 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.64/5.87 & ( ( X2 != zero_zero_nat )
% 5.64/5.87 => ( ( ( X2 = one_one_nat )
% 5.64/5.87 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.87 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.64/5.87 & ( ( X2 != one_one_nat )
% 5.64/5.87 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.87 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_insert.simps(1)
% 5.64/5.87 thf(fact_2482_vebt__pred_Osimps_I1_J,axiom,
% 5.64/5.87 ! [Uu2: $o,Uv2: $o] :
% 5.64/5.87 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat )
% 5.64/5.87 = none_nat ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_pred.simps(1)
% 5.64/5.87 thf(fact_2483_zero__le,axiom,
% 5.64/5.87 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 5.64/5.87
% 5.64/5.87 % zero_le
% 5.64/5.87 thf(fact_2484_le__numeral__extra_I3_J,axiom,
% 5.64/5.87 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.64/5.87
% 5.64/5.87 % le_numeral_extra(3)
% 5.64/5.87 thf(fact_2485_le__numeral__extra_I3_J,axiom,
% 5.64/5.87 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.64/5.87
% 5.64/5.87 % le_numeral_extra(3)
% 5.64/5.87 thf(fact_2486_le__numeral__extra_I3_J,axiom,
% 5.64/5.87 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.64/5.87
% 5.64/5.87 % le_numeral_extra(3)
% 5.64/5.87 thf(fact_2487_le__numeral__extra_I3_J,axiom,
% 5.64/5.87 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.64/5.87
% 5.64/5.87 % le_numeral_extra(3)
% 5.64/5.87 thf(fact_2488_less__numeral__extra_I3_J,axiom,
% 5.64/5.87 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.64/5.87
% 5.64/5.87 % less_numeral_extra(3)
% 5.64/5.87 thf(fact_2489_less__numeral__extra_I3_J,axiom,
% 5.64/5.87 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.64/5.87
% 5.64/5.87 % less_numeral_extra(3)
% 5.64/5.87 thf(fact_2490_less__numeral__extra_I3_J,axiom,
% 5.64/5.87 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % less_numeral_extra(3)
% 5.64/5.87 thf(fact_2491_less__numeral__extra_I3_J,axiom,
% 5.64/5.87 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % less_numeral_extra(3)
% 5.64/5.87 thf(fact_2492_zero__less__iff__neq__zero,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 = ( N != zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_less_iff_neq_zero
% 5.64/5.87 thf(fact_2493_gr__implies__not__zero,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ M @ N )
% 5.64/5.87 => ( N != zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % gr_implies_not_zero
% 5.64/5.87 thf(fact_2494_not__less__zero,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % not_less_zero
% 5.64/5.87 thf(fact_2495_gr__zeroI,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % gr_zeroI
% 5.64/5.87 thf(fact_2496_field__lbound__gt__zero,axiom,
% 5.64/5.87 ! [D1: real,D22: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.64/5.87 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.64/5.87 => ? [E2: real] :
% 5.64/5.87 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.64/5.87 & ( ord_less_real @ E2 @ D1 )
% 5.64/5.87 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % field_lbound_gt_zero
% 5.64/5.87 thf(fact_2497_field__lbound__gt__zero,axiom,
% 5.64/5.87 ! [D1: rat,D22: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.64/5.87 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.64/5.87 => ? [E2: rat] :
% 5.64/5.87 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.64/5.87 & ( ord_less_rat @ E2 @ D1 )
% 5.64/5.87 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % field_lbound_gt_zero
% 5.64/5.87 thf(fact_2498_zero__neq__numeral,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( zero_zero_complex
% 5.64/5.87 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_numeral
% 5.64/5.87 thf(fact_2499_zero__neq__numeral,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( zero_zero_real
% 5.64/5.87 != ( numeral_numeral_real @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_numeral
% 5.64/5.87 thf(fact_2500_zero__neq__numeral,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( zero_zero_rat
% 5.64/5.87 != ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_numeral
% 5.64/5.87 thf(fact_2501_zero__neq__numeral,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( zero_zero_nat
% 5.64/5.87 != ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_numeral
% 5.64/5.87 thf(fact_2502_zero__neq__numeral,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ( zero_zero_int
% 5.64/5.87 != ( numeral_numeral_int @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_numeral
% 5.64/5.87 thf(fact_2503_mult__not__zero,axiom,
% 5.64/5.87 ! [A: complex,B: complex] :
% 5.64/5.87 ( ( ( times_times_complex @ A @ B )
% 5.64/5.87 != zero_zero_complex )
% 5.64/5.87 => ( ( A != zero_zero_complex )
% 5.64/5.87 & ( B != zero_zero_complex ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_not_zero
% 5.64/5.87 thf(fact_2504_mult__not__zero,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ( times_times_real @ A @ B )
% 5.64/5.87 != zero_zero_real )
% 5.64/5.87 => ( ( A != zero_zero_real )
% 5.64/5.87 & ( B != zero_zero_real ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_not_zero
% 5.64/5.87 thf(fact_2505_mult__not__zero,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ( times_times_rat @ A @ B )
% 5.64/5.87 != zero_zero_rat )
% 5.64/5.87 => ( ( A != zero_zero_rat )
% 5.64/5.87 & ( B != zero_zero_rat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_not_zero
% 5.64/5.87 thf(fact_2506_mult__not__zero,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( ( times_times_nat @ A @ B )
% 5.64/5.87 != zero_zero_nat )
% 5.64/5.87 => ( ( A != zero_zero_nat )
% 5.64/5.87 & ( B != zero_zero_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_not_zero
% 5.64/5.87 thf(fact_2507_mult__not__zero,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( ( times_times_int @ A @ B )
% 5.64/5.87 != zero_zero_int )
% 5.64/5.87 => ( ( A != zero_zero_int )
% 5.64/5.87 & ( B != zero_zero_int ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_not_zero
% 5.64/5.87 thf(fact_2508_divisors__zero,axiom,
% 5.64/5.87 ! [A: complex,B: complex] :
% 5.64/5.87 ( ( ( times_times_complex @ A @ B )
% 5.64/5.87 = zero_zero_complex )
% 5.64/5.87 => ( ( A = zero_zero_complex )
% 5.64/5.87 | ( B = zero_zero_complex ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divisors_zero
% 5.64/5.87 thf(fact_2509_divisors__zero,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( ( times_times_real @ A @ B )
% 5.64/5.87 = zero_zero_real )
% 5.64/5.87 => ( ( A = zero_zero_real )
% 5.64/5.87 | ( B = zero_zero_real ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divisors_zero
% 5.64/5.87 thf(fact_2510_divisors__zero,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( ( times_times_rat @ A @ B )
% 5.64/5.87 = zero_zero_rat )
% 5.64/5.87 => ( ( A = zero_zero_rat )
% 5.64/5.87 | ( B = zero_zero_rat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divisors_zero
% 5.64/5.87 thf(fact_2511_divisors__zero,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( ( times_times_nat @ A @ B )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 => ( ( A = zero_zero_nat )
% 5.64/5.87 | ( B = zero_zero_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divisors_zero
% 5.64/5.87 thf(fact_2512_divisors__zero,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( ( times_times_int @ A @ B )
% 5.64/5.87 = zero_zero_int )
% 5.64/5.87 => ( ( A = zero_zero_int )
% 5.64/5.87 | ( B = zero_zero_int ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % divisors_zero
% 5.64/5.87 thf(fact_2513_no__zero__divisors,axiom,
% 5.64/5.87 ! [A: complex,B: complex] :
% 5.64/5.87 ( ( A != zero_zero_complex )
% 5.64/5.87 => ( ( B != zero_zero_complex )
% 5.64/5.87 => ( ( times_times_complex @ A @ B )
% 5.64/5.87 != zero_zero_complex ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % no_zero_divisors
% 5.64/5.87 thf(fact_2514_no__zero__divisors,axiom,
% 5.64/5.87 ! [A: real,B: real] :
% 5.64/5.87 ( ( A != zero_zero_real )
% 5.64/5.87 => ( ( B != zero_zero_real )
% 5.64/5.87 => ( ( times_times_real @ A @ B )
% 5.64/5.87 != zero_zero_real ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % no_zero_divisors
% 5.64/5.87 thf(fact_2515_no__zero__divisors,axiom,
% 5.64/5.87 ! [A: rat,B: rat] :
% 5.64/5.87 ( ( A != zero_zero_rat )
% 5.64/5.87 => ( ( B != zero_zero_rat )
% 5.64/5.87 => ( ( times_times_rat @ A @ B )
% 5.64/5.87 != zero_zero_rat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % no_zero_divisors
% 5.64/5.87 thf(fact_2516_no__zero__divisors,axiom,
% 5.64/5.87 ! [A: nat,B: nat] :
% 5.64/5.87 ( ( A != zero_zero_nat )
% 5.64/5.87 => ( ( B != zero_zero_nat )
% 5.64/5.87 => ( ( times_times_nat @ A @ B )
% 5.64/5.87 != zero_zero_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % no_zero_divisors
% 5.64/5.87 thf(fact_2517_no__zero__divisors,axiom,
% 5.64/5.87 ! [A: int,B: int] :
% 5.64/5.87 ( ( A != zero_zero_int )
% 5.64/5.87 => ( ( B != zero_zero_int )
% 5.64/5.87 => ( ( times_times_int @ A @ B )
% 5.64/5.87 != zero_zero_int ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % no_zero_divisors
% 5.64/5.87 thf(fact_2518_mult__left__cancel,axiom,
% 5.64/5.87 ! [C: complex,A: complex,B: complex] :
% 5.64/5.87 ( ( C != zero_zero_complex )
% 5.64/5.87 => ( ( ( times_times_complex @ C @ A )
% 5.64/5.87 = ( times_times_complex @ C @ B ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_left_cancel
% 5.64/5.87 thf(fact_2519_mult__left__cancel,axiom,
% 5.64/5.87 ! [C: real,A: real,B: real] :
% 5.64/5.87 ( ( C != zero_zero_real )
% 5.64/5.87 => ( ( ( times_times_real @ C @ A )
% 5.64/5.87 = ( times_times_real @ C @ B ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_left_cancel
% 5.64/5.87 thf(fact_2520_mult__left__cancel,axiom,
% 5.64/5.87 ! [C: rat,A: rat,B: rat] :
% 5.64/5.87 ( ( C != zero_zero_rat )
% 5.64/5.87 => ( ( ( times_times_rat @ C @ A )
% 5.64/5.87 = ( times_times_rat @ C @ B ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_left_cancel
% 5.64/5.87 thf(fact_2521_mult__left__cancel,axiom,
% 5.64/5.87 ! [C: nat,A: nat,B: nat] :
% 5.64/5.87 ( ( C != zero_zero_nat )
% 5.64/5.87 => ( ( ( times_times_nat @ C @ A )
% 5.64/5.87 = ( times_times_nat @ C @ B ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_left_cancel
% 5.64/5.87 thf(fact_2522_mult__left__cancel,axiom,
% 5.64/5.87 ! [C: int,A: int,B: int] :
% 5.64/5.87 ( ( C != zero_zero_int )
% 5.64/5.87 => ( ( ( times_times_int @ C @ A )
% 5.64/5.87 = ( times_times_int @ C @ B ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_left_cancel
% 5.64/5.87 thf(fact_2523_mult__right__cancel,axiom,
% 5.64/5.87 ! [C: complex,A: complex,B: complex] :
% 5.64/5.87 ( ( C != zero_zero_complex )
% 5.64/5.87 => ( ( ( times_times_complex @ A @ C )
% 5.64/5.87 = ( times_times_complex @ B @ C ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_right_cancel
% 5.64/5.87 thf(fact_2524_mult__right__cancel,axiom,
% 5.64/5.87 ! [C: real,A: real,B: real] :
% 5.64/5.87 ( ( C != zero_zero_real )
% 5.64/5.87 => ( ( ( times_times_real @ A @ C )
% 5.64/5.87 = ( times_times_real @ B @ C ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_right_cancel
% 5.64/5.87 thf(fact_2525_mult__right__cancel,axiom,
% 5.64/5.87 ! [C: rat,A: rat,B: rat] :
% 5.64/5.87 ( ( C != zero_zero_rat )
% 5.64/5.87 => ( ( ( times_times_rat @ A @ C )
% 5.64/5.87 = ( times_times_rat @ B @ C ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_right_cancel
% 5.64/5.87 thf(fact_2526_mult__right__cancel,axiom,
% 5.64/5.87 ! [C: nat,A: nat,B: nat] :
% 5.64/5.87 ( ( C != zero_zero_nat )
% 5.64/5.87 => ( ( ( times_times_nat @ A @ C )
% 5.64/5.87 = ( times_times_nat @ B @ C ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_right_cancel
% 5.64/5.87 thf(fact_2527_mult__right__cancel,axiom,
% 5.64/5.87 ! [C: int,A: int,B: int] :
% 5.64/5.87 ( ( C != zero_zero_int )
% 5.64/5.87 => ( ( ( times_times_int @ A @ C )
% 5.64/5.87 = ( times_times_int @ B @ C ) )
% 5.64/5.87 = ( A = B ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mult_right_cancel
% 5.64/5.87 thf(fact_2528_zero__neq__one,axiom,
% 5.64/5.87 zero_zero_complex != one_one_complex ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_one
% 5.64/5.87 thf(fact_2529_zero__neq__one,axiom,
% 5.64/5.87 zero_zero_real != one_one_real ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_one
% 5.64/5.87 thf(fact_2530_zero__neq__one,axiom,
% 5.64/5.87 zero_zero_rat != one_one_rat ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_one
% 5.64/5.87 thf(fact_2531_zero__neq__one,axiom,
% 5.64/5.87 zero_zero_nat != one_one_nat ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_one
% 5.64/5.87 thf(fact_2532_zero__neq__one,axiom,
% 5.64/5.87 zero_zero_int != one_one_int ).
% 5.64/5.87
% 5.64/5.87 % zero_neq_one
% 5.64/5.87 thf(fact_2533_verit__sum__simplify,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % verit_sum_simplify
% 5.64/5.87 thf(fact_2534_verit__sum__simplify,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % verit_sum_simplify
% 5.64/5.87 thf(fact_2535_verit__sum__simplify,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % verit_sum_simplify
% 5.64/5.87 thf(fact_2536_verit__sum__simplify,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % verit_sum_simplify
% 5.64/5.87 thf(fact_2537_verit__sum__simplify,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % verit_sum_simplify
% 5.64/5.87 thf(fact_2538_add_Ogroup__left__neutral,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.group_left_neutral
% 5.64/5.87 thf(fact_2539_add_Ogroup__left__neutral,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.group_left_neutral
% 5.64/5.87 thf(fact_2540_add_Ogroup__left__neutral,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.group_left_neutral
% 5.64/5.87 thf(fact_2541_add_Ogroup__left__neutral,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.group_left_neutral
% 5.64/5.87 thf(fact_2542_add_Ocomm__neutral,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.comm_neutral
% 5.64/5.87 thf(fact_2543_add_Ocomm__neutral,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.comm_neutral
% 5.64/5.87 thf(fact_2544_add_Ocomm__neutral,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.comm_neutral
% 5.64/5.87 thf(fact_2545_add_Ocomm__neutral,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.comm_neutral
% 5.64/5.87 thf(fact_2546_add_Ocomm__neutral,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % add.comm_neutral
% 5.64/5.87 thf(fact_2547_comm__monoid__add__class_Oadd__0,axiom,
% 5.64/5.87 ! [A: complex] :
% 5.64/5.87 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % comm_monoid_add_class.add_0
% 5.64/5.87 thf(fact_2548_comm__monoid__add__class_Oadd__0,axiom,
% 5.64/5.87 ! [A: real] :
% 5.64/5.87 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % comm_monoid_add_class.add_0
% 5.64/5.87 thf(fact_2549_comm__monoid__add__class_Oadd__0,axiom,
% 5.64/5.87 ! [A: rat] :
% 5.64/5.87 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % comm_monoid_add_class.add_0
% 5.64/5.87 thf(fact_2550_comm__monoid__add__class_Oadd__0,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % comm_monoid_add_class.add_0
% 5.64/5.87 thf(fact_2551_comm__monoid__add__class_Oadd__0,axiom,
% 5.64/5.87 ! [A: int] :
% 5.64/5.87 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.64/5.87 = A ) ).
% 5.64/5.87
% 5.64/5.87 % comm_monoid_add_class.add_0
% 5.64/5.87 thf(fact_2552_eq__iff__diff__eq__0,axiom,
% 5.64/5.87 ( ( ^ [Y6: complex,Z3: complex] : ( Y6 = Z3 ) )
% 5.64/5.87 = ( ^ [A3: complex,B3: complex] :
% 5.64/5.87 ( ( minus_minus_complex @ A3 @ B3 )
% 5.64/5.87 = zero_zero_complex ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_iff_diff_eq_0
% 5.64/5.87 thf(fact_2553_eq__iff__diff__eq__0,axiom,
% 5.64/5.87 ( ( ^ [Y6: real,Z3: real] : ( Y6 = Z3 ) )
% 5.64/5.87 = ( ^ [A3: real,B3: real] :
% 5.64/5.87 ( ( minus_minus_real @ A3 @ B3 )
% 5.64/5.87 = zero_zero_real ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_iff_diff_eq_0
% 5.64/5.87 thf(fact_2554_eq__iff__diff__eq__0,axiom,
% 5.64/5.87 ( ( ^ [Y6: rat,Z3: rat] : ( Y6 = Z3 ) )
% 5.64/5.87 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.87 ( ( minus_minus_rat @ A3 @ B3 )
% 5.64/5.87 = zero_zero_rat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_iff_diff_eq_0
% 5.64/5.87 thf(fact_2555_eq__iff__diff__eq__0,axiom,
% 5.64/5.87 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/5.87 = ( ^ [A3: int,B3: int] :
% 5.64/5.87 ( ( minus_minus_int @ A3 @ B3 )
% 5.64/5.87 = zero_zero_int ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % eq_iff_diff_eq_0
% 5.64/5.87 thf(fact_2556_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.64/5.87 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.64/5.87 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.membermima.simps(2)
% 5.64/5.87 thf(fact_2557_power__not__zero,axiom,
% 5.64/5.87 ! [A: rat,N: nat] :
% 5.64/5.87 ( ( A != zero_zero_rat )
% 5.64/5.87 => ( ( power_power_rat @ A @ N )
% 5.64/5.87 != zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_not_zero
% 5.64/5.87 thf(fact_2558_power__not__zero,axiom,
% 5.64/5.87 ! [A: nat,N: nat] :
% 5.64/5.87 ( ( A != zero_zero_nat )
% 5.64/5.87 => ( ( power_power_nat @ A @ N )
% 5.64/5.87 != zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_not_zero
% 5.64/5.87 thf(fact_2559_power__not__zero,axiom,
% 5.64/5.87 ! [A: real,N: nat] :
% 5.64/5.87 ( ( A != zero_zero_real )
% 5.64/5.87 => ( ( power_power_real @ A @ N )
% 5.64/5.87 != zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_not_zero
% 5.64/5.87 thf(fact_2560_power__not__zero,axiom,
% 5.64/5.87 ! [A: int,N: nat] :
% 5.64/5.87 ( ( A != zero_zero_int )
% 5.64/5.87 => ( ( power_power_int @ A @ N )
% 5.64/5.87 != zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_not_zero
% 5.64/5.87 thf(fact_2561_power__not__zero,axiom,
% 5.64/5.87 ! [A: complex,N: nat] :
% 5.64/5.87 ( ( A != zero_zero_complex )
% 5.64/5.87 => ( ( power_power_complex @ A @ N )
% 5.64/5.87 != zero_zero_complex ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_not_zero
% 5.64/5.87 thf(fact_2562_num_Osize_I4_J,axiom,
% 5.64/5.87 ( ( size_size_num @ one )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % num.size(4)
% 5.64/5.87 thf(fact_2563_not0__implies__Suc,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( N != zero_zero_nat )
% 5.64/5.87 => ? [M4: nat] :
% 5.64/5.87 ( N
% 5.64/5.87 = ( suc @ M4 ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % not0_implies_Suc
% 5.64/5.87 thf(fact_2564_Zero__not__Suc,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( zero_zero_nat
% 5.64/5.87 != ( suc @ M ) ) ).
% 5.64/5.87
% 5.64/5.87 % Zero_not_Suc
% 5.64/5.87 thf(fact_2565_Zero__neq__Suc,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( zero_zero_nat
% 5.64/5.87 != ( suc @ M ) ) ).
% 5.64/5.87
% 5.64/5.87 % Zero_neq_Suc
% 5.64/5.87 thf(fact_2566_Suc__neq__Zero,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( suc @ M )
% 5.64/5.87 != zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_neq_Zero
% 5.64/5.87 thf(fact_2567_zero__induct,axiom,
% 5.64/5.87 ! [P: nat > $o,K: nat] :
% 5.64/5.87 ( ( P @ K )
% 5.64/5.87 => ( ! [N3: nat] :
% 5.64/5.87 ( ( P @ ( suc @ N3 ) )
% 5.64/5.87 => ( P @ N3 ) )
% 5.64/5.87 => ( P @ zero_zero_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_induct
% 5.64/5.87 thf(fact_2568_diff__induct,axiom,
% 5.64/5.87 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.64/5.87 ( ! [X4: nat] : ( P @ X4 @ zero_zero_nat )
% 5.64/5.87 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.64/5.87 => ( ! [X4: nat,Y3: nat] :
% 5.64/5.87 ( ( P @ X4 @ Y3 )
% 5.64/5.87 => ( P @ ( suc @ X4 ) @ ( suc @ Y3 ) ) )
% 5.64/5.87 => ( P @ M @ N ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % diff_induct
% 5.64/5.87 thf(fact_2569_nat__induct,axiom,
% 5.64/5.87 ! [P: nat > $o,N: nat] :
% 5.64/5.87 ( ( P @ zero_zero_nat )
% 5.64/5.87 => ( ! [N3: nat] :
% 5.64/5.87 ( ( P @ N3 )
% 5.64/5.87 => ( P @ ( suc @ N3 ) ) )
% 5.64/5.87 => ( P @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_induct
% 5.64/5.87 thf(fact_2570_vebt__buildup_Ocases,axiom,
% 5.64/5.87 ! [X2: nat] :
% 5.64/5.87 ( ( X2 != zero_zero_nat )
% 5.64/5.87 => ( ( X2
% 5.64/5.87 != ( suc @ zero_zero_nat ) )
% 5.64/5.87 => ~ ! [Va2: nat] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_buildup.cases
% 5.64/5.87 thf(fact_2571_old_Onat_Oexhaust,axiom,
% 5.64/5.87 ! [Y4: nat] :
% 5.64/5.87 ( ( Y4 != zero_zero_nat )
% 5.64/5.87 => ~ ! [Nat3: nat] :
% 5.64/5.87 ( Y4
% 5.64/5.87 != ( suc @ Nat3 ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % old.nat.exhaust
% 5.64/5.87 thf(fact_2572_nat_OdiscI,axiom,
% 5.64/5.87 ! [Nat: nat,X22: nat] :
% 5.64/5.87 ( ( Nat
% 5.64/5.87 = ( suc @ X22 ) )
% 5.64/5.87 => ( Nat != zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat.discI
% 5.64/5.87 thf(fact_2573_old_Onat_Odistinct_I1_J,axiom,
% 5.64/5.87 ! [Nat2: nat] :
% 5.64/5.87 ( zero_zero_nat
% 5.64/5.87 != ( suc @ Nat2 ) ) ).
% 5.64/5.87
% 5.64/5.87 % old.nat.distinct(1)
% 5.64/5.87 thf(fact_2574_old_Onat_Odistinct_I2_J,axiom,
% 5.64/5.87 ! [Nat2: nat] :
% 5.64/5.87 ( ( suc @ Nat2 )
% 5.64/5.87 != zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % old.nat.distinct(2)
% 5.64/5.87 thf(fact_2575_nat_Odistinct_I1_J,axiom,
% 5.64/5.87 ! [X22: nat] :
% 5.64/5.87 ( zero_zero_nat
% 5.64/5.87 != ( suc @ X22 ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat.distinct(1)
% 5.64/5.87 thf(fact_2576_infinite__descent0,axiom,
% 5.64/5.87 ! [P: nat > $o,N: nat] :
% 5.64/5.87 ( ( P @ zero_zero_nat )
% 5.64/5.87 => ( ! [N3: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.87 => ( ~ ( P @ N3 )
% 5.64/5.87 => ? [M5: nat] :
% 5.64/5.87 ( ( ord_less_nat @ M5 @ N3 )
% 5.64/5.87 & ~ ( P @ M5 ) ) ) )
% 5.64/5.87 => ( P @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % infinite_descent0
% 5.64/5.87 thf(fact_2577_gr__implies__not0,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ M @ N )
% 5.64/5.87 => ( N != zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % gr_implies_not0
% 5.64/5.87 thf(fact_2578_less__zeroE,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % less_zeroE
% 5.64/5.87 thf(fact_2579_not__less0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % not_less0
% 5.64/5.87 thf(fact_2580_not__gr0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.64/5.87 = ( N = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % not_gr0
% 5.64/5.87 thf(fact_2581_gr0I,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( N != zero_zero_nat )
% 5.64/5.87 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % gr0I
% 5.64/5.87 thf(fact_2582_bot__nat__0_Oextremum__strict,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % bot_nat_0.extremum_strict
% 5.64/5.87 thf(fact_2583_le__0__eq,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.64/5.87 = ( N = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % le_0_eq
% 5.64/5.87 thf(fact_2584_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.87 => ( A = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % bot_nat_0.extremum_uniqueI
% 5.64/5.87 thf(fact_2585_bot__nat__0_Oextremum__unique,axiom,
% 5.64/5.87 ! [A: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.87 = ( A = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % bot_nat_0.extremum_unique
% 5.64/5.87 thf(fact_2586_less__eq__nat_Osimps_I1_J,axiom,
% 5.64/5.87 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.64/5.87
% 5.64/5.87 % less_eq_nat.simps(1)
% 5.64/5.87 thf(fact_2587_add__eq__self__zero,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ( plus_plus_nat @ M @ N )
% 5.64/5.87 = M )
% 5.64/5.87 => ( N = zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % add_eq_self_zero
% 5.64/5.87 thf(fact_2588_plus__nat_Oadd__0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.64/5.87 = N ) ).
% 5.64/5.87
% 5.64/5.87 % plus_nat.add_0
% 5.64/5.87 thf(fact_2589_diffs0__imp__equal,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ( minus_minus_nat @ M @ N )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 => ( ( ( minus_minus_nat @ N @ M )
% 5.64/5.87 = zero_zero_nat )
% 5.64/5.87 => ( M = N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % diffs0_imp_equal
% 5.64/5.87 thf(fact_2590_minus__nat_Odiff__0,axiom,
% 5.64/5.87 ! [M: nat] :
% 5.64/5.87 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.64/5.87 = M ) ).
% 5.64/5.87
% 5.64/5.87 % minus_nat.diff_0
% 5.64/5.87 thf(fact_2591_nat__mult__eq__cancel__disj,axiom,
% 5.64/5.87 ! [K: nat,M: nat,N: nat] :
% 5.64/5.87 ( ( ( times_times_nat @ K @ M )
% 5.64/5.87 = ( times_times_nat @ K @ N ) )
% 5.64/5.87 = ( ( K = zero_zero_nat )
% 5.64/5.87 | ( M = N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_mult_eq_cancel_disj
% 5.64/5.87 thf(fact_2592_mult__0,axiom,
% 5.64/5.87 ! [N: nat] :
% 5.64/5.87 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.64/5.87 = zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % mult_0
% 5.64/5.87 thf(fact_2593_split__mod,axiom,
% 5.64/5.87 ! [P: nat > $o,M: nat,N: nat] :
% 5.64/5.87 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.64/5.87 = ( ( ( N = zero_zero_nat )
% 5.64/5.87 => ( P @ M ) )
% 5.64/5.87 & ( ( N != zero_zero_nat )
% 5.64/5.87 => ! [I4: nat,J3: nat] :
% 5.64/5.87 ( ( ord_less_nat @ J3 @ N )
% 5.64/5.87 => ( ( M
% 5.64/5.87 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.64/5.87 => ( P @ J3 ) ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % split_mod
% 5.64/5.87 thf(fact_2594_power__eq__iff__eq__base,axiom,
% 5.64/5.87 ! [N: nat,A: rat,B: rat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.87 => ( ( ( power_power_rat @ A @ N )
% 5.64/5.87 = ( power_power_rat @ B @ N ) )
% 5.64/5.87 = ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_iff_eq_base
% 5.64/5.87 thf(fact_2595_power__eq__iff__eq__base,axiom,
% 5.64/5.87 ! [N: nat,A: nat,B: nat] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ( ( power_power_nat @ A @ N )
% 5.64/5.87 = ( power_power_nat @ B @ N ) )
% 5.64/5.87 = ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_iff_eq_base
% 5.64/5.87 thf(fact_2596_power__eq__iff__eq__base,axiom,
% 5.64/5.87 ! [N: nat,A: int,B: int] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ( ( power_power_int @ A @ N )
% 5.64/5.87 = ( power_power_int @ B @ N ) )
% 5.64/5.87 = ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_iff_eq_base
% 5.64/5.87 thf(fact_2597_power__eq__iff__eq__base,axiom,
% 5.64/5.87 ! [N: nat,A: real,B: real] :
% 5.64/5.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.87 => ( ( ( power_power_real @ A @ N )
% 5.64/5.87 = ( power_power_real @ B @ N ) )
% 5.64/5.87 = ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_iff_eq_base
% 5.64/5.87 thf(fact_2598_power__eq__imp__eq__base,axiom,
% 5.64/5.87 ! [A: rat,N: nat,B: rat] :
% 5.64/5.87 ( ( ( power_power_rat @ A @ N )
% 5.64/5.87 = ( power_power_rat @ B @ N ) )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_imp_eq_base
% 5.64/5.87 thf(fact_2599_power__eq__imp__eq__base,axiom,
% 5.64/5.87 ! [A: nat,N: nat,B: nat] :
% 5.64/5.87 ( ( ( power_power_nat @ A @ N )
% 5.64/5.87 = ( power_power_nat @ B @ N ) )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_imp_eq_base
% 5.64/5.87 thf(fact_2600_power__eq__imp__eq__base,axiom,
% 5.64/5.87 ! [A: int,N: nat,B: int] :
% 5.64/5.87 ( ( ( power_power_int @ A @ N )
% 5.64/5.87 = ( power_power_int @ B @ N ) )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_imp_eq_base
% 5.64/5.87 thf(fact_2601_power__eq__imp__eq__base,axiom,
% 5.64/5.87 ! [A: real,N: nat,B: real] :
% 5.64/5.87 ( ( ( power_power_real @ A @ N )
% 5.64/5.87 = ( power_power_real @ B @ N ) )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( A = B ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_eq_imp_eq_base
% 5.64/5.87 thf(fact_2602_lambda__zero,axiom,
% 5.64/5.87 ( ( ^ [H: complex] : zero_zero_complex )
% 5.64/5.87 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.64/5.87
% 5.64/5.87 % lambda_zero
% 5.64/5.87 thf(fact_2603_lambda__zero,axiom,
% 5.64/5.87 ( ( ^ [H: real] : zero_zero_real )
% 5.64/5.87 = ( times_times_real @ zero_zero_real ) ) ).
% 5.64/5.87
% 5.64/5.87 % lambda_zero
% 5.64/5.87 thf(fact_2604_lambda__zero,axiom,
% 5.64/5.87 ( ( ^ [H: rat] : zero_zero_rat )
% 5.64/5.87 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.64/5.87
% 5.64/5.87 % lambda_zero
% 5.64/5.87 thf(fact_2605_lambda__zero,axiom,
% 5.64/5.87 ( ( ^ [H: nat] : zero_zero_nat )
% 5.64/5.87 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % lambda_zero
% 5.64/5.87 thf(fact_2606_lambda__zero,axiom,
% 5.64/5.87 ( ( ^ [H: int] : zero_zero_int )
% 5.64/5.87 = ( times_times_int @ zero_zero_int ) ) ).
% 5.64/5.87
% 5.64/5.87 % lambda_zero
% 5.64/5.87 thf(fact_2607_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.64/5.87 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X2: nat] :
% 5.64/5.87 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X2 )
% 5.64/5.87 = ( ( X2 = Mi )
% 5.64/5.87 | ( X2 = Ma ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.membermima.simps(3)
% 5.64/5.87 thf(fact_2608_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.64/5.87 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.87 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.64/5.87 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.87 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.64/5.87 thf(fact_2609_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.64/5.87 ! [C: nat,A: nat,B: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.87 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.87 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.64/5.87 thf(fact_2610_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.64/5.87 ! [C: int,A: int,B: int] :
% 5.64/5.87 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.87 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.87 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.64/5.87 thf(fact_2611_cong__exp__iff__simps_I9_J,axiom,
% 5.64/5.87 ! [M: num,Q3: num,N: num] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.87 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.87 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.64/5.87 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(9)
% 5.64/5.87 thf(fact_2612_cong__exp__iff__simps_I9_J,axiom,
% 5.64/5.87 ! [M: num,Q3: num,N: num] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.87 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.87 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.64/5.87 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(9)
% 5.64/5.87 thf(fact_2613_cong__exp__iff__simps_I9_J,axiom,
% 5.64/5.87 ! [M: num,Q3: num,N: num] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.87 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(9)
% 5.64/5.87 thf(fact_2614_cong__exp__iff__simps_I4_J,axiom,
% 5.64/5.87 ! [M: num,N: num] :
% 5.64/5.87 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.64/5.87 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(4)
% 5.64/5.87 thf(fact_2615_cong__exp__iff__simps_I4_J,axiom,
% 5.64/5.87 ! [M: num,N: num] :
% 5.64/5.87 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.64/5.87 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(4)
% 5.64/5.87 thf(fact_2616_cong__exp__iff__simps_I4_J,axiom,
% 5.64/5.87 ! [M: num,N: num] :
% 5.64/5.87 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.64/5.87 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % cong_exp_iff_simps(4)
% 5.64/5.87 thf(fact_2617_mod__eqE,axiom,
% 5.64/5.87 ! [A: int,C: int,B: int] :
% 5.64/5.87 ( ( ( modulo_modulo_int @ A @ C )
% 5.64/5.87 = ( modulo_modulo_int @ B @ C ) )
% 5.64/5.87 => ~ ! [D3: int] :
% 5.64/5.87 ( B
% 5.64/5.87 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_eqE
% 5.64/5.87 thf(fact_2618_mod__eqE,axiom,
% 5.64/5.87 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.87 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.64/5.87 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.64/5.87 => ~ ! [D3: code_integer] :
% 5.64/5.87 ( B
% 5.64/5.87 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_eqE
% 5.64/5.87 thf(fact_2619_div__add1__eq,axiom,
% 5.64/5.87 ! [A: nat,B: nat,C: nat] :
% 5.64/5.87 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.87 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_add1_eq
% 5.64/5.87 thf(fact_2620_div__add1__eq,axiom,
% 5.64/5.87 ! [A: int,B: int,C: int] :
% 5.64/5.87 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.87 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_add1_eq
% 5.64/5.87 thf(fact_2621_div__add1__eq,axiom,
% 5.64/5.87 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.87 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.64/5.87 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % div_add1_eq
% 5.64/5.87 thf(fact_2622_Suc__times__mod__eq,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.64/5.87 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.64/5.87 = one_one_nat ) ) ).
% 5.64/5.87
% 5.64/5.87 % Suc_times_mod_eq
% 5.64/5.87 thf(fact_2623_mod__induct,axiom,
% 5.64/5.87 ! [P: nat > $o,N: nat,P2: nat,M: nat] :
% 5.64/5.87 ( ( P @ N )
% 5.64/5.87 => ( ( ord_less_nat @ N @ P2 )
% 5.64/5.87 => ( ( ord_less_nat @ M @ P2 )
% 5.64/5.87 => ( ! [N3: nat] :
% 5.64/5.87 ( ( ord_less_nat @ N3 @ P2 )
% 5.64/5.87 => ( ( P @ N3 )
% 5.64/5.87 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P2 ) ) ) )
% 5.64/5.87 => ( P @ M ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_induct
% 5.64/5.87 thf(fact_2624_mod__Suc__le__divisor,axiom,
% 5.64/5.87 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.64/5.87
% 5.64/5.87 % mod_Suc_le_divisor
% 5.64/5.87 thf(fact_2625_power__strict__mono,axiom,
% 5.64/5.87 ! [A: rat,B: rat,N: nat] :
% 5.64/5.87 ( ( ord_less_rat @ A @ B )
% 5.64/5.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_mono
% 5.64/5.87 thf(fact_2626_power__strict__mono,axiom,
% 5.64/5.87 ! [A: nat,B: nat,N: nat] :
% 5.64/5.87 ( ( ord_less_nat @ A @ B )
% 5.64/5.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_mono
% 5.64/5.87 thf(fact_2627_power__strict__mono,axiom,
% 5.64/5.87 ! [A: int,B: int,N: nat] :
% 5.64/5.87 ( ( ord_less_int @ A @ B )
% 5.64/5.87 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_mono
% 5.64/5.87 thf(fact_2628_power__strict__mono,axiom,
% 5.64/5.87 ! [A: real,B: real,N: nat] :
% 5.64/5.87 ( ( ord_less_real @ A @ B )
% 5.64/5.87 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.87 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.87 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % power_strict_mono
% 5.64/5.87 thf(fact_2629_mod__if,axiom,
% 5.64/5.87 ( modulo_modulo_nat
% 5.64/5.87 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M2 @ N2 ) @ M2 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_if
% 5.64/5.87 thf(fact_2630_mod__geq,axiom,
% 5.64/5.87 ! [M: nat,N: nat] :
% 5.64/5.87 ( ~ ( ord_less_nat @ M @ N )
% 5.64/5.87 => ( ( modulo_modulo_nat @ M @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % mod_geq
% 5.64/5.87 thf(fact_2631_le__mod__geq,axiom,
% 5.64/5.87 ! [N: nat,M: nat] :
% 5.64/5.87 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.87 => ( ( modulo_modulo_nat @ M @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % le_mod_geq
% 5.64/5.87 thf(fact_2632_nat__mod__eq__iff,axiom,
% 5.64/5.87 ! [X2: nat,N: nat,Y4: nat] :
% 5.64/5.87 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.64/5.87 = ( modulo_modulo_nat @ Y4 @ N ) )
% 5.64/5.87 = ( ? [Q1: nat,Q22: nat] :
% 5.64/5.87 ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N @ Q1 ) )
% 5.64/5.87 = ( plus_plus_nat @ Y4 @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % nat_mod_eq_iff
% 5.64/5.87 thf(fact_2633_VEBT__internal_OminNull_Ocases,axiom,
% 5.64/5.87 ! [X2: vEBT_VEBT] :
% 5.64/5.87 ( ( X2
% 5.64/5.87 != ( vEBT_Leaf @ $false @ $false ) )
% 5.64/5.87 => ( ! [Uv: $o] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( vEBT_Leaf @ $true @ Uv ) )
% 5.64/5.87 => ( ! [Uu: $o] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( vEBT_Leaf @ Uu @ $true ) )
% 5.64/5.87 => ( ! [Uw: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) )
% 5.64/5.87 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.87 ( X2
% 5.64/5.87 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % VEBT_internal.minNull.cases
% 5.64/5.87 thf(fact_2634_vebt__pred_Osimps_I2_J,axiom,
% 5.64/5.87 ! [A: $o,Uw2: $o] :
% 5.64/5.87 ( ( A
% 5.64/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.87 & ( ~ A
% 5.64/5.87 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.87 = none_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_pred.simps(2)
% 5.64/5.87 thf(fact_2635_vebt__mint_Osimps_I1_J,axiom,
% 5.64/5.87 ! [A: $o,B: $o] :
% 5.64/5.87 ( ( A
% 5.64/5.87 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.87 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.87 & ( ~ A
% 5.64/5.87 => ( ( B
% 5.64/5.87 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.87 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.87 & ( ~ B
% 5.64/5.87 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.87 = none_nat ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_mint.simps(1)
% 5.64/5.87 thf(fact_2636_vebt__succ_Osimps_I1_J,axiom,
% 5.64/5.87 ! [B: $o,Uu2: $o] :
% 5.64/5.87 ( ( B
% 5.64/5.87 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 5.64/5.87 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.87 & ( ~ B
% 5.64/5.87 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu2 @ B ) @ zero_zero_nat )
% 5.64/5.87 = none_nat ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_succ.simps(1)
% 5.64/5.87 thf(fact_2637_vebt__maxt_Osimps_I1_J,axiom,
% 5.64/5.87 ! [B: $o,A: $o] :
% 5.64/5.87 ( ( B
% 5.64/5.87 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.87 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.87 & ( ~ B
% 5.64/5.87 => ( ( A
% 5.64/5.87 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.87 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.87 & ( ~ A
% 5.64/5.87 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.87 = none_nat ) ) ) ) ) ).
% 5.64/5.87
% 5.64/5.87 % vebt_maxt.simps(1)
% 5.64/5.87 thf(fact_2638_not__numeral__le__zero,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.64/5.87
% 5.64/5.87 % not_numeral_le_zero
% 5.64/5.87 thf(fact_2639_not__numeral__le__zero,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.64/5.87
% 5.64/5.87 % not_numeral_le_zero
% 5.64/5.87 thf(fact_2640_not__numeral__le__zero,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.64/5.87
% 5.64/5.87 % not_numeral_le_zero
% 5.64/5.87 thf(fact_2641_not__numeral__le__zero,axiom,
% 5.64/5.87 ! [N: num] :
% 5.64/5.87 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.64/5.87
% 5.64/5.87 % not_numeral_le_zero
% 5.64/5.87 thf(fact_2642_zero__le__numeral,axiom,
% 5.64/5.87 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.87
% 5.64/5.87 % zero_le_numeral
% 5.64/5.87 thf(fact_2643_zero__le__numeral,axiom,
% 5.64/5.87 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_numeral
% 5.64/5.88 thf(fact_2644_zero__le__numeral,axiom,
% 5.64/5.88 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_numeral
% 5.64/5.88 thf(fact_2645_zero__le__numeral,axiom,
% 5.64/5.88 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_numeral
% 5.64/5.88 thf(fact_2646_mult__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono
% 5.64/5.88 thf(fact_2647_mult__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono
% 5.64/5.88 thf(fact_2648_mult__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono
% 5.64/5.88 thf(fact_2649_mult__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono
% 5.64/5.88 thf(fact_2650_mult__mono_H,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono'
% 5.64/5.88 thf(fact_2651_mult__mono_H,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono'
% 5.64/5.88 thf(fact_2652_mult__mono_H,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono'
% 5.64/5.88 thf(fact_2653_mult__mono_H,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_mono'
% 5.64/5.88 thf(fact_2654_zero__le__square,axiom,
% 5.64/5.88 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_square
% 5.64/5.88 thf(fact_2655_zero__le__square,axiom,
% 5.64/5.88 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_square
% 5.64/5.88 thf(fact_2656_zero__le__square,axiom,
% 5.64/5.88 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_square
% 5.64/5.88 thf(fact_2657_split__mult__pos__le,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_pos_le
% 5.64/5.88 thf(fact_2658_split__mult__pos__le,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.64/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_pos_le
% 5.64/5.88 thf(fact_2659_split__mult__pos__le,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_pos_le
% 5.64/5.88 thf(fact_2660_mult__left__mono__neg,axiom,
% 5.64/5.88 ! [B: rat,A: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono_neg
% 5.64/5.88 thf(fact_2661_mult__left__mono__neg,axiom,
% 5.64/5.88 ! [B: int,A: int,C: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono_neg
% 5.64/5.88 thf(fact_2662_mult__left__mono__neg,axiom,
% 5.64/5.88 ! [B: real,A: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono_neg
% 5.64/5.88 thf(fact_2663_mult__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonpos
% 5.64/5.88 thf(fact_2664_mult__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonpos
% 5.64/5.88 thf(fact_2665_mult__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonpos
% 5.64/5.88 thf(fact_2666_mult__left__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono
% 5.64/5.88 thf(fact_2667_mult__left__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono
% 5.64/5.88 thf(fact_2668_mult__left__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono
% 5.64/5.88 thf(fact_2669_mult__left__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_mono
% 5.64/5.88 thf(fact_2670_mult__right__mono__neg,axiom,
% 5.64/5.88 ! [B: rat,A: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono_neg
% 5.64/5.88 thf(fact_2671_mult__right__mono__neg,axiom,
% 5.64/5.88 ! [B: int,A: int,C: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono_neg
% 5.64/5.88 thf(fact_2672_mult__right__mono__neg,axiom,
% 5.64/5.88 ! [B: real,A: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono_neg
% 5.64/5.88 thf(fact_2673_mult__right__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono
% 5.64/5.88 thf(fact_2674_mult__right__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono
% 5.64/5.88 thf(fact_2675_mult__right__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono
% 5.64/5.88 thf(fact_2676_mult__right__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_mono
% 5.64/5.88 thf(fact_2677_mult__le__0__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.64/5.88 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.64/5.88 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_0_iff
% 5.64/5.88 thf(fact_2678_mult__le__0__iff,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.64/5.88 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.64/5.88 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_0_iff
% 5.64/5.88 thf(fact_2679_mult__le__0__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.64/5.88 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.64/5.88 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_0_iff
% 5.64/5.88 thf(fact_2680_split__mult__neg__le,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.64/5.88 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_neg_le
% 5.64/5.88 thf(fact_2681_split__mult__neg__le,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.64/5.88 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.88 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_neg_le
% 5.64/5.88 thf(fact_2682_split__mult__neg__le,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.64/5.88 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_neg_le
% 5.64/5.88 thf(fact_2683_split__mult__neg__le,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.64/5.88 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.64/5.88
% 5.64/5.88 % split_mult_neg_le
% 5.64/5.88 thf(fact_2684_mult__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonneg
% 5.64/5.88 thf(fact_2685_mult__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonneg
% 5.64/5.88 thf(fact_2686_mult__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonneg
% 5.64/5.88 thf(fact_2687_mult__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonneg
% 5.64/5.88 thf(fact_2688_mult__nonneg__nonpos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos
% 5.64/5.88 thf(fact_2689_mult__nonneg__nonpos,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos
% 5.64/5.88 thf(fact_2690_mult__nonneg__nonpos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos
% 5.64/5.88 thf(fact_2691_mult__nonneg__nonpos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos
% 5.64/5.88 thf(fact_2692_mult__nonpos__nonneg,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonneg
% 5.64/5.88 thf(fact_2693_mult__nonpos__nonneg,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonneg
% 5.64/5.88 thf(fact_2694_mult__nonpos__nonneg,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonneg
% 5.64/5.88 thf(fact_2695_mult__nonpos__nonneg,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonpos_nonneg
% 5.64/5.88 thf(fact_2696_mult__nonneg__nonpos2,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos2
% 5.64/5.88 thf(fact_2697_mult__nonneg__nonpos2,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos2
% 5.64/5.88 thf(fact_2698_mult__nonneg__nonpos2,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos2
% 5.64/5.88 thf(fact_2699_mult__nonneg__nonpos2,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_nonneg_nonpos2
% 5.64/5.88 thf(fact_2700_zero__le__mult__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_mult_iff
% 5.64/5.88 thf(fact_2701_zero__le__mult__iff,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_mult_iff
% 5.64/5.88 thf(fact_2702_zero__le__mult__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_mult_iff
% 5.64/5.88 thf(fact_2703_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.64/5.88 thf(fact_2704_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.64/5.88 thf(fact_2705_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.64/5.88 thf(fact_2706_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.64/5.88 thf(fact_2707_not__numeral__less__zero,axiom,
% 5.64/5.88 ! [N: num] :
% 5.64/5.88 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.64/5.88
% 5.64/5.88 % not_numeral_less_zero
% 5.64/5.88 thf(fact_2708_not__numeral__less__zero,axiom,
% 5.64/5.88 ! [N: num] :
% 5.64/5.88 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.64/5.88
% 5.64/5.88 % not_numeral_less_zero
% 5.64/5.88 thf(fact_2709_not__numeral__less__zero,axiom,
% 5.64/5.88 ! [N: num] :
% 5.64/5.88 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.64/5.88
% 5.64/5.88 % not_numeral_less_zero
% 5.64/5.88 thf(fact_2710_not__numeral__less__zero,axiom,
% 5.64/5.88 ! [N: num] :
% 5.64/5.88 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.64/5.88
% 5.64/5.88 % not_numeral_less_zero
% 5.64/5.88 thf(fact_2711_zero__less__numeral,axiom,
% 5.64/5.88 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_numeral
% 5.64/5.88 thf(fact_2712_zero__less__numeral,axiom,
% 5.64/5.88 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_numeral
% 5.64/5.88 thf(fact_2713_zero__less__numeral,axiom,
% 5.64/5.88 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_numeral
% 5.64/5.88 thf(fact_2714_zero__less__numeral,axiom,
% 5.64/5.88 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_numeral
% 5.64/5.88 thf(fact_2715_not__one__le__zero,axiom,
% 5.64/5.88 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_le_zero
% 5.64/5.88 thf(fact_2716_not__one__le__zero,axiom,
% 5.64/5.88 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_le_zero
% 5.64/5.88 thf(fact_2717_not__one__le__zero,axiom,
% 5.64/5.88 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_le_zero
% 5.64/5.88 thf(fact_2718_not__one__le__zero,axiom,
% 5.64/5.88 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_le_zero
% 5.64/5.88 thf(fact_2719_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.64/5.88
% 5.64/5.88 % linordered_nonzero_semiring_class.zero_le_one
% 5.64/5.88 thf(fact_2720_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.64/5.88
% 5.64/5.88 % linordered_nonzero_semiring_class.zero_le_one
% 5.64/5.88 thf(fact_2721_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.64/5.88
% 5.64/5.88 % linordered_nonzero_semiring_class.zero_le_one
% 5.64/5.88 thf(fact_2722_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.64/5.88
% 5.64/5.88 % linordered_nonzero_semiring_class.zero_le_one
% 5.64/5.88 thf(fact_2723_zero__less__one__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one_class.zero_le_one
% 5.64/5.88 thf(fact_2724_zero__less__one__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one_class.zero_le_one
% 5.64/5.88 thf(fact_2725_zero__less__one__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one_class.zero_le_one
% 5.64/5.88 thf(fact_2726_zero__less__one__class_Ozero__le__one,axiom,
% 5.64/5.88 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one_class.zero_le_one
% 5.64/5.88 thf(fact_2727_add__nonpos__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.64/5.88 => ( ( ( plus_plus_rat @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_rat )
% 5.64/5.88 = ( ( X2 = zero_zero_rat )
% 5.64/5.88 & ( Y4 = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_eq_0_iff
% 5.64/5.88 thf(fact_2728_add__nonpos__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: nat,Y4: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_eq_nat @ Y4 @ zero_zero_nat )
% 5.64/5.88 => ( ( ( plus_plus_nat @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_nat )
% 5.64/5.88 = ( ( X2 = zero_zero_nat )
% 5.64/5.88 & ( Y4 = zero_zero_nat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_eq_0_iff
% 5.64/5.88 thf(fact_2729_add__nonpos__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: int,Y4: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_eq_int @ Y4 @ zero_zero_int )
% 5.64/5.88 => ( ( ( plus_plus_int @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_int )
% 5.64/5.88 = ( ( X2 = zero_zero_int )
% 5.64/5.88 & ( Y4 = zero_zero_int ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_eq_0_iff
% 5.64/5.88 thf(fact_2730_add__nonpos__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.64/5.88 => ( ( ( plus_plus_real @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_real )
% 5.64/5.88 = ( ( X2 = zero_zero_real )
% 5.64/5.88 & ( Y4 = zero_zero_real ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_eq_0_iff
% 5.64/5.88 thf(fact_2731_add__nonneg__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.88 => ( ( ( plus_plus_rat @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_rat )
% 5.64/5.88 = ( ( X2 = zero_zero_rat )
% 5.64/5.88 & ( Y4 = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_eq_0_iff
% 5.64/5.88 thf(fact_2732_add__nonneg__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: nat,Y4: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.64/5.88 => ( ( ( plus_plus_nat @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_nat )
% 5.64/5.88 = ( ( X2 = zero_zero_nat )
% 5.64/5.88 & ( Y4 = zero_zero_nat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_eq_0_iff
% 5.64/5.88 thf(fact_2733_add__nonneg__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: int,Y4: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.88 => ( ( ( plus_plus_int @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_int )
% 5.64/5.88 = ( ( X2 = zero_zero_int )
% 5.64/5.88 & ( Y4 = zero_zero_int ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_eq_0_iff
% 5.64/5.88 thf(fact_2734_add__nonneg__eq__0__iff,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.88 => ( ( ( plus_plus_real @ X2 @ Y4 )
% 5.64/5.88 = zero_zero_real )
% 5.64/5.88 = ( ( X2 = zero_zero_real )
% 5.64/5.88 & ( Y4 = zero_zero_real ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_eq_0_iff
% 5.64/5.88 thf(fact_2735_add__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_nonpos
% 5.64/5.88 thf(fact_2736_add__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.64/5.88 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_nonpos
% 5.64/5.88 thf(fact_2737_add__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_nonpos
% 5.64/5.88 thf(fact_2738_add__nonpos__nonpos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonpos_nonpos
% 5.64/5.88 thf(fact_2739_add__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_nonneg
% 5.64/5.88 thf(fact_2740_add__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_nonneg
% 5.64/5.88 thf(fact_2741_add__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_nonneg
% 5.64/5.88 thf(fact_2742_add__nonneg__nonneg,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_nonneg_nonneg
% 5.64/5.88 thf(fact_2743_add__increasing2,axiom,
% 5.64/5.88 ! [C: rat,B: rat,A: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.88 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing2
% 5.64/5.88 thf(fact_2744_add__increasing2,axiom,
% 5.64/5.88 ! [C: nat,B: nat,A: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.88 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing2
% 5.64/5.88 thf(fact_2745_add__increasing2,axiom,
% 5.64/5.88 ! [C: int,B: int,A: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ( ord_less_eq_int @ B @ A )
% 5.64/5.88 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing2
% 5.64/5.88 thf(fact_2746_add__increasing2,axiom,
% 5.64/5.88 ! [C: real,B: real,A: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ( ord_less_eq_real @ B @ A )
% 5.64/5.88 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing2
% 5.64/5.88 thf(fact_2747_add__decreasing2,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing2
% 5.64/5.88 thf(fact_2748_add__decreasing2,axiom,
% 5.64/5.88 ! [C: nat,A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing2
% 5.64/5.88 thf(fact_2749_add__decreasing2,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing2
% 5.64/5.88 thf(fact_2750_add__decreasing2,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing2
% 5.64/5.88 thf(fact_2751_add__increasing,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing
% 5.64/5.88 thf(fact_2752_add__increasing,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.88 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing
% 5.64/5.88 thf(fact_2753_add__increasing,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.88 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing
% 5.64/5.88 thf(fact_2754_add__increasing,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.88 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_increasing
% 5.64/5.88 thf(fact_2755_add__decreasing,axiom,
% 5.64/5.88 ! [A: rat,C: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ C @ B )
% 5.64/5.88 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing
% 5.64/5.88 thf(fact_2756_add__decreasing,axiom,
% 5.64/5.88 ! [A: nat,C: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_eq_nat @ C @ B )
% 5.64/5.88 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing
% 5.64/5.88 thf(fact_2757_add__decreasing,axiom,
% 5.64/5.88 ! [A: int,C: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_eq_int @ C @ B )
% 5.64/5.88 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing
% 5.64/5.88 thf(fact_2758_add__decreasing,axiom,
% 5.64/5.88 ! [A: real,C: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ C @ B )
% 5.64/5.88 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_decreasing
% 5.64/5.88 thf(fact_2759_mult__neg__neg,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_neg
% 5.64/5.88 thf(fact_2760_mult__neg__neg,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_neg
% 5.64/5.88 thf(fact_2761_mult__neg__neg,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_neg
% 5.64/5.88 thf(fact_2762_not__square__less__zero,axiom,
% 5.64/5.88 ! [A: real] :
% 5.64/5.88 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.64/5.88
% 5.64/5.88 % not_square_less_zero
% 5.64/5.88 thf(fact_2763_not__square__less__zero,axiom,
% 5.64/5.88 ! [A: rat] :
% 5.64/5.88 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.64/5.88
% 5.64/5.88 % not_square_less_zero
% 5.64/5.88 thf(fact_2764_not__square__less__zero,axiom,
% 5.64/5.88 ! [A: int] :
% 5.64/5.88 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.64/5.88
% 5.64/5.88 % not_square_less_zero
% 5.64/5.88 thf(fact_2765_mult__less__0__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.64/5.88 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_0_iff
% 5.64/5.88 thf(fact_2766_mult__less__0__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.64/5.88 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_0_iff
% 5.64/5.88 thf(fact_2767_mult__less__0__iff,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.64/5.88 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.64/5.88 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.88 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_0_iff
% 5.64/5.88 thf(fact_2768_mult__neg__pos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_pos
% 5.64/5.88 thf(fact_2769_mult__neg__pos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_pos
% 5.64/5.88 thf(fact_2770_mult__neg__pos,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_pos
% 5.64/5.88 thf(fact_2771_mult__neg__pos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_neg_pos
% 5.64/5.88 thf(fact_2772_mult__pos__neg,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg
% 5.64/5.88 thf(fact_2773_mult__pos__neg,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg
% 5.64/5.88 thf(fact_2774_mult__pos__neg,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg
% 5.64/5.88 thf(fact_2775_mult__pos__neg,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg
% 5.64/5.88 thf(fact_2776_mult__pos__pos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_pos
% 5.64/5.88 thf(fact_2777_mult__pos__pos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_pos
% 5.64/5.88 thf(fact_2778_mult__pos__pos,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_pos
% 5.64/5.88 thf(fact_2779_mult__pos__pos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_pos
% 5.64/5.88 thf(fact_2780_mult__pos__neg2,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg2
% 5.64/5.88 thf(fact_2781_mult__pos__neg2,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg2
% 5.64/5.88 thf(fact_2782_mult__pos__neg2,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg2
% 5.64/5.88 thf(fact_2783_mult__pos__neg2,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_pos_neg2
% 5.64/5.88 thf(fact_2784_zero__less__mult__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.64/5.88 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_iff
% 5.64/5.88 thf(fact_2785_zero__less__mult__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.64/5.88 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_iff
% 5.64/5.88 thf(fact_2786_zero__less__mult__iff,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.64/5.88 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.88 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_iff
% 5.64/5.88 thf(fact_2787_zero__less__mult__pos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos
% 5.64/5.88 thf(fact_2788_zero__less__mult__pos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos
% 5.64/5.88 thf(fact_2789_zero__less__mult__pos,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos
% 5.64/5.88 thf(fact_2790_zero__less__mult__pos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos
% 5.64/5.88 thf(fact_2791_zero__less__mult__pos2,axiom,
% 5.64/5.88 ! [B: real,A: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos2
% 5.64/5.88 thf(fact_2792_zero__less__mult__pos2,axiom,
% 5.64/5.88 ! [B: rat,A: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos2
% 5.64/5.88 thf(fact_2793_zero__less__mult__pos2,axiom,
% 5.64/5.88 ! [B: nat,A: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos2
% 5.64/5.88 thf(fact_2794_zero__less__mult__pos2,axiom,
% 5.64/5.88 ! [B: int,A: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_mult_pos2
% 5.64/5.88 thf(fact_2795_mult__less__cancel__left__neg,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.88 = ( ord_less_real @ B @ A ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_neg
% 5.64/5.88 thf(fact_2796_mult__less__cancel__left__neg,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.88 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_neg
% 5.64/5.88 thf(fact_2797_mult__less__cancel__left__neg,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.88 = ( ord_less_int @ B @ A ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_neg
% 5.64/5.88 thf(fact_2798_mult__less__cancel__left__pos,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.88 = ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_pos
% 5.64/5.88 thf(fact_2799_mult__less__cancel__left__pos,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.88 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_pos
% 5.64/5.88 thf(fact_2800_mult__less__cancel__left__pos,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.88 = ( ord_less_int @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_pos
% 5.64/5.88 thf(fact_2801_mult__strict__left__mono__neg,axiom,
% 5.64/5.88 ! [B: real,A: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ B @ A )
% 5.64/5.88 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono_neg
% 5.64/5.88 thf(fact_2802_mult__strict__left__mono__neg,axiom,
% 5.64/5.88 ! [B: rat,A: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ B @ A )
% 5.64/5.88 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono_neg
% 5.64/5.88 thf(fact_2803_mult__strict__left__mono__neg,axiom,
% 5.64/5.88 ! [B: int,A: int,C: int] :
% 5.64/5.88 ( ( ord_less_int @ B @ A )
% 5.64/5.88 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono_neg
% 5.64/5.88 thf(fact_2804_mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono
% 5.64/5.88 thf(fact_2805_mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono
% 5.64/5.88 thf(fact_2806_mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono
% 5.64/5.88 thf(fact_2807_mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_left_mono
% 5.64/5.88 thf(fact_2808_mult__less__cancel__left__disj,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 & ( ord_less_real @ A @ B ) )
% 5.64/5.88 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_disj
% 5.64/5.88 thf(fact_2809_mult__less__cancel__left__disj,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 & ( ord_less_rat @ A @ B ) )
% 5.64/5.88 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_disj
% 5.64/5.88 thf(fact_2810_mult__less__cancel__left__disj,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 & ( ord_less_int @ A @ B ) )
% 5.64/5.88 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left_disj
% 5.64/5.88 thf(fact_2811_mult__strict__right__mono__neg,axiom,
% 5.64/5.88 ! [B: real,A: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ B @ A )
% 5.64/5.88 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono_neg
% 5.64/5.88 thf(fact_2812_mult__strict__right__mono__neg,axiom,
% 5.64/5.88 ! [B: rat,A: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ B @ A )
% 5.64/5.88 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono_neg
% 5.64/5.88 thf(fact_2813_mult__strict__right__mono__neg,axiom,
% 5.64/5.88 ! [B: int,A: int,C: int] :
% 5.64/5.88 ( ( ord_less_int @ B @ A )
% 5.64/5.88 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono_neg
% 5.64/5.88 thf(fact_2814_mult__strict__right__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono
% 5.64/5.88 thf(fact_2815_mult__strict__right__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono
% 5.64/5.88 thf(fact_2816_mult__strict__right__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono
% 5.64/5.88 thf(fact_2817_mult__strict__right__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_right_mono
% 5.64/5.88 thf(fact_2818_mult__less__cancel__right__disj,axiom,
% 5.64/5.88 ! [A: real,C: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 & ( ord_less_real @ A @ B ) )
% 5.64/5.88 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_right_disj
% 5.64/5.88 thf(fact_2819_mult__less__cancel__right__disj,axiom,
% 5.64/5.88 ! [A: rat,C: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 & ( ord_less_rat @ A @ B ) )
% 5.64/5.88 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_right_disj
% 5.64/5.88 thf(fact_2820_mult__less__cancel__right__disj,axiom,
% 5.64/5.88 ! [A: int,C: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 & ( ord_less_int @ A @ B ) )
% 5.64/5.88 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_right_disj
% 5.64/5.88 thf(fact_2821_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.64/5.88 thf(fact_2822_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.64/5.88 thf(fact_2823_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.64/5.88 thf(fact_2824_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.64/5.88 thf(fact_2825_not__one__less__zero,axiom,
% 5.64/5.88 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_less_zero
% 5.64/5.88 thf(fact_2826_not__one__less__zero,axiom,
% 5.64/5.88 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_less_zero
% 5.64/5.88 thf(fact_2827_not__one__less__zero,axiom,
% 5.64/5.88 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_less_zero
% 5.64/5.88 thf(fact_2828_not__one__less__zero,axiom,
% 5.64/5.88 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.64/5.88
% 5.64/5.88 % not_one_less_zero
% 5.64/5.88 thf(fact_2829_zero__less__one,axiom,
% 5.64/5.88 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one
% 5.64/5.88 thf(fact_2830_zero__less__one,axiom,
% 5.64/5.88 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one
% 5.64/5.88 thf(fact_2831_zero__less__one,axiom,
% 5.64/5.88 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one
% 5.64/5.88 thf(fact_2832_zero__less__one,axiom,
% 5.64/5.88 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.64/5.88
% 5.64/5.88 % zero_less_one
% 5.64/5.88 thf(fact_2833_less__numeral__extra_I1_J,axiom,
% 5.64/5.88 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.64/5.88
% 5.64/5.88 % less_numeral_extra(1)
% 5.64/5.88 thf(fact_2834_less__numeral__extra_I1_J,axiom,
% 5.64/5.88 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.64/5.88
% 5.64/5.88 % less_numeral_extra(1)
% 5.64/5.88 thf(fact_2835_less__numeral__extra_I1_J,axiom,
% 5.64/5.88 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.64/5.88
% 5.64/5.88 % less_numeral_extra(1)
% 5.64/5.88 thf(fact_2836_less__numeral__extra_I1_J,axiom,
% 5.64/5.88 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.64/5.88
% 5.64/5.88 % less_numeral_extra(1)
% 5.64/5.88 thf(fact_2837_add__less__zeroD,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y4 ) @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.88 | ( ord_less_real @ Y4 @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_less_zeroD
% 5.64/5.88 thf(fact_2838_add__less__zeroD,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y4 ) @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.64/5.88 | ( ord_less_rat @ Y4 @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_less_zeroD
% 5.64/5.88 thf(fact_2839_add__less__zeroD,axiom,
% 5.64/5.88 ! [X2: int,Y4: int] :
% 5.64/5.88 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y4 ) @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.64/5.88 | ( ord_less_int @ Y4 @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_less_zeroD
% 5.64/5.88 thf(fact_2840_add__neg__neg,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_neg_neg
% 5.64/5.88 thf(fact_2841_add__neg__neg,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_neg_neg
% 5.64/5.88 thf(fact_2842_add__neg__neg,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.64/5.88 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.64/5.88 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_neg_neg
% 5.64/5.88 thf(fact_2843_add__neg__neg,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.88 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_neg_neg
% 5.64/5.88 thf(fact_2844_add__pos__pos,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_pos_pos
% 5.64/5.88 thf(fact_2845_add__pos__pos,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_pos_pos
% 5.64/5.88 thf(fact_2846_add__pos__pos,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_pos_pos
% 5.64/5.88 thf(fact_2847_add__pos__pos,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_pos_pos
% 5.64/5.88 thf(fact_2848_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ B )
% 5.64/5.88 => ~ ! [C3: nat] :
% 5.64/5.88 ( ( B
% 5.64/5.88 = ( plus_plus_nat @ A @ C3 ) )
% 5.64/5.88 => ( C3 = zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % canonically_ordered_monoid_add_class.lessE
% 5.64/5.88 thf(fact_2849_pos__add__strict,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_real @ B @ C )
% 5.64/5.88 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % pos_add_strict
% 5.64/5.88 thf(fact_2850_pos__add__strict,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_rat @ B @ C )
% 5.64/5.88 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % pos_add_strict
% 5.64/5.88 thf(fact_2851_pos__add__strict,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_nat @ B @ C )
% 5.64/5.88 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % pos_add_strict
% 5.64/5.88 thf(fact_2852_pos__add__strict,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_int @ B @ C )
% 5.64/5.88 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % pos_add_strict
% 5.64/5.88 thf(fact_2853_le__iff__diff__le__0,axiom,
% 5.64/5.88 ( ord_less_eq_rat
% 5.64/5.88 = ( ^ [A3: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % le_iff_diff_le_0
% 5.64/5.88 thf(fact_2854_le__iff__diff__le__0,axiom,
% 5.64/5.88 ( ord_less_eq_int
% 5.64/5.88 = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % le_iff_diff_le_0
% 5.64/5.88 thf(fact_2855_le__iff__diff__le__0,axiom,
% 5.64/5.88 ( ord_less_eq_real
% 5.64/5.88 = ( ^ [A3: real,B3: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % le_iff_diff_le_0
% 5.64/5.88 thf(fact_2856_divide__le__0__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.64/5.88 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.64/5.88 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_le_0_iff
% 5.64/5.88 thf(fact_2857_divide__le__0__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.64/5.88 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.64/5.88 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_le_0_iff
% 5.64/5.88 thf(fact_2858_divide__right__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_right_mono
% 5.64/5.88 thf(fact_2859_divide__right__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_right_mono
% 5.64/5.88 thf(fact_2860_zero__le__divide__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_divide_iff
% 5.64/5.88 thf(fact_2861_zero__le__divide__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.64/5.88 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_divide_iff
% 5.64/5.88 thf(fact_2862_divide__nonneg__nonneg,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonneg_nonneg
% 5.64/5.88 thf(fact_2863_divide__nonneg__nonneg,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonneg_nonneg
% 5.64/5.88 thf(fact_2864_divide__nonneg__nonpos,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonneg_nonpos
% 5.64/5.88 thf(fact_2865_divide__nonneg__nonpos,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.88 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonneg_nonpos
% 5.64/5.88 thf(fact_2866_divide__nonpos__nonneg,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.88 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonpos_nonneg
% 5.64/5.88 thf(fact_2867_divide__nonpos__nonneg,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.88 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonpos_nonneg
% 5.64/5.88 thf(fact_2868_divide__nonpos__nonpos,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_eq_rat @ Y4 @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonpos_nonpos
% 5.64/5.88 thf(fact_2869_divide__nonpos__nonpos,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_nonpos_nonpos
% 5.64/5.88 thf(fact_2870_divide__right__mono__neg,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_right_mono_neg
% 5.64/5.88 thf(fact_2871_divide__right__mono__neg,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_right_mono_neg
% 5.64/5.88 thf(fact_2872_less__iff__diff__less__0,axiom,
% 5.64/5.88 ( ord_less_real
% 5.64/5.88 = ( ^ [A3: real,B3: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B3 ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % less_iff_diff_less_0
% 5.64/5.88 thf(fact_2873_less__iff__diff__less__0,axiom,
% 5.64/5.88 ( ord_less_rat
% 5.64/5.88 = ( ^ [A3: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % less_iff_diff_less_0
% 5.64/5.88 thf(fact_2874_less__iff__diff__less__0,axiom,
% 5.64/5.88 ( ord_less_int
% 5.64/5.88 = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % less_iff_diff_less_0
% 5.64/5.88 thf(fact_2875_divide__neg__neg,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_neg_neg
% 5.64/5.88 thf(fact_2876_divide__neg__neg,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_neg_neg
% 5.64/5.88 thf(fact_2877_divide__neg__pos,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.88 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_neg_pos
% 5.64/5.88 thf(fact_2878_divide__neg__pos,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.88 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_neg_pos
% 5.64/5.88 thf(fact_2879_divide__pos__neg,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.88 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_pos_neg
% 5.64/5.88 thf(fact_2880_divide__pos__neg,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.64/5.88 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_pos_neg
% 5.64/5.88 thf(fact_2881_divide__pos__pos,axiom,
% 5.64/5.88 ! [X2: real,Y4: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_pos_pos
% 5.64/5.88 thf(fact_2882_divide__pos__pos,axiom,
% 5.64/5.88 ! [X2: rat,Y4: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_pos_pos
% 5.64/5.88 thf(fact_2883_divide__less__0__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.64/5.88 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_less_0_iff
% 5.64/5.88 thf(fact_2884_divide__less__0__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.64/5.88 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_less_0_iff
% 5.64/5.88 thf(fact_2885_divide__less__cancel,axiom,
% 5.64/5.88 ! [A: real,C: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ B @ A ) )
% 5.64/5.88 & ( C != zero_zero_real ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_less_cancel
% 5.64/5.88 thf(fact_2886_divide__less__cancel,axiom,
% 5.64/5.88 ! [A: rat,C: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ B @ A ) )
% 5.64/5.88 & ( C != zero_zero_rat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_less_cancel
% 5.64/5.88 thf(fact_2887_zero__less__divide__iff,axiom,
% 5.64/5.88 ! [A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.64/5.88 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.88 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_divide_iff
% 5.64/5.88 thf(fact_2888_zero__less__divide__iff,axiom,
% 5.64/5.88 ! [A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.64/5.88 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.88 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_divide_iff
% 5.64/5.88 thf(fact_2889_divide__strict__right__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_strict_right_mono
% 5.64/5.88 thf(fact_2890_divide__strict__right__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_strict_right_mono
% 5.64/5.88 thf(fact_2891_divide__strict__right__mono__neg,axiom,
% 5.64/5.88 ! [B: real,A: real,C: real] :
% 5.64/5.88 ( ( ord_less_real @ B @ A )
% 5.64/5.88 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_strict_right_mono_neg
% 5.64/5.88 thf(fact_2892_divide__strict__right__mono__neg,axiom,
% 5.64/5.88 ! [B: rat,A: rat,C: rat] :
% 5.64/5.88 ( ( ord_less_rat @ B @ A )
% 5.64/5.88 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_strict_right_mono_neg
% 5.64/5.88 thf(fact_2893_power__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % power_mono
% 5.64/5.88 thf(fact_2894_power__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % power_mono
% 5.64/5.88 thf(fact_2895_power__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % power_mono
% 5.64/5.88 thf(fact_2896_power__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % power_mono
% 5.64/5.88 thf(fact_2897_zero__le__power,axiom,
% 5.64/5.88 ! [A: rat,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_power
% 5.64/5.88 thf(fact_2898_zero__le__power,axiom,
% 5.64/5.88 ! [A: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_power
% 5.64/5.88 thf(fact_2899_zero__le__power,axiom,
% 5.64/5.88 ! [A: int,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_power
% 5.64/5.88 thf(fact_2900_zero__le__power,axiom,
% 5.64/5.88 ! [A: real,N: nat] :
% 5.64/5.88 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_le_power
% 5.64/5.88 thf(fact_2901_zero__less__power,axiom,
% 5.64/5.88 ! [A: real,N: nat] :
% 5.64/5.88 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_power
% 5.64/5.88 thf(fact_2902_zero__less__power,axiom,
% 5.64/5.88 ! [A: rat,N: nat] :
% 5.64/5.88 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_power
% 5.64/5.88 thf(fact_2903_zero__less__power,axiom,
% 5.64/5.88 ! [A: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_power
% 5.64/5.88 thf(fact_2904_zero__less__power,axiom,
% 5.64/5.88 ! [A: int,N: nat] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % zero_less_power
% 5.64/5.88 thf(fact_2905_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.64/5.88 ! [X2: vEBT_VEBT] :
% 5.64/5.88 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.64/5.88 => ( ! [Uv: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( vEBT_Leaf @ $true @ Uv ) )
% 5.64/5.88 => ( ! [Uu: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( vEBT_Leaf @ Uu @ $true ) )
% 5.64/5.88 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % VEBT_internal.minNull.elims(3)
% 5.64/5.88 thf(fact_2906_frac__eq__eq,axiom,
% 5.64/5.88 ! [Y4: complex,Z: complex,X2: complex,W: complex] :
% 5.64/5.88 ( ( Y4 != zero_zero_complex )
% 5.64/5.88 => ( ( Z != zero_zero_complex )
% 5.64/5.88 => ( ( ( divide1717551699836669952omplex @ X2 @ Y4 )
% 5.64/5.88 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.64/5.88 = ( ( times_times_complex @ X2 @ Z )
% 5.64/5.88 = ( times_times_complex @ W @ Y4 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % frac_eq_eq
% 5.64/5.88 thf(fact_2907_frac__eq__eq,axiom,
% 5.64/5.88 ! [Y4: real,Z: real,X2: real,W: real] :
% 5.64/5.88 ( ( Y4 != zero_zero_real )
% 5.64/5.88 => ( ( Z != zero_zero_real )
% 5.64/5.88 => ( ( ( divide_divide_real @ X2 @ Y4 )
% 5.64/5.88 = ( divide_divide_real @ W @ Z ) )
% 5.64/5.88 = ( ( times_times_real @ X2 @ Z )
% 5.64/5.88 = ( times_times_real @ W @ Y4 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % frac_eq_eq
% 5.64/5.88 thf(fact_2908_frac__eq__eq,axiom,
% 5.64/5.88 ! [Y4: rat,Z: rat,X2: rat,W: rat] :
% 5.64/5.88 ( ( Y4 != zero_zero_rat )
% 5.64/5.88 => ( ( Z != zero_zero_rat )
% 5.64/5.88 => ( ( ( divide_divide_rat @ X2 @ Y4 )
% 5.64/5.88 = ( divide_divide_rat @ W @ Z ) )
% 5.64/5.88 = ( ( times_times_rat @ X2 @ Z )
% 5.64/5.88 = ( times_times_rat @ W @ Y4 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % frac_eq_eq
% 5.64/5.88 thf(fact_2909_divide__eq__eq,axiom,
% 5.64/5.88 ! [B: complex,C: complex,A: complex] :
% 5.64/5.88 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.64/5.88 = A )
% 5.64/5.88 = ( ( ( C != zero_zero_complex )
% 5.64/5.88 => ( B
% 5.64/5.88 = ( times_times_complex @ A @ C ) ) )
% 5.64/5.88 & ( ( C = zero_zero_complex )
% 5.64/5.88 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_eq_eq
% 5.64/5.88 thf(fact_2910_divide__eq__eq,axiom,
% 5.64/5.88 ! [B: real,C: real,A: real] :
% 5.64/5.88 ( ( ( divide_divide_real @ B @ C )
% 5.64/5.88 = A )
% 5.64/5.88 = ( ( ( C != zero_zero_real )
% 5.64/5.88 => ( B
% 5.64/5.88 = ( times_times_real @ A @ C ) ) )
% 5.64/5.88 & ( ( C = zero_zero_real )
% 5.64/5.88 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_eq_eq
% 5.64/5.88 thf(fact_2911_divide__eq__eq,axiom,
% 5.64/5.88 ! [B: rat,C: rat,A: rat] :
% 5.64/5.88 ( ( ( divide_divide_rat @ B @ C )
% 5.64/5.88 = A )
% 5.64/5.88 = ( ( ( C != zero_zero_rat )
% 5.64/5.88 => ( B
% 5.64/5.88 = ( times_times_rat @ A @ C ) ) )
% 5.64/5.88 & ( ( C = zero_zero_rat )
% 5.64/5.88 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_eq_eq
% 5.64/5.88 thf(fact_2912_eq__divide__eq,axiom,
% 5.64/5.88 ! [A: complex,B: complex,C: complex] :
% 5.64/5.88 ( ( A
% 5.64/5.88 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.88 = ( ( ( C != zero_zero_complex )
% 5.64/5.88 => ( ( times_times_complex @ A @ C )
% 5.64/5.88 = B ) )
% 5.64/5.88 & ( ( C = zero_zero_complex )
% 5.64/5.88 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % eq_divide_eq
% 5.64/5.88 thf(fact_2913_eq__divide__eq,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real] :
% 5.64/5.88 ( ( A
% 5.64/5.88 = ( divide_divide_real @ B @ C ) )
% 5.64/5.88 = ( ( ( C != zero_zero_real )
% 5.64/5.88 => ( ( times_times_real @ A @ C )
% 5.64/5.88 = B ) )
% 5.64/5.88 & ( ( C = zero_zero_real )
% 5.64/5.88 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % eq_divide_eq
% 5.64/5.88 thf(fact_2914_eq__divide__eq,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat] :
% 5.64/5.88 ( ( A
% 5.64/5.88 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.88 = ( ( ( C != zero_zero_rat )
% 5.64/5.88 => ( ( times_times_rat @ A @ C )
% 5.64/5.88 = B ) )
% 5.64/5.88 & ( ( C = zero_zero_rat )
% 5.64/5.88 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % eq_divide_eq
% 5.64/5.88 thf(fact_2915_divide__eq__imp,axiom,
% 5.64/5.88 ! [C: complex,B: complex,A: complex] :
% 5.64/5.88 ( ( C != zero_zero_complex )
% 5.64/5.88 => ( ( B
% 5.64/5.88 = ( times_times_complex @ A @ C ) )
% 5.64/5.88 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.64/5.88 = A ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_eq_imp
% 5.64/5.88 thf(fact_2916_divide__eq__imp,axiom,
% 5.64/5.88 ! [C: real,B: real,A: real] :
% 5.64/5.88 ( ( C != zero_zero_real )
% 5.64/5.88 => ( ( B
% 5.64/5.88 = ( times_times_real @ A @ C ) )
% 5.64/5.88 => ( ( divide_divide_real @ B @ C )
% 5.64/5.88 = A ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_eq_imp
% 5.64/5.88 thf(fact_2917_divide__eq__imp,axiom,
% 5.64/5.88 ! [C: rat,B: rat,A: rat] :
% 5.64/5.88 ( ( C != zero_zero_rat )
% 5.64/5.88 => ( ( B
% 5.64/5.88 = ( times_times_rat @ A @ C ) )
% 5.64/5.88 => ( ( divide_divide_rat @ B @ C )
% 5.64/5.88 = A ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divide_eq_imp
% 5.64/5.88 thf(fact_2918_eq__divide__imp,axiom,
% 5.64/5.88 ! [C: complex,A: complex,B: complex] :
% 5.64/5.88 ( ( C != zero_zero_complex )
% 5.64/5.88 => ( ( ( times_times_complex @ A @ C )
% 5.64/5.88 = B )
% 5.64/5.88 => ( A
% 5.64/5.88 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % eq_divide_imp
% 5.64/5.88 thf(fact_2919_eq__divide__imp,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( C != zero_zero_real )
% 5.64/5.88 => ( ( ( times_times_real @ A @ C )
% 5.64/5.88 = B )
% 5.64/5.88 => ( A
% 5.64/5.88 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % eq_divide_imp
% 5.64/5.88 thf(fact_2920_eq__divide__imp,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( C != zero_zero_rat )
% 5.64/5.88 => ( ( ( times_times_rat @ A @ C )
% 5.64/5.88 = B )
% 5.64/5.88 => ( A
% 5.64/5.88 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % eq_divide_imp
% 5.64/5.88 thf(fact_2921_nonzero__divide__eq__eq,axiom,
% 5.64/5.88 ! [C: complex,B: complex,A: complex] :
% 5.64/5.88 ( ( C != zero_zero_complex )
% 5.64/5.88 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.64/5.88 = A )
% 5.64/5.88 = ( B
% 5.64/5.88 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nonzero_divide_eq_eq
% 5.64/5.88 thf(fact_2922_nonzero__divide__eq__eq,axiom,
% 5.64/5.88 ! [C: real,B: real,A: real] :
% 5.64/5.88 ( ( C != zero_zero_real )
% 5.64/5.88 => ( ( ( divide_divide_real @ B @ C )
% 5.64/5.88 = A )
% 5.64/5.88 = ( B
% 5.64/5.88 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nonzero_divide_eq_eq
% 5.64/5.88 thf(fact_2923_nonzero__divide__eq__eq,axiom,
% 5.64/5.88 ! [C: rat,B: rat,A: rat] :
% 5.64/5.88 ( ( C != zero_zero_rat )
% 5.64/5.88 => ( ( ( divide_divide_rat @ B @ C )
% 5.64/5.88 = A )
% 5.64/5.88 = ( B
% 5.64/5.88 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nonzero_divide_eq_eq
% 5.64/5.88 thf(fact_2924_nonzero__eq__divide__eq,axiom,
% 5.64/5.88 ! [C: complex,A: complex,B: complex] :
% 5.64/5.88 ( ( C != zero_zero_complex )
% 5.64/5.88 => ( ( A
% 5.64/5.88 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.88 = ( ( times_times_complex @ A @ C )
% 5.64/5.88 = B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nonzero_eq_divide_eq
% 5.64/5.88 thf(fact_2925_nonzero__eq__divide__eq,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( C != zero_zero_real )
% 5.64/5.88 => ( ( A
% 5.64/5.88 = ( divide_divide_real @ B @ C ) )
% 5.64/5.88 = ( ( times_times_real @ A @ C )
% 5.64/5.88 = B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nonzero_eq_divide_eq
% 5.64/5.88 thf(fact_2926_nonzero__eq__divide__eq,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( C != zero_zero_rat )
% 5.64/5.88 => ( ( A
% 5.64/5.88 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.88 = ( ( times_times_rat @ A @ C )
% 5.64/5.88 = B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nonzero_eq_divide_eq
% 5.64/5.88 thf(fact_2927_right__inverse__eq,axiom,
% 5.64/5.88 ! [B: complex,A: complex] :
% 5.64/5.88 ( ( B != zero_zero_complex )
% 5.64/5.88 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.64/5.88 = one_one_complex )
% 5.64/5.88 = ( A = B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % right_inverse_eq
% 5.64/5.88 thf(fact_2928_right__inverse__eq,axiom,
% 5.64/5.88 ! [B: real,A: real] :
% 5.64/5.88 ( ( B != zero_zero_real )
% 5.64/5.88 => ( ( ( divide_divide_real @ A @ B )
% 5.64/5.88 = one_one_real )
% 5.64/5.88 = ( A = B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % right_inverse_eq
% 5.64/5.88 thf(fact_2929_right__inverse__eq,axiom,
% 5.64/5.88 ! [B: rat,A: rat] :
% 5.64/5.88 ( ( B != zero_zero_rat )
% 5.64/5.88 => ( ( ( divide_divide_rat @ A @ B )
% 5.64/5.88 = one_one_rat )
% 5.64/5.88 = ( A = B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % right_inverse_eq
% 5.64/5.88 thf(fact_2930_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.64/5.88 ! [X2: vEBT_VEBT] :
% 5.64/5.88 ( ( vEBT_VEBT_minNull @ X2 )
% 5.64/5.88 => ( ( X2
% 5.64/5.88 != ( vEBT_Leaf @ $false @ $false ) )
% 5.64/5.88 => ~ ! [Uw: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % VEBT_internal.minNull.elims(2)
% 5.64/5.88 thf(fact_2931_power__0,axiom,
% 5.64/5.88 ! [A: rat] :
% 5.64/5.88 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.64/5.88 = one_one_rat ) ).
% 5.64/5.88
% 5.64/5.88 % power_0
% 5.64/5.88 thf(fact_2932_power__0,axiom,
% 5.64/5.88 ! [A: nat] :
% 5.64/5.88 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.64/5.88 = one_one_nat ) ).
% 5.64/5.88
% 5.64/5.88 % power_0
% 5.64/5.88 thf(fact_2933_power__0,axiom,
% 5.64/5.88 ! [A: real] :
% 5.64/5.88 ( ( power_power_real @ A @ zero_zero_nat )
% 5.64/5.88 = one_one_real ) ).
% 5.64/5.88
% 5.64/5.88 % power_0
% 5.64/5.88 thf(fact_2934_power__0,axiom,
% 5.64/5.88 ! [A: int] :
% 5.64/5.88 ( ( power_power_int @ A @ zero_zero_nat )
% 5.64/5.88 = one_one_int ) ).
% 5.64/5.88
% 5.64/5.88 % power_0
% 5.64/5.88 thf(fact_2935_power__0,axiom,
% 5.64/5.88 ! [A: complex] :
% 5.64/5.88 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.64/5.88 = one_one_complex ) ).
% 5.64/5.88
% 5.64/5.88 % power_0
% 5.64/5.88 thf(fact_2936_less__Suc__eq__0__disj,axiom,
% 5.64/5.88 ! [M: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.64/5.88 = ( ( M = zero_zero_nat )
% 5.64/5.88 | ? [J3: nat] :
% 5.64/5.88 ( ( M
% 5.64/5.88 = ( suc @ J3 ) )
% 5.64/5.88 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % less_Suc_eq_0_disj
% 5.64/5.88 thf(fact_2937_gr0__implies__Suc,axiom,
% 5.64/5.88 ! [N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.88 => ? [M4: nat] :
% 5.64/5.88 ( N
% 5.64/5.88 = ( suc @ M4 ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % gr0_implies_Suc
% 5.64/5.88 thf(fact_2938_All__less__Suc2,axiom,
% 5.64/5.88 ! [N: nat,P: nat > $o] :
% 5.64/5.88 ( ( ! [I4: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.64/5.88 => ( P @ I4 ) ) )
% 5.64/5.88 = ( ( P @ zero_zero_nat )
% 5.64/5.88 & ! [I4: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I4 @ N )
% 5.64/5.88 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % All_less_Suc2
% 5.64/5.88 thf(fact_2939_gr0__conv__Suc,axiom,
% 5.64/5.88 ! [N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.88 = ( ? [M2: nat] :
% 5.64/5.88 ( N
% 5.64/5.88 = ( suc @ M2 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % gr0_conv_Suc
% 5.64/5.88 thf(fact_2940_Ex__less__Suc2,axiom,
% 5.64/5.88 ! [N: nat,P: nat > $o] :
% 5.64/5.88 ( ( ? [I4: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I4 @ ( suc @ N ) )
% 5.64/5.88 & ( P @ I4 ) ) )
% 5.64/5.88 = ( ( P @ zero_zero_nat )
% 5.64/5.88 | ? [I4: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I4 @ N )
% 5.64/5.88 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % Ex_less_Suc2
% 5.64/5.88 thf(fact_2941_add__is__1,axiom,
% 5.64/5.88 ! [M: nat,N: nat] :
% 5.64/5.88 ( ( ( plus_plus_nat @ M @ N )
% 5.64/5.88 = ( suc @ zero_zero_nat ) )
% 5.64/5.88 = ( ( ( M
% 5.64/5.88 = ( suc @ zero_zero_nat ) )
% 5.64/5.88 & ( N = zero_zero_nat ) )
% 5.64/5.88 | ( ( M = zero_zero_nat )
% 5.64/5.88 & ( N
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % add_is_1
% 5.64/5.88 thf(fact_2942_one__is__add,axiom,
% 5.64/5.88 ! [M: nat,N: nat] :
% 5.64/5.88 ( ( ( suc @ zero_zero_nat )
% 5.64/5.88 = ( plus_plus_nat @ M @ N ) )
% 5.64/5.88 = ( ( ( M
% 5.64/5.88 = ( suc @ zero_zero_nat ) )
% 5.64/5.88 & ( N = zero_zero_nat ) )
% 5.64/5.88 | ( ( M = zero_zero_nat )
% 5.64/5.88 & ( N
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % one_is_add
% 5.64/5.88 thf(fact_2943_ex__least__nat__le,axiom,
% 5.64/5.88 ! [P: nat > $o,N: nat] :
% 5.64/5.88 ( ( P @ N )
% 5.64/5.88 => ( ~ ( P @ zero_zero_nat )
% 5.64/5.88 => ? [K3: nat] :
% 5.64/5.88 ( ( ord_less_eq_nat @ K3 @ N )
% 5.64/5.88 & ! [I2: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I2 @ K3 )
% 5.64/5.88 => ~ ( P @ I2 ) )
% 5.64/5.88 & ( P @ K3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % ex_least_nat_le
% 5.64/5.88 thf(fact_2944_option_Osize_I4_J,axiom,
% 5.64/5.88 ! [X22: product_prod_nat_nat] :
% 5.64/5.88 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % option.size(4)
% 5.64/5.88 thf(fact_2945_option_Osize_I4_J,axiom,
% 5.64/5.88 ! [X22: nat] :
% 5.64/5.88 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % option.size(4)
% 5.64/5.88 thf(fact_2946_option_Osize_I4_J,axiom,
% 5.64/5.88 ! [X22: num] :
% 5.64/5.88 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % option.size(4)
% 5.64/5.88 thf(fact_2947_less__imp__add__positive,axiom,
% 5.64/5.88 ! [I: nat,J: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I @ J )
% 5.64/5.88 => ? [K3: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 5.64/5.88 & ( ( plus_plus_nat @ I @ K3 )
% 5.64/5.88 = J ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % less_imp_add_positive
% 5.64/5.88 thf(fact_2948_option_Osize_I3_J,axiom,
% 5.64/5.88 ( ( size_size_option_nat @ none_nat )
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % option.size(3)
% 5.64/5.88 thf(fact_2949_option_Osize_I3_J,axiom,
% 5.64/5.88 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % option.size(3)
% 5.64/5.88 thf(fact_2950_option_Osize_I3_J,axiom,
% 5.64/5.88 ( ( size_size_option_num @ none_num )
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % option.size(3)
% 5.64/5.88 thf(fact_2951_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I1_J,axiom,
% 5.64/5.88 ! [A: $o,B: $o,X2: nat] :
% 5.64/5.88 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.88 = one_one_nat ) ).
% 5.64/5.88
% 5.64/5.88 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(1)
% 5.64/5.88 thf(fact_2952_One__nat__def,axiom,
% 5.64/5.88 ( one_one_nat
% 5.64/5.88 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % One_nat_def
% 5.64/5.88 thf(fact_2953_diff__less,axiom,
% 5.64/5.88 ! [N: nat,M: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.88 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % diff_less
% 5.64/5.88 thf(fact_2954_nat__mult__less__cancel1,axiom,
% 5.64/5.88 ! [K: nat,M: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.88 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.88 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nat_mult_less_cancel1
% 5.64/5.88 thf(fact_2955_nat__mult__eq__cancel1,axiom,
% 5.64/5.88 ! [K: nat,M: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.88 => ( ( ( times_times_nat @ K @ M )
% 5.64/5.88 = ( times_times_nat @ K @ N ) )
% 5.64/5.88 = ( M = N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nat_mult_eq_cancel1
% 5.64/5.88 thf(fact_2956_mult__less__mono2,axiom,
% 5.64/5.88 ! [I: nat,J: nat,K: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I @ J )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_mono2
% 5.64/5.88 thf(fact_2957_mult__less__mono1,axiom,
% 5.64/5.88 ! [I: nat,J: nat,K: nat] :
% 5.64/5.88 ( ( ord_less_nat @ I @ J )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_mono1
% 5.64/5.88 thf(fact_2958_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.64/5.88 ! [M: nat,N: nat] :
% 5.64/5.88 ( ( ( divide_divide_nat @ M @ N )
% 5.64/5.88 = zero_zero_nat )
% 5.64/5.88 = ( ( ord_less_nat @ M @ N )
% 5.64/5.88 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % Euclidean_Division.div_eq_0_iff
% 5.64/5.88 thf(fact_2959_divmod__digit__0_I2_J,axiom,
% 5.64/5.88 ! [B: nat,A: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.88 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.64/5.88 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divmod_digit_0(2)
% 5.64/5.88 thf(fact_2960_divmod__digit__0_I2_J,axiom,
% 5.64/5.88 ! [B: int,A: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.88 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.64/5.88 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divmod_digit_0(2)
% 5.64/5.88 thf(fact_2961_divmod__digit__0_I2_J,axiom,
% 5.64/5.88 ! [B: code_integer,A: code_integer] :
% 5.64/5.88 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.88 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.88 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.64/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divmod_digit_0(2)
% 5.64/5.88 thf(fact_2962_diff__add__0,axiom,
% 5.64/5.88 ! [N: nat,M: nat] :
% 5.64/5.88 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.88 = zero_zero_nat ) ).
% 5.64/5.88
% 5.64/5.88 % diff_add_0
% 5.64/5.88 thf(fact_2963_bits__stable__imp__add__self,axiom,
% 5.64/5.88 ! [A: nat] :
% 5.64/5.88 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.88 = A )
% 5.64/5.88 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.88 = zero_zero_nat ) ) ).
% 5.64/5.88
% 5.64/5.88 % bits_stable_imp_add_self
% 5.64/5.88 thf(fact_2964_bits__stable__imp__add__self,axiom,
% 5.64/5.88 ! [A: int] :
% 5.64/5.88 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.88 = A )
% 5.64/5.88 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.64/5.88 = zero_zero_int ) ) ).
% 5.64/5.88
% 5.64/5.88 % bits_stable_imp_add_self
% 5.64/5.88 thf(fact_2965_bits__stable__imp__add__self,axiom,
% 5.64/5.88 ! [A: code_integer] :
% 5.64/5.88 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.88 = A )
% 5.64/5.88 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.64/5.88 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.88
% 5.64/5.88 % bits_stable_imp_add_self
% 5.64/5.88 thf(fact_2966_nat__power__less__imp__less,axiom,
% 5.64/5.88 ! [I: nat,M: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.64/5.88 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.64/5.88 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nat_power_less_imp_less
% 5.64/5.88 thf(fact_2967_mult__eq__self__implies__10,axiom,
% 5.64/5.88 ! [M: nat,N: nat] :
% 5.64/5.88 ( ( M
% 5.64/5.88 = ( times_times_nat @ M @ N ) )
% 5.64/5.88 => ( ( N = one_one_nat )
% 5.64/5.88 | ( M = zero_zero_nat ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_eq_self_implies_10
% 5.64/5.88 thf(fact_2968_vebt__member_Osimps_I3_J,axiom,
% 5.64/5.88 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.64/5.88 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_member.simps(3)
% 5.64/5.88 thf(fact_2969_verit__le__mono__div,axiom,
% 5.64/5.88 ! [A4: nat,B4: nat,N: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A4 @ B4 )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.88 => ( ord_less_eq_nat
% 5.64/5.88 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 5.64/5.88 @ ( if_nat
% 5.64/5.88 @ ( ( modulo_modulo_nat @ B4 @ N )
% 5.64/5.88 = zero_zero_nat )
% 5.64/5.88 @ one_one_nat
% 5.64/5.88 @ zero_zero_nat ) )
% 5.64/5.88 @ ( divide_divide_nat @ B4 @ N ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % verit_le_mono_div
% 5.64/5.88 thf(fact_2970_vebt__insert_Ocases,axiom,
% 5.64/5.88 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.88 ( ! [A5: $o,B5: $o,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X4 ) )
% 5.64/5.88 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) @ X4 ) )
% 5.64/5.88 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X4 ) )
% 5.64/5.88 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) )
% 5.64/5.88 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_insert.cases
% 5.64/5.88 thf(fact_2971_VEBT__internal_Omembermima_Ocases,axiom,
% 5.64/5.88 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.88 ( ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) )
% 5.64/5.88 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.64/5.88 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X4 ) )
% 5.64/5.88 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X4 ) )
% 5.64/5.88 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X4 ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % VEBT_internal.membermima.cases
% 5.64/5.88 thf(fact_2972_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Ocases,axiom,
% 5.64/5.88 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.88 ( ! [A5: $o,B5: $o,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X4 ) )
% 5.64/5.88 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X4 ) )
% 5.64/5.88 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X4 ) )
% 5.64/5.88 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X4 ) )
% 5.64/5.88 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.cases
% 5.64/5.88 thf(fact_2973_vebt__succ_Ocases,axiom,
% 5.64/5.88 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.88 ( ! [Uu: $o,B5: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B5 ) @ zero_zero_nat ) )
% 5.64/5.88 => ( ! [Uv: $o,Uw: $o,N3: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N3 ) ) )
% 5.64/5.88 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 5.64/5.88 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve ) )
% 5.64/5.88 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 5.64/5.88 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_succ.cases
% 5.64/5.88 thf(fact_2974_vebt__pred_Ocases,axiom,
% 5.64/5.88 ! [X2: produc9072475918466114483BT_nat] :
% 5.64/5.88 ( ! [Uu: $o,Uv: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) )
% 5.64/5.88 => ( ! [A5: $o,Uw: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 5.64/5.88 => ( ! [A5: $o,B5: $o,Va2: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 5.64/5.88 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 5.64/5.88 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Vf ) )
% 5.64/5.88 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 5.64/5.88 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X4: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ X4 ) ) ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_pred.cases
% 5.64/5.88 thf(fact_2975_vebt__insert_Osimps_I2_J,axiom,
% 5.64/5.88 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.64/5.88 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S2 ) @ X2 )
% 5.64/5.88 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_insert.simps(2)
% 5.64/5.88 thf(fact_2976_vebt__pred_Osimps_I3_J,axiom,
% 5.64/5.88 ! [B: $o,A: $o,Va: nat] :
% 5.64/5.88 ( ( B
% 5.64/5.88 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.88 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.88 & ( ~ B
% 5.64/5.88 => ( ( A
% 5.64/5.88 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.88 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.88 & ( ~ A
% 5.64/5.88 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.88 = none_nat ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_pred.simps(3)
% 5.64/5.88 thf(fact_2977_divmod__digit__0_I1_J,axiom,
% 5.64/5.88 ! [B: nat,A: nat] :
% 5.64/5.88 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.88 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.88 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divmod_digit_0(1)
% 5.64/5.88 thf(fact_2978_divmod__digit__0_I1_J,axiom,
% 5.64/5.88 ! [B: int,A: int] :
% 5.64/5.88 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.88 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.88 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divmod_digit_0(1)
% 5.64/5.88 thf(fact_2979_divmod__digit__0_I1_J,axiom,
% 5.64/5.88 ! [B: code_integer,A: code_integer] :
% 5.64/5.88 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.88 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.88 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.88 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % divmod_digit_0(1)
% 5.64/5.88 thf(fact_2980_cong__exp__iff__simps_I8_J,axiom,
% 5.64/5.88 ! [M: num,Q3: num] :
% 5.64/5.88 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.88 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % cong_exp_iff_simps(8)
% 5.64/5.88 thf(fact_2981_cong__exp__iff__simps_I8_J,axiom,
% 5.64/5.88 ! [M: num,Q3: num] :
% 5.64/5.88 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.88 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % cong_exp_iff_simps(8)
% 5.64/5.88 thf(fact_2982_cong__exp__iff__simps_I8_J,axiom,
% 5.64/5.88 ! [M: num,Q3: num] :
% 5.64/5.88 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.88 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % cong_exp_iff_simps(8)
% 5.64/5.88 thf(fact_2983_cong__exp__iff__simps_I6_J,axiom,
% 5.64/5.88 ! [Q3: num,N: num] :
% 5.64/5.88 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.88 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % cong_exp_iff_simps(6)
% 5.64/5.88 thf(fact_2984_cong__exp__iff__simps_I6_J,axiom,
% 5.64/5.88 ! [Q3: num,N: num] :
% 5.64/5.88 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.88 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % cong_exp_iff_simps(6)
% 5.64/5.88 thf(fact_2985_cong__exp__iff__simps_I6_J,axiom,
% 5.64/5.88 ! [Q3: num,N: num] :
% 5.64/5.88 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.88 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % cong_exp_iff_simps(6)
% 5.64/5.88 thf(fact_2986_cancel__div__mod__rules_I2_J,axiom,
% 5.64/5.88 ! [B: nat,A: nat,C: nat] :
% 5.64/5.88 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.64/5.88 = ( plus_plus_nat @ A @ C ) ) ).
% 5.64/5.88
% 5.64/5.88 % cancel_div_mod_rules(2)
% 5.64/5.88 thf(fact_2987_cancel__div__mod__rules_I2_J,axiom,
% 5.64/5.88 ! [B: int,A: int,C: int] :
% 5.64/5.88 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.64/5.88 = ( plus_plus_int @ A @ C ) ) ).
% 5.64/5.88
% 5.64/5.88 % cancel_div_mod_rules(2)
% 5.64/5.88 thf(fact_2988_cancel__div__mod__rules_I2_J,axiom,
% 5.64/5.88 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.88 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.64/5.88 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.64/5.88
% 5.64/5.88 % cancel_div_mod_rules(2)
% 5.64/5.88 thf(fact_2989_cancel__div__mod__rules_I1_J,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.64/5.88 = ( plus_plus_nat @ A @ C ) ) ).
% 5.64/5.88
% 5.64/5.88 % cancel_div_mod_rules(1)
% 5.64/5.88 thf(fact_2990_cancel__div__mod__rules_I1_J,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.64/5.88 = ( plus_plus_int @ A @ C ) ) ).
% 5.64/5.88
% 5.64/5.88 % cancel_div_mod_rules(1)
% 5.64/5.88 thf(fact_2991_cancel__div__mod__rules_I1_J,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.88 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.64/5.88 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.64/5.88
% 5.64/5.88 % cancel_div_mod_rules(1)
% 5.64/5.88 thf(fact_2992_mod__div__decomp,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( A
% 5.64/5.88 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mod_div_decomp
% 5.64/5.88 thf(fact_2993_mod__div__decomp,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( A
% 5.64/5.88 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mod_div_decomp
% 5.64/5.88 thf(fact_2994_mod__div__decomp,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( A
% 5.64/5.88 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mod_div_decomp
% 5.64/5.88 thf(fact_2995_div__mult__mod__eq,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % div_mult_mod_eq
% 5.64/5.88 thf(fact_2996_div__mult__mod__eq,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % div_mult_mod_eq
% 5.64/5.88 thf(fact_2997_div__mult__mod__eq,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % div_mult_mod_eq
% 5.64/5.88 thf(fact_2998_mod__div__mult__eq,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mod_div_mult_eq
% 5.64/5.88 thf(fact_2999_mod__div__mult__eq,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mod_div_mult_eq
% 5.64/5.88 thf(fact_3000_mod__div__mult__eq,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mod_div_mult_eq
% 5.64/5.88 thf(fact_3001_mod__mult__div__eq,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mod_mult_div_eq
% 5.64/5.88 thf(fact_3002_mod__mult__div__eq,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mod_mult_div_eq
% 5.64/5.88 thf(fact_3003_mod__mult__div__eq,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mod_mult_div_eq
% 5.64/5.88 thf(fact_3004_mult__div__mod__eq,axiom,
% 5.64/5.88 ! [B: nat,A: nat] :
% 5.64/5.88 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mult_div_mod_eq
% 5.64/5.88 thf(fact_3005_mult__div__mod__eq,axiom,
% 5.64/5.88 ! [B: int,A: int] :
% 5.64/5.88 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mult_div_mod_eq
% 5.64/5.88 thf(fact_3006_mult__div__mod__eq,axiom,
% 5.64/5.88 ! [B: code_integer,A: code_integer] :
% 5.64/5.88 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.64/5.88 = A ) ).
% 5.64/5.88
% 5.64/5.88 % mult_div_mod_eq
% 5.64/5.88 thf(fact_3007_div__mult1__eq,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat] :
% 5.64/5.88 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.88 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % div_mult1_eq
% 5.64/5.88 thf(fact_3008_div__mult1__eq,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int] :
% 5.64/5.88 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.88 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % div_mult1_eq
% 5.64/5.88 thf(fact_3009_div__mult1__eq,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.88 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.64/5.88 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % div_mult1_eq
% 5.64/5.88 thf(fact_3010_minus__div__mult__eq__mod,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.64/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_div_mult_eq_mod
% 5.64/5.88 thf(fact_3011_minus__div__mult__eq__mod,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.64/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_div_mult_eq_mod
% 5.64/5.88 thf(fact_3012_minus__div__mult__eq__mod,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.64/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_div_mult_eq_mod
% 5.64/5.88 thf(fact_3013_minus__mod__eq__div__mult,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.64/5.88 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mod_eq_div_mult
% 5.64/5.88 thf(fact_3014_minus__mod__eq__div__mult,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.64/5.88 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mod_eq_div_mult
% 5.64/5.88 thf(fact_3015_minus__mod__eq__div__mult,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.64/5.88 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mod_eq_div_mult
% 5.64/5.88 thf(fact_3016_minus__mod__eq__mult__div,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.64/5.88 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mod_eq_mult_div
% 5.64/5.88 thf(fact_3017_minus__mod__eq__mult__div,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.64/5.88 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mod_eq_mult_div
% 5.64/5.88 thf(fact_3018_minus__mod__eq__mult__div,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.64/5.88 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mod_eq_mult_div
% 5.64/5.88 thf(fact_3019_minus__mult__div__eq__mod,axiom,
% 5.64/5.88 ! [A: nat,B: nat] :
% 5.64/5.88 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.64/5.88 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mult_div_eq_mod
% 5.64/5.88 thf(fact_3020_minus__mult__div__eq__mod,axiom,
% 5.64/5.88 ! [A: int,B: int] :
% 5.64/5.88 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.64/5.88 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mult_div_eq_mod
% 5.64/5.88 thf(fact_3021_minus__mult__div__eq__mod,axiom,
% 5.64/5.88 ! [A: code_integer,B: code_integer] :
% 5.64/5.88 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.64/5.88 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.64/5.88
% 5.64/5.88 % minus_mult_div_eq_mod
% 5.64/5.88 thf(fact_3022_nat__mod__eq__lemma,axiom,
% 5.64/5.88 ! [X2: nat,N: nat,Y4: nat] :
% 5.64/5.88 ( ( ( modulo_modulo_nat @ X2 @ N )
% 5.64/5.88 = ( modulo_modulo_nat @ Y4 @ N ) )
% 5.64/5.88 => ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.88 => ? [Q2: nat] :
% 5.64/5.88 ( X2
% 5.64/5.88 = ( plus_plus_nat @ Y4 @ ( times_times_nat @ N @ Q2 ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % nat_mod_eq_lemma
% 5.64/5.88 thf(fact_3023_mod__eq__nat2E,axiom,
% 5.64/5.88 ! [M: nat,Q3: nat,N: nat] :
% 5.64/5.88 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.64/5.88 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.64/5.88 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.88 => ~ ! [S: nat] :
% 5.64/5.88 ( N
% 5.64/5.88 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mod_eq_nat2E
% 5.64/5.88 thf(fact_3024_mod__eq__nat1E,axiom,
% 5.64/5.88 ! [M: nat,Q3: nat,N: nat] :
% 5.64/5.88 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.64/5.88 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.64/5.88 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.88 => ~ ! [S: nat] :
% 5.64/5.88 ( M
% 5.64/5.88 != ( plus_plus_nat @ N @ ( times_times_nat @ Q3 @ S ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mod_eq_nat1E
% 5.64/5.88 thf(fact_3025_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.64/5.88 ! [X2: vEBT_VEBT,Y4: $o] :
% 5.64/5.88 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.64/5.88 = Y4 )
% 5.64/5.88 => ( ( ( X2
% 5.64/5.88 = ( vEBT_Leaf @ $false @ $false ) )
% 5.64/5.88 => ~ Y4 )
% 5.64/5.88 => ( ( ? [Uv: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 = ( vEBT_Leaf @ $true @ Uv ) )
% 5.64/5.88 => Y4 )
% 5.64/5.88 => ( ( ? [Uu: $o] :
% 5.64/5.88 ( X2
% 5.64/5.88 = ( vEBT_Leaf @ Uu @ $true ) )
% 5.64/5.88 => Y4 )
% 5.64/5.88 => ( ( ? [Uw: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.88 ( X2
% 5.64/5.88 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) )
% 5.64/5.88 => ~ Y4 )
% 5.64/5.88 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.88 ( X2
% 5.64/5.88 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.64/5.88 => Y4 ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % VEBT_internal.minNull.elims(1)
% 5.64/5.88 thf(fact_3026_div__mod__decomp,axiom,
% 5.64/5.88 ! [A4: nat,N: nat] :
% 5.64/5.88 ( A4
% 5.64/5.88 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N ) @ N ) @ ( modulo_modulo_nat @ A4 @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % div_mod_decomp
% 5.64/5.88 thf(fact_3027_mod__mult2__eq,axiom,
% 5.64/5.88 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.88 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q3 ) )
% 5.64/5.88 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mod_mult2_eq
% 5.64/5.88 thf(fact_3028_modulo__nat__def,axiom,
% 5.64/5.88 ( modulo_modulo_nat
% 5.64/5.88 = ( ^ [M2: nat,N2: nat] : ( minus_minus_nat @ M2 @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N2 ) @ N2 ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % modulo_nat_def
% 5.64/5.88 thf(fact_3029_vebt__succ_Osimps_I2_J,axiom,
% 5.64/5.88 ! [Uv2: $o,Uw2: $o,N: nat] :
% 5.64/5.88 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N ) )
% 5.64/5.88 = none_nat ) ).
% 5.64/5.88
% 5.64/5.88 % vebt_succ.simps(2)
% 5.64/5.88 thf(fact_3030_mult__le__cancel__left,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_cancel_left
% 5.64/5.88 thf(fact_3031_mult__le__cancel__left,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_cancel_left
% 5.64/5.88 thf(fact_3032_mult__le__cancel__left,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_cancel_left
% 5.64/5.88 thf(fact_3033_mult__le__cancel__right,axiom,
% 5.64/5.88 ! [A: rat,C: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_eq_rat @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_cancel_right
% 5.64/5.88 thf(fact_3034_mult__le__cancel__right,axiom,
% 5.64/5.88 ! [A: int,C: int,B: int] :
% 5.64/5.88 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_eq_int @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_cancel_right
% 5.64/5.88 thf(fact_3035_mult__le__cancel__right,axiom,
% 5.64/5.88 ! [A: real,C: real,B: real] :
% 5.64/5.88 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.88 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_eq_real @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_le_cancel_right
% 5.64/5.88 thf(fact_3036_mult__left__less__imp__less,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_less_imp_less
% 5.64/5.88 thf(fact_3037_mult__left__less__imp__less,axiom,
% 5.64/5.88 ! [C: nat,A: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_less_imp_less
% 5.64/5.88 thf(fact_3038_mult__left__less__imp__less,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_less_imp_less
% 5.64/5.88 thf(fact_3039_mult__left__less__imp__less,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_left_less_imp_less
% 5.64/5.88 thf(fact_3040_mult__strict__mono,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_rat @ C @ D )
% 5.64/5.88 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono
% 5.64/5.88 thf(fact_3041_mult__strict__mono,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_nat @ C @ D )
% 5.64/5.88 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono
% 5.64/5.88 thf(fact_3042_mult__strict__mono,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_int @ C @ D )
% 5.64/5.88 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono
% 5.64/5.88 thf(fact_3043_mult__strict__mono,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_real @ C @ D )
% 5.64/5.88 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono
% 5.64/5.88 thf(fact_3044_mult__less__cancel__left,axiom,
% 5.64/5.88 ! [C: rat,A: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.88 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left
% 5.64/5.88 thf(fact_3045_mult__less__cancel__left,axiom,
% 5.64/5.88 ! [C: int,A: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.88 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left
% 5.64/5.88 thf(fact_3046_mult__less__cancel__left,axiom,
% 5.64/5.88 ! [C: real,A: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.88 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ A @ B ) )
% 5.64/5.88 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.88 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_less_cancel_left
% 5.64/5.88 thf(fact_3047_mult__right__less__imp__less,axiom,
% 5.64/5.88 ! [A: rat,C: rat,B: rat] :
% 5.64/5.88 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_less_imp_less
% 5.64/5.88 thf(fact_3048_mult__right__less__imp__less,axiom,
% 5.64/5.88 ! [A: nat,C: nat,B: nat] :
% 5.64/5.88 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_less_imp_less
% 5.64/5.88 thf(fact_3049_mult__right__less__imp__less,axiom,
% 5.64/5.88 ! [A: int,C: int,B: int] :
% 5.64/5.88 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_less_imp_less
% 5.64/5.88 thf(fact_3050_mult__right__less__imp__less,axiom,
% 5.64/5.88 ! [A: real,C: real,B: real] :
% 5.64/5.88 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_right_less_imp_less
% 5.64/5.88 thf(fact_3051_mult__strict__mono_H,axiom,
% 5.64/5.88 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.88 ( ( ord_less_rat @ A @ B )
% 5.64/5.88 => ( ( ord_less_rat @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.88 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono'
% 5.64/5.88 thf(fact_3052_mult__strict__mono_H,axiom,
% 5.64/5.88 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.88 ( ( ord_less_nat @ A @ B )
% 5.64/5.88 => ( ( ord_less_nat @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.88 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono'
% 5.64/5.88 thf(fact_3053_mult__strict__mono_H,axiom,
% 5.64/5.88 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.88 ( ( ord_less_int @ A @ B )
% 5.64/5.88 => ( ( ord_less_int @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.88 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.88 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/5.88
% 5.64/5.88 % mult_strict_mono'
% 5.64/5.88 thf(fact_3054_mult__strict__mono_H,axiom,
% 5.64/5.88 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.88 ( ( ord_less_real @ A @ B )
% 5.64/5.88 => ( ( ord_less_real @ C @ D )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.88 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.88 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_strict_mono'
% 5.64/5.89 thf(fact_3055_mult__less__cancel__right,axiom,
% 5.64/5.89 ! [A: rat,C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ A @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right
% 5.64/5.89 thf(fact_3056_mult__less__cancel__right,axiom,
% 5.64/5.89 ! [A: int,C: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ A @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right
% 5.64/5.89 thf(fact_3057_mult__less__cancel__right,axiom,
% 5.64/5.89 ! [A: real,C: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ A @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right
% 5.64/5.89 thf(fact_3058_mult__le__cancel__left__neg,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.89 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left_neg
% 5.64/5.89 thf(fact_3059_mult__le__cancel__left__neg,axiom,
% 5.64/5.89 ! [C: int,A: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.89 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left_neg
% 5.64/5.89 thf(fact_3060_mult__le__cancel__left__neg,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.89 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left_neg
% 5.64/5.89 thf(fact_3061_mult__le__cancel__left__pos,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.89 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left_pos
% 5.64/5.89 thf(fact_3062_mult__le__cancel__left__pos,axiom,
% 5.64/5.89 ! [C: int,A: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.89 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left_pos
% 5.64/5.89 thf(fact_3063_mult__le__cancel__left__pos,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.89 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left_pos
% 5.64/5.89 thf(fact_3064_mult__left__le__imp__le,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_imp_le
% 5.64/5.89 thf(fact_3065_mult__left__le__imp__le,axiom,
% 5.64/5.89 ! [C: nat,A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/5.89 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_imp_le
% 5.64/5.89 thf(fact_3066_mult__left__le__imp__le,axiom,
% 5.64/5.89 ! [C: int,A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_imp_le
% 5.64/5.89 thf(fact_3067_mult__left__le__imp__le,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_imp_le
% 5.64/5.89 thf(fact_3068_mult__right__le__imp__le,axiom,
% 5.64/5.89 ! [A: rat,C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_imp_le
% 5.64/5.89 thf(fact_3069_mult__right__le__imp__le,axiom,
% 5.64/5.89 ! [A: nat,C: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/5.89 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_imp_le
% 5.64/5.89 thf(fact_3070_mult__right__le__imp__le,axiom,
% 5.64/5.89 ! [A: int,C: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_imp_le
% 5.64/5.89 thf(fact_3071_mult__right__le__imp__le,axiom,
% 5.64/5.89 ! [A: real,C: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_imp_le
% 5.64/5.89 thf(fact_3072_mult__le__less__imp__less,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.89 => ( ( ord_less_rat @ C @ D )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_less_imp_less
% 5.64/5.89 thf(fact_3073_mult__le__less__imp__less,axiom,
% 5.64/5.89 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.89 => ( ( ord_less_nat @ C @ D )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.89 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_less_imp_less
% 5.64/5.89 thf(fact_3074_mult__le__less__imp__less,axiom,
% 5.64/5.89 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.89 => ( ( ord_less_int @ C @ D )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_less_imp_less
% 5.64/5.89 thf(fact_3075_mult__le__less__imp__less,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.89 => ( ( ord_less_real @ C @ D )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_less_imp_less
% 5.64/5.89 thf(fact_3076_mult__less__le__imp__less,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.89 ( ( ord_less_rat @ A @ B )
% 5.64/5.89 => ( ( ord_less_eq_rat @ C @ D )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_le_imp_less
% 5.64/5.89 thf(fact_3077_mult__less__le__imp__less,axiom,
% 5.64/5.89 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.89 ( ( ord_less_nat @ A @ B )
% 5.64/5.89 => ( ( ord_less_eq_nat @ C @ D )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/5.89 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_le_imp_less
% 5.64/5.89 thf(fact_3078_mult__less__le__imp__less,axiom,
% 5.64/5.89 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.89 ( ( ord_less_int @ A @ B )
% 5.64/5.89 => ( ( ord_less_eq_int @ C @ D )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_le_imp_less
% 5.64/5.89 thf(fact_3079_mult__less__le__imp__less,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.89 ( ( ord_less_real @ A @ B )
% 5.64/5.89 => ( ( ord_less_eq_real @ C @ D )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_le_imp_less
% 5.64/5.89 thf(fact_3080_field__le__epsilon,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ! [E2: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.64/5.89 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y4 @ E2 ) ) )
% 5.64/5.89 => ( ord_less_eq_rat @ X2 @ Y4 ) ) ).
% 5.64/5.89
% 5.64/5.89 % field_le_epsilon
% 5.64/5.89 thf(fact_3081_field__le__epsilon,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ! [E2: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.64/5.89 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y4 @ E2 ) ) )
% 5.64/5.89 => ( ord_less_eq_real @ X2 @ Y4 ) ) ).
% 5.64/5.89
% 5.64/5.89 % field_le_epsilon
% 5.64/5.89 thf(fact_3082_add__strict__increasing2,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_rat @ B @ C )
% 5.64/5.89 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing2
% 5.64/5.89 thf(fact_3083_add__strict__increasing2,axiom,
% 5.64/5.89 ! [A: nat,B: nat,C: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ B @ C )
% 5.64/5.89 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing2
% 5.64/5.89 thf(fact_3084_add__strict__increasing2,axiom,
% 5.64/5.89 ! [A: int,B: int,C: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ B @ C )
% 5.64/5.89 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing2
% 5.64/5.89 thf(fact_3085_add__strict__increasing2,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_real @ B @ C )
% 5.64/5.89 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing2
% 5.64/5.89 thf(fact_3086_add__strict__increasing,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ B @ C )
% 5.64/5.89 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing
% 5.64/5.89 thf(fact_3087_add__strict__increasing,axiom,
% 5.64/5.89 ! [A: nat,B: nat,C: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ B @ C )
% 5.64/5.89 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing
% 5.64/5.89 thf(fact_3088_add__strict__increasing,axiom,
% 5.64/5.89 ! [A: int,B: int,C: int] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ B @ C )
% 5.64/5.89 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing
% 5.64/5.89 thf(fact_3089_add__strict__increasing,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ B @ C )
% 5.64/5.89 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_strict_increasing
% 5.64/5.89 thf(fact_3090_add__pos__nonneg,axiom,
% 5.64/5.89 ! [A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.89 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_pos_nonneg
% 5.64/5.89 thf(fact_3091_add__pos__nonneg,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_pos_nonneg
% 5.64/5.89 thf(fact_3092_add__pos__nonneg,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_pos_nonneg
% 5.64/5.89 thf(fact_3093_add__pos__nonneg,axiom,
% 5.64/5.89 ! [A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.89 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_pos_nonneg
% 5.64/5.89 thf(fact_3094_add__nonpos__neg,axiom,
% 5.64/5.89 ! [A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonpos_neg
% 5.64/5.89 thf(fact_3095_add__nonpos__neg,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.64/5.89 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.64/5.89 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonpos_neg
% 5.64/5.89 thf(fact_3096_add__nonpos__neg,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.89 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonpos_neg
% 5.64/5.89 thf(fact_3097_add__nonpos__neg,axiom,
% 5.64/5.89 ! [A: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonpos_neg
% 5.64/5.89 thf(fact_3098_add__nonneg__pos,axiom,
% 5.64/5.89 ! [A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.64/5.89 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonneg_pos
% 5.64/5.89 thf(fact_3099_add__nonneg__pos,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonneg_pos
% 5.64/5.89 thf(fact_3100_add__nonneg__pos,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonneg_pos
% 5.64/5.89 thf(fact_3101_add__nonneg__pos,axiom,
% 5.64/5.89 ! [A: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.89 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_nonneg_pos
% 5.64/5.89 thf(fact_3102_add__neg__nonpos,axiom,
% 5.64/5.89 ! [A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_neg_nonpos
% 5.64/5.89 thf(fact_3103_add__neg__nonpos,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.64/5.89 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.64/5.89 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_neg_nonpos
% 5.64/5.89 thf(fact_3104_add__neg__nonpos,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.89 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_neg_nonpos
% 5.64/5.89 thf(fact_3105_add__neg__nonpos,axiom,
% 5.64/5.89 ! [A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_neg_nonpos
% 5.64/5.89 thf(fact_3106_frac__le,axiom,
% 5.64/5.89 ! [Y4: rat,X2: rat,W: rat,Z: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.64/5.89 => ( ( ord_less_eq_rat @ W @ Z )
% 5.64/5.89 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y4 @ W ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_le
% 5.64/5.89 thf(fact_3107_frac__le,axiom,
% 5.64/5.89 ! [Y4: real,X2: real,W: real,Z: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.64/5.89 => ( ( ord_less_eq_real @ W @ Z )
% 5.64/5.89 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y4 @ W ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_le
% 5.64/5.89 thf(fact_3108_frac__less,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat,W: rat,Z: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_rat @ X2 @ Y4 )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.64/5.89 => ( ( ord_less_eq_rat @ W @ Z )
% 5.64/5.89 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y4 @ W ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_less
% 5.64/5.89 thf(fact_3109_frac__less,axiom,
% 5.64/5.89 ! [X2: real,Y4: real,W: real,Z: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.64/5.89 => ( ( ord_less_eq_real @ W @ Z )
% 5.64/5.89 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y4 @ W ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_less
% 5.64/5.89 thf(fact_3110_frac__less2,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat,W: rat,Z: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.64/5.89 => ( ( ord_less_rat @ W @ Z )
% 5.64/5.89 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y4 @ W ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_less2
% 5.64/5.89 thf(fact_3111_frac__less2,axiom,
% 5.64/5.89 ! [X2: real,Y4: real,W: real,Z: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.64/5.89 => ( ( ord_less_real @ W @ Z )
% 5.64/5.89 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y4 @ W ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_less2
% 5.64/5.89 thf(fact_3112_divide__le__cancel,axiom,
% 5.64/5.89 ! [A: rat,C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ B ) )
% 5.64/5.89 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_cancel
% 5.64/5.89 thf(fact_3113_divide__le__cancel,axiom,
% 5.64/5.89 ! [A: real,C: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ A @ B ) )
% 5.64/5.89 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_cancel
% 5.64/5.89 thf(fact_3114_divide__nonneg__neg,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonneg_neg
% 5.64/5.89 thf(fact_3115_divide__nonneg__neg,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonneg_neg
% 5.64/5.89 thf(fact_3116_divide__nonneg__pos,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonneg_pos
% 5.64/5.89 thf(fact_3117_divide__nonneg__pos,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonneg_pos
% 5.64/5.89 thf(fact_3118_divide__nonpos__neg,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ Y4 @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonpos_neg
% 5.64/5.89 thf(fact_3119_divide__nonpos__neg,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ Y4 @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonpos_neg
% 5.64/5.89 thf(fact_3120_divide__nonpos__pos,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonpos_pos
% 5.64/5.89 thf(fact_3121_divide__nonpos__pos,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y4 ) @ zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_nonpos_pos
% 5.64/5.89 thf(fact_3122_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ A @ B )
% 5.64/5.89 => ( ( divide_divide_nat @ A @ B )
% 5.64/5.89 = zero_zero_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % unique_euclidean_semiring_numeral_class.div_less
% 5.64/5.89 thf(fact_3123_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ A @ B )
% 5.64/5.89 => ( ( divide_divide_int @ A @ B )
% 5.64/5.89 = zero_zero_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % unique_euclidean_semiring_numeral_class.div_less
% 5.64/5.89 thf(fact_3124_div__positive,axiom,
% 5.64/5.89 ! [B: nat,A: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_positive
% 5.64/5.89 thf(fact_3125_div__positive,axiom,
% 5.64/5.89 ! [B: int,A: int] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ( ord_less_eq_int @ B @ A )
% 5.64/5.89 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_positive
% 5.64/5.89 thf(fact_3126_mult__left__le,axiom,
% 5.64/5.89 ! [C: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le
% 5.64/5.89 thf(fact_3127_mult__left__le,axiom,
% 5.64/5.89 ! [C: nat,A: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le
% 5.64/5.89 thf(fact_3128_mult__left__le,axiom,
% 5.64/5.89 ! [C: int,A: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le
% 5.64/5.89 thf(fact_3129_mult__left__le,axiom,
% 5.64/5.89 ! [C: real,A: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le
% 5.64/5.89 thf(fact_3130_mult__le__one,axiom,
% 5.64/5.89 ! [A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.89 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_one
% 5.64/5.89 thf(fact_3131_mult__le__one,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.64/5.89 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_one
% 5.64/5.89 thf(fact_3132_mult__le__one,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_one
% 5.64/5.89 thf(fact_3133_mult__le__one,axiom,
% 5.64/5.89 ! [A: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.89 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_one
% 5.64/5.89 thf(fact_3134_mult__right__le__one__le,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ Y4 @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y4 ) @ X2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_one_le
% 5.64/5.89 thf(fact_3135_mult__right__le__one__le,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_int @ Y4 @ one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y4 ) @ X2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_one_le
% 5.64/5.89 thf(fact_3136_mult__right__le__one__le,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y4 ) @ X2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_right_le_one_le
% 5.64/5.89 thf(fact_3137_mult__left__le__one__le,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ Y4 @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ Y4 @ X2 ) @ X2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_one_le
% 5.64/5.89 thf(fact_3138_mult__left__le__one__le,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_int @ Y4 @ one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( times_times_int @ Y4 @ X2 ) @ X2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_one_le
% 5.64/5.89 thf(fact_3139_mult__left__le__one__le,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ Y4 @ X2 ) @ X2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_left_le_one_le
% 5.64/5.89 thf(fact_3140_sum__squares__ge__zero,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y4 @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_ge_zero
% 5.64/5.89 thf(fact_3141_sum__squares__ge__zero,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y4 @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_ge_zero
% 5.64/5.89 thf(fact_3142_sum__squares__ge__zero,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_ge_zero
% 5.64/5.89 thf(fact_3143_sum__squares__le__zero__iff,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y4 @ Y4 ) ) @ zero_zero_rat )
% 5.64/5.89 = ( ( X2 = zero_zero_rat )
% 5.64/5.89 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_le_zero_iff
% 5.64/5.89 thf(fact_3144_sum__squares__le__zero__iff,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y4 @ Y4 ) ) @ zero_zero_int )
% 5.64/5.89 = ( ( X2 = zero_zero_int )
% 5.64/5.89 & ( Y4 = zero_zero_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_le_zero_iff
% 5.64/5.89 thf(fact_3145_sum__squares__le__zero__iff,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) ) @ zero_zero_real )
% 5.64/5.89 = ( ( X2 = zero_zero_real )
% 5.64/5.89 & ( Y4 = zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_le_zero_iff
% 5.64/5.89 thf(fact_3146_power__less__imp__less__base,axiom,
% 5.64/5.89 ! [A: rat,N: nat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.89 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_less_imp_less_base
% 5.64/5.89 thf(fact_3147_power__less__imp__less__base,axiom,
% 5.64/5.89 ! [A: nat,N: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_less_imp_less_base
% 5.64/5.89 thf(fact_3148_power__less__imp__less__base,axiom,
% 5.64/5.89 ! [A: int,N: nat,B: int] :
% 5.64/5.89 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ord_less_int @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_less_imp_less_base
% 5.64/5.89 thf(fact_3149_power__less__imp__less__base,axiom,
% 5.64/5.89 ! [A: real,N: nat,B: real] :
% 5.64/5.89 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.89 => ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_less_imp_less_base
% 5.64/5.89 thf(fact_3150_not__sum__squares__lt__zero,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) ) @ zero_zero_real ) ).
% 5.64/5.89
% 5.64/5.89 % not_sum_squares_lt_zero
% 5.64/5.89 thf(fact_3151_not__sum__squares__lt__zero,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y4 @ Y4 ) ) @ zero_zero_rat ) ).
% 5.64/5.89
% 5.64/5.89 % not_sum_squares_lt_zero
% 5.64/5.89 thf(fact_3152_not__sum__squares__lt__zero,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] :
% 5.64/5.89 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y4 @ Y4 ) ) @ zero_zero_int ) ).
% 5.64/5.89
% 5.64/5.89 % not_sum_squares_lt_zero
% 5.64/5.89 thf(fact_3153_sum__squares__gt__zero__iff,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) ) )
% 5.64/5.89 = ( ( X2 != zero_zero_real )
% 5.64/5.89 | ( Y4 != zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_gt_zero_iff
% 5.64/5.89 thf(fact_3154_sum__squares__gt__zero__iff,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y4 @ Y4 ) ) )
% 5.64/5.89 = ( ( X2 != zero_zero_rat )
% 5.64/5.89 | ( Y4 != zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_gt_zero_iff
% 5.64/5.89 thf(fact_3155_sum__squares__gt__zero__iff,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y4 @ Y4 ) ) )
% 5.64/5.89 = ( ( X2 != zero_zero_int )
% 5.64/5.89 | ( Y4 != zero_zero_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % sum_squares_gt_zero_iff
% 5.64/5.89 thf(fact_3156_zero__less__two,axiom,
% 5.64/5.89 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.64/5.89
% 5.64/5.89 % zero_less_two
% 5.64/5.89 thf(fact_3157_zero__less__two,axiom,
% 5.64/5.89 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.64/5.89
% 5.64/5.89 % zero_less_two
% 5.64/5.89 thf(fact_3158_zero__less__two,axiom,
% 5.64/5.89 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.64/5.89
% 5.64/5.89 % zero_less_two
% 5.64/5.89 thf(fact_3159_zero__less__two,axiom,
% 5.64/5.89 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.64/5.89
% 5.64/5.89 % zero_less_two
% 5.64/5.89 thf(fact_3160_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.64/5.89 ! [C: nat,A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.64/5.89 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.89 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.64/5.89 thf(fact_3161_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.64/5.89 ! [C: int,A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.89 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.64/5.89 thf(fact_3162_divide__less__eq,axiom,
% 5.64/5.89 ! [B: real,C: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_less_eq
% 5.64/5.89 thf(fact_3163_divide__less__eq,axiom,
% 5.64/5.89 ! [B: rat,C: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_less_eq
% 5.64/5.89 thf(fact_3164_less__divide__eq,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_divide_eq
% 5.64/5.89 thf(fact_3165_less__divide__eq,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_divide_eq
% 5.64/5.89 thf(fact_3166_neg__divide__less__eq,axiom,
% 5.64/5.89 ! [C: real,B: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_divide_less_eq
% 5.64/5.89 thf(fact_3167_neg__divide__less__eq,axiom,
% 5.64/5.89 ! [C: rat,B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_divide_less_eq
% 5.64/5.89 thf(fact_3168_neg__less__divide__eq,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_less_divide_eq
% 5.64/5.89 thf(fact_3169_neg__less__divide__eq,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_less_divide_eq
% 5.64/5.89 thf(fact_3170_pos__divide__less__eq,axiom,
% 5.64/5.89 ! [C: real,B: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_divide_less_eq
% 5.64/5.89 thf(fact_3171_pos__divide__less__eq,axiom,
% 5.64/5.89 ! [C: rat,B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_divide_less_eq
% 5.64/5.89 thf(fact_3172_pos__less__divide__eq,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_less_divide_eq
% 5.64/5.89 thf(fact_3173_pos__less__divide__eq,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_less_divide_eq
% 5.64/5.89 thf(fact_3174_mult__imp__div__pos__less,axiom,
% 5.64/5.89 ! [Y4: real,X2: real,Z: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y4 ) )
% 5.64/5.89 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_div_pos_less
% 5.64/5.89 thf(fact_3175_mult__imp__div__pos__less,axiom,
% 5.64/5.89 ! [Y4: rat,X2: rat,Z: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y4 ) )
% 5.64/5.89 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_div_pos_less
% 5.64/5.89 thf(fact_3176_mult__imp__less__div__pos,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_real @ ( times_times_real @ Z @ Y4 ) @ X2 )
% 5.64/5.89 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_less_div_pos
% 5.64/5.89 thf(fact_3177_mult__imp__less__div__pos,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y4 ) @ X2 )
% 5.64/5.89 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_less_div_pos
% 5.64/5.89 thf(fact_3178_divide__strict__left__mono,axiom,
% 5.64/5.89 ! [B: real,A: real,C: real] :
% 5.64/5.89 ( ( ord_less_real @ B @ A )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.89 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_strict_left_mono
% 5.64/5.89 thf(fact_3179_divide__strict__left__mono,axiom,
% 5.64/5.89 ! [B: rat,A: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_rat @ B @ A )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.89 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_strict_left_mono
% 5.64/5.89 thf(fact_3180_divide__strict__left__mono__neg,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_real @ A @ B )
% 5.64/5.89 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.89 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_strict_left_mono_neg
% 5.64/5.89 thf(fact_3181_divide__strict__left__mono__neg,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_rat @ A @ B )
% 5.64/5.89 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.89 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_strict_left_mono_neg
% 5.64/5.89 thf(fact_3182_less__divide__eq__1,axiom,
% 5.64/5.89 ! [B: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 & ( ord_less_real @ A @ B ) )
% 5.64/5.89 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.89 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_divide_eq_1
% 5.64/5.89 thf(fact_3183_less__divide__eq__1,axiom,
% 5.64/5.89 ! [B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 & ( ord_less_rat @ A @ B ) )
% 5.64/5.89 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.89 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_divide_eq_1
% 5.64/5.89 thf(fact_3184_divide__less__eq__1,axiom,
% 5.64/5.89 ! [B: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 & ( ord_less_real @ B @ A ) )
% 5.64/5.89 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.89 & ( ord_less_real @ A @ B ) )
% 5.64/5.89 | ( A = zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_less_eq_1
% 5.64/5.89 thf(fact_3185_divide__less__eq__1,axiom,
% 5.64/5.89 ! [B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 & ( ord_less_rat @ B @ A ) )
% 5.64/5.89 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.89 & ( ord_less_rat @ A @ B ) )
% 5.64/5.89 | ( A = zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_less_eq_1
% 5.64/5.89 thf(fact_3186_power__le__one,axiom,
% 5.64/5.89 ! [A: rat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_one
% 5.64/5.89 thf(fact_3187_power__le__one,axiom,
% 5.64/5.89 ! [A: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_one
% 5.64/5.89 thf(fact_3188_power__le__one,axiom,
% 5.64/5.89 ! [A: int,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_one
% 5.64/5.89 thf(fact_3189_power__le__one,axiom,
% 5.64/5.89 ! [A: real,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_one
% 5.64/5.89 thf(fact_3190_eq__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: complex,C: complex] :
% 5.64/5.89 ( ( ( numera6690914467698888265omplex @ W )
% 5.64/5.89 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.89 = ( ( ( C != zero_zero_complex )
% 5.64/5.89 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.64/5.89 = B ) )
% 5.64/5.89 & ( ( C = zero_zero_complex )
% 5.64/5.89 => ( ( numera6690914467698888265omplex @ W )
% 5.64/5.89 = zero_zero_complex ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % eq_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3191_eq__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: real,C: real] :
% 5.64/5.89 ( ( ( numeral_numeral_real @ W )
% 5.64/5.89 = ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ( ( C != zero_zero_real )
% 5.64/5.89 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.64/5.89 = B ) )
% 5.64/5.89 & ( ( C = zero_zero_real )
% 5.64/5.89 => ( ( numeral_numeral_real @ W )
% 5.64/5.89 = zero_zero_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % eq_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3192_eq__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: rat,C: rat] :
% 5.64/5.89 ( ( ( numeral_numeral_rat @ W )
% 5.64/5.89 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( C != zero_zero_rat )
% 5.64/5.89 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.64/5.89 = B ) )
% 5.64/5.89 & ( ( C = zero_zero_rat )
% 5.64/5.89 => ( ( numeral_numeral_rat @ W )
% 5.64/5.89 = zero_zero_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % eq_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3193_divide__eq__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: complex,C: complex,W: num] :
% 5.64/5.89 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.64/5.89 = ( numera6690914467698888265omplex @ W ) )
% 5.64/5.89 = ( ( ( C != zero_zero_complex )
% 5.64/5.89 => ( B
% 5.64/5.89 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.64/5.89 & ( ( C = zero_zero_complex )
% 5.64/5.89 => ( ( numera6690914467698888265omplex @ W )
% 5.64/5.89 = zero_zero_complex ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_eq_eq_numeral(1)
% 5.64/5.89 thf(fact_3194_divide__eq__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: real,C: real,W: num] :
% 5.64/5.89 ( ( ( divide_divide_real @ B @ C )
% 5.64/5.89 = ( numeral_numeral_real @ W ) )
% 5.64/5.89 = ( ( ( C != zero_zero_real )
% 5.64/5.89 => ( B
% 5.64/5.89 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.64/5.89 & ( ( C = zero_zero_real )
% 5.64/5.89 => ( ( numeral_numeral_real @ W )
% 5.64/5.89 = zero_zero_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_eq_eq_numeral(1)
% 5.64/5.89 thf(fact_3195_divide__eq__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: rat,C: rat,W: num] :
% 5.64/5.89 ( ( ( divide_divide_rat @ B @ C )
% 5.64/5.89 = ( numeral_numeral_rat @ W ) )
% 5.64/5.89 = ( ( ( C != zero_zero_rat )
% 5.64/5.89 => ( B
% 5.64/5.89 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.64/5.89 & ( ( C = zero_zero_rat )
% 5.64/5.89 => ( ( numeral_numeral_rat @ W )
% 5.64/5.89 = zero_zero_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_eq_eq_numeral(1)
% 5.64/5.89 thf(fact_3196_add__divide__eq__if__simps_I2_J,axiom,
% 5.64/5.89 ! [Z: complex,A: complex,B: complex] :
% 5.64/5.89 ( ( ( Z = zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.64/5.89 = B ) )
% 5.64/5.89 & ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(2)
% 5.64/5.89 thf(fact_3197_add__divide__eq__if__simps_I2_J,axiom,
% 5.64/5.89 ! [Z: real,A: real,B: real] :
% 5.64/5.89 ( ( ( Z = zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.64/5.89 = B ) )
% 5.64/5.89 & ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(2)
% 5.64/5.89 thf(fact_3198_add__divide__eq__if__simps_I2_J,axiom,
% 5.64/5.89 ! [Z: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ( Z = zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.64/5.89 = B ) )
% 5.64/5.89 & ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(2)
% 5.64/5.89 thf(fact_3199_add__divide__eq__if__simps_I1_J,axiom,
% 5.64/5.89 ! [Z: complex,A: complex,B: complex] :
% 5.64/5.89 ( ( ( Z = zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.64/5.89 = A ) )
% 5.64/5.89 & ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(1)
% 5.64/5.89 thf(fact_3200_add__divide__eq__if__simps_I1_J,axiom,
% 5.64/5.89 ! [Z: real,A: real,B: real] :
% 5.64/5.89 ( ( ( Z = zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.64/5.89 = A ) )
% 5.64/5.89 & ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(1)
% 5.64/5.89 thf(fact_3201_add__divide__eq__if__simps_I1_J,axiom,
% 5.64/5.89 ! [Z: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ( Z = zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.64/5.89 = A ) )
% 5.64/5.89 & ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(1)
% 5.64/5.89 thf(fact_3202_add__frac__eq,axiom,
% 5.64/5.89 ! [Y4: complex,Z: complex,X2: complex,W: complex] :
% 5.64/5.89 ( ( Y4 != zero_zero_complex )
% 5.64/5.89 => ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y4 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y4 ) ) @ ( times_times_complex @ Y4 @ Z ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_frac_eq
% 5.64/5.89 thf(fact_3203_add__frac__eq,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real,W: real] :
% 5.64/5.89 ( ( Y4 != zero_zero_real )
% 5.64/5.89 => ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_frac_eq
% 5.64/5.89 thf(fact_3204_add__frac__eq,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat,W: rat] :
% 5.64/5.89 ( ( Y4 != zero_zero_rat )
% 5.64/5.89 => ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_frac_eq
% 5.64/5.89 thf(fact_3205_add__frac__num,axiom,
% 5.64/5.89 ! [Y4: complex,X2: complex,Z: complex] :
% 5.64/5.89 ( ( Y4 != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y4 ) @ Z )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_frac_num
% 5.64/5.89 thf(fact_3206_add__frac__num,axiom,
% 5.64/5.89 ! [Y4: real,X2: real,Z: real] :
% 5.64/5.89 ( ( Y4 != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y4 ) @ Z )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_frac_num
% 5.64/5.89 thf(fact_3207_add__frac__num,axiom,
% 5.64/5.89 ! [Y4: rat,X2: rat,Z: rat] :
% 5.64/5.89 ( ( Y4 != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ Z )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_frac_num
% 5.64/5.89 thf(fact_3208_add__num__frac,axiom,
% 5.64/5.89 ! [Y4: complex,Z: complex,X2: complex] :
% 5.64/5.89 ( ( Y4 != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y4 ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_num_frac
% 5.64/5.89 thf(fact_3209_add__num__frac,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real] :
% 5.64/5.89 ( ( Y4 != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_num_frac
% 5.64/5.89 thf(fact_3210_add__num__frac,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat] :
% 5.64/5.89 ( ( Y4 != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y4 ) )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y4 ) ) @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_num_frac
% 5.64/5.89 thf(fact_3211_add__divide__eq__iff,axiom,
% 5.64/5.89 ! [Z: complex,X2: complex,Y4: complex] :
% 5.64/5.89 ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y4 @ Z ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_iff
% 5.64/5.89 thf(fact_3212_add__divide__eq__iff,axiom,
% 5.64/5.89 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.89 ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y4 @ Z ) )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_iff
% 5.64/5.89 thf(fact_3213_add__divide__eq__iff,axiom,
% 5.64/5.89 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.89 ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y4 @ Z ) )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_iff
% 5.64/5.89 thf(fact_3214_divide__add__eq__iff,axiom,
% 5.64/5.89 ! [Z: complex,X2: complex,Y4: complex] :
% 5.64/5.89 ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y4 )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_add_eq_iff
% 5.64/5.89 thf(fact_3215_divide__add__eq__iff,axiom,
% 5.64/5.89 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.89 ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y4 )
% 5.64/5.89 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_add_eq_iff
% 5.64/5.89 thf(fact_3216_divide__add__eq__iff,axiom,
% 5.64/5.89 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.89 ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y4 )
% 5.64/5.89 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_add_eq_iff
% 5.64/5.89 thf(fact_3217_power__le__imp__le__base,axiom,
% 5.64/5.89 ! [A: rat,N: nat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_imp_le_base
% 5.64/5.89 thf(fact_3218_power__le__imp__le__base,axiom,
% 5.64/5.89 ! [A: nat,N: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_imp_le_base
% 5.64/5.89 thf(fact_3219_power__le__imp__le__base,axiom,
% 5.64/5.89 ! [A: int,N: nat,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_imp_le_base
% 5.64/5.89 thf(fact_3220_power__le__imp__le__base,axiom,
% 5.64/5.89 ! [A: real,N: nat,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.89 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_le_imp_le_base
% 5.64/5.89 thf(fact_3221_power__inject__base,axiom,
% 5.64/5.89 ! [A: rat,N: nat,B: rat] :
% 5.64/5.89 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.64/5.89 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.89 => ( A = B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_inject_base
% 5.64/5.89 thf(fact_3222_power__inject__base,axiom,
% 5.64/5.89 ! [A: nat,N: nat,B: nat] :
% 5.64/5.89 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.64/5.89 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( A = B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_inject_base
% 5.64/5.89 thf(fact_3223_power__inject__base,axiom,
% 5.64/5.89 ! [A: int,N: nat,B: int] :
% 5.64/5.89 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.64/5.89 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.89 => ( A = B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_inject_base
% 5.64/5.89 thf(fact_3224_power__inject__base,axiom,
% 5.64/5.89 ! [A: real,N: nat,B: real] :
% 5.64/5.89 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.64/5.89 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.89 => ( A = B ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_inject_base
% 5.64/5.89 thf(fact_3225_div__add__self2,axiom,
% 5.64/5.89 ! [B: nat,A: nat] :
% 5.64/5.89 ( ( B != zero_zero_nat )
% 5.64/5.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.64/5.89 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_add_self2
% 5.64/5.89 thf(fact_3226_div__add__self2,axiom,
% 5.64/5.89 ! [B: int,A: int] :
% 5.64/5.89 ( ( B != zero_zero_int )
% 5.64/5.89 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.64/5.89 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_add_self2
% 5.64/5.89 thf(fact_3227_div__add__self1,axiom,
% 5.64/5.89 ! [B: nat,A: nat] :
% 5.64/5.89 ( ( B != zero_zero_nat )
% 5.64/5.89 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.64/5.89 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_add_self1
% 5.64/5.89 thf(fact_3228_div__add__self1,axiom,
% 5.64/5.89 ! [B: int,A: int] :
% 5.64/5.89 ( ( B != zero_zero_int )
% 5.64/5.89 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.64/5.89 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_add_self1
% 5.64/5.89 thf(fact_3229_add__divide__eq__if__simps_I4_J,axiom,
% 5.64/5.89 ! [Z: complex,A: complex,B: complex] :
% 5.64/5.89 ( ( ( Z = zero_zero_complex )
% 5.64/5.89 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.64/5.89 = A ) )
% 5.64/5.89 & ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(4)
% 5.64/5.89 thf(fact_3230_add__divide__eq__if__simps_I4_J,axiom,
% 5.64/5.89 ! [Z: real,A: real,B: real] :
% 5.64/5.89 ( ( ( Z = zero_zero_real )
% 5.64/5.89 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.64/5.89 = A ) )
% 5.64/5.89 & ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.64/5.89 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(4)
% 5.64/5.89 thf(fact_3231_add__divide__eq__if__simps_I4_J,axiom,
% 5.64/5.89 ! [Z: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ( Z = zero_zero_rat )
% 5.64/5.89 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.64/5.89 = A ) )
% 5.64/5.89 & ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.64/5.89 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_divide_eq_if_simps(4)
% 5.64/5.89 thf(fact_3232_diff__frac__eq,axiom,
% 5.64/5.89 ! [Y4: complex,Z: complex,X2: complex,W: complex] :
% 5.64/5.89 ( ( Y4 != zero_zero_complex )
% 5.64/5.89 => ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y4 ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y4 ) ) @ ( times_times_complex @ Y4 @ Z ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_frac_eq
% 5.64/5.89 thf(fact_3233_diff__frac__eq,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real,W: real] :
% 5.64/5.89 ( ( Y4 != zero_zero_real )
% 5.64/5.89 => ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.64/5.89 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_frac_eq
% 5.64/5.89 thf(fact_3234_diff__frac__eq,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat,W: rat] :
% 5.64/5.89 ( ( Y4 != zero_zero_rat )
% 5.64/5.89 => ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.64/5.89 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_frac_eq
% 5.64/5.89 thf(fact_3235_diff__divide__eq__iff,axiom,
% 5.64/5.89 ! [Z: complex,X2: complex,Y4: complex] :
% 5.64/5.89 ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y4 @ Z ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_divide_eq_iff
% 5.64/5.89 thf(fact_3236_diff__divide__eq__iff,axiom,
% 5.64/5.89 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.89 ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y4 @ Z ) )
% 5.64/5.89 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_divide_eq_iff
% 5.64/5.89 thf(fact_3237_diff__divide__eq__iff,axiom,
% 5.64/5.89 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.89 ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y4 @ Z ) )
% 5.64/5.89 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_divide_eq_iff
% 5.64/5.89 thf(fact_3238_divide__diff__eq__iff,axiom,
% 5.64/5.89 ! [Z: complex,X2: complex,Y4: complex] :
% 5.64/5.89 ( ( Z != zero_zero_complex )
% 5.64/5.89 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y4 )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_diff_eq_iff
% 5.64/5.89 thf(fact_3239_divide__diff__eq__iff,axiom,
% 5.64/5.89 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.89 ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y4 )
% 5.64/5.89 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_diff_eq_iff
% 5.64/5.89 thf(fact_3240_divide__diff__eq__iff,axiom,
% 5.64/5.89 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.89 ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y4 )
% 5.64/5.89 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_diff_eq_iff
% 5.64/5.89 thf(fact_3241_vebt__member_Osimps_I4_J,axiom,
% 5.64/5.89 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.64/5.89 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_member.simps(4)
% 5.64/5.89 thf(fact_3242_mod__double__modulus,axiom,
% 5.64/5.89 ! [M: code_integer,X2: code_integer] :
% 5.64/5.89 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.64/5.89 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.64/5.89 => ( ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.89 = ( modulo364778990260209775nteger @ X2 @ M ) )
% 5.64/5.89 | ( ( modulo364778990260209775nteger @ X2 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.89 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mod_double_modulus
% 5.64/5.89 thf(fact_3243_mod__double__modulus,axiom,
% 5.64/5.89 ! [M: nat,X2: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.64/5.89 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.89 = ( modulo_modulo_nat @ X2 @ M ) )
% 5.64/5.89 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.89 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mod_double_modulus
% 5.64/5.89 thf(fact_3244_mod__double__modulus,axiom,
% 5.64/5.89 ! [M: int,X2: int] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ M )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.89 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.89 = ( modulo_modulo_int @ X2 @ M ) )
% 5.64/5.89 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.89 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mod_double_modulus
% 5.64/5.89 thf(fact_3245_divmod__digit__1_I2_J,axiom,
% 5.64/5.89 ! [A: code_integer,B: code_integer] :
% 5.64/5.89 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.89 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.89 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.89 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.89 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divmod_digit_1(2)
% 5.64/5.89 thf(fact_3246_divmod__digit__1_I2_J,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.89 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.89 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divmod_digit_1(2)
% 5.64/5.89 thf(fact_3247_divmod__digit__1_I2_J,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.89 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.64/5.89 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divmod_digit_1(2)
% 5.64/5.89 thf(fact_3248_numeral__1__eq__Suc__0,axiom,
% 5.64/5.89 ( ( numeral_numeral_nat @ one )
% 5.64/5.89 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.89
% 5.64/5.89 % numeral_1_eq_Suc_0
% 5.64/5.89 thf(fact_3249_num_Osize_I5_J,axiom,
% 5.64/5.89 ! [X22: num] :
% 5.64/5.89 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.64/5.89 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % num.size(5)
% 5.64/5.89 thf(fact_3250_ex__least__nat__less,axiom,
% 5.64/5.89 ! [P: nat > $o,N: nat] :
% 5.64/5.89 ( ( P @ N )
% 5.64/5.89 => ( ~ ( P @ zero_zero_nat )
% 5.64/5.89 => ? [K3: nat] :
% 5.64/5.89 ( ( ord_less_nat @ K3 @ N )
% 5.64/5.89 & ! [I2: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ I2 @ K3 )
% 5.64/5.89 => ~ ( P @ I2 ) )
% 5.64/5.89 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % ex_least_nat_less
% 5.64/5.89 thf(fact_3251_diff__Suc__less,axiom,
% 5.64/5.89 ! [N: nat,I: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.64/5.89
% 5.64/5.89 % diff_Suc_less
% 5.64/5.89 thf(fact_3252_one__less__mult,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.89 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.64/5.89 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % one_less_mult
% 5.64/5.89 thf(fact_3253_n__less__m__mult__n,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.64/5.89 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % n_less_m_mult_n
% 5.64/5.89 thf(fact_3254_n__less__n__mult__m,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.64/5.89 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % n_less_n_mult_m
% 5.64/5.89 thf(fact_3255_nat__induct__non__zero,axiom,
% 5.64/5.89 ! [N: nat,P: nat > $o] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ( P @ one_one_nat )
% 5.64/5.89 => ( ! [N3: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.89 => ( ( P @ N3 )
% 5.64/5.89 => ( P @ ( suc @ N3 ) ) ) )
% 5.64/5.89 => ( P @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % nat_induct_non_zero
% 5.64/5.89 thf(fact_3256_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 5.64/5.89 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_s5460976970255530739at_nat @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3257_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: complex,Xs2: list_complex] :
% 5.64/5.89 ( ( member_complex @ X2 @ ( set_complex2 @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3258_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: real,Xs2: list_real] :
% 5.64/5.89 ( ( member_real @ X2 @ ( set_real2 @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3259_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 5.64/5.89 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3260_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: $o,Xs2: list_o] :
% 5.64/5.89 ( ( member_o @ X2 @ ( set_o2 @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3261_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: nat,Xs2: list_nat] :
% 5.64/5.89 ( ( member_nat @ X2 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3262_length__pos__if__in__set,axiom,
% 5.64/5.89 ! [X2: int,Xs2: list_int] :
% 5.64/5.89 ( ( member_int @ X2 @ ( set_int2 @ Xs2 ) )
% 5.64/5.89 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % length_pos_if_in_set
% 5.64/5.89 thf(fact_3263_nat__mult__le__cancel1,axiom,
% 5.64/5.89 ! [K: nat,M: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.89 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.89 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % nat_mult_le_cancel1
% 5.64/5.89 thf(fact_3264_power__gt__expt,axiom,
% 5.64/5.89 ! [N: nat,K: nat] :
% 5.64/5.89 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.89 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_gt_expt
% 5.64/5.89 thf(fact_3265_nat__diff__split,axiom,
% 5.64/5.89 ! [P: nat > $o,A: nat,B: nat] :
% 5.64/5.89 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.89 = ( ( ( ord_less_nat @ A @ B )
% 5.64/5.89 => ( P @ zero_zero_nat ) )
% 5.64/5.89 & ! [D2: nat] :
% 5.64/5.89 ( ( A
% 5.64/5.89 = ( plus_plus_nat @ B @ D2 ) )
% 5.64/5.89 => ( P @ D2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % nat_diff_split
% 5.64/5.89 thf(fact_3266_nat__diff__split__asm,axiom,
% 5.64/5.89 ! [P: nat > $o,A: nat,B: nat] :
% 5.64/5.89 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.89 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.64/5.89 & ~ ( P @ zero_zero_nat ) )
% 5.64/5.89 | ? [D2: nat] :
% 5.64/5.89 ( ( A
% 5.64/5.89 = ( plus_plus_nat @ B @ D2 ) )
% 5.64/5.89 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % nat_diff_split_asm
% 5.64/5.89 thf(fact_3267_div__le__mono2,axiom,
% 5.64/5.89 ! [M: nat,N: nat,K: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.89 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.89 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_le_mono2
% 5.64/5.89 thf(fact_3268_div__greater__zero__iff,axiom,
% 5.64/5.89 ! [M: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.89 = ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.89 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_greater_zero_iff
% 5.64/5.89 thf(fact_3269_nat__one__le__power,axiom,
% 5.64/5.89 ! [I: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.64/5.89 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % nat_one_le_power
% 5.64/5.89 thf(fact_3270_nat__mult__div__cancel1,axiom,
% 5.64/5.89 ! [K: nat,M: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.89 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.89 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % nat_mult_div_cancel1
% 5.64/5.89 thf(fact_3271_div__less__iff__less__mult,axiom,
% 5.64/5.89 ! [Q3: nat,M: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.64/5.89 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N )
% 5.64/5.89 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q3 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_less_iff_less_mult
% 5.64/5.89 thf(fact_3272_div__eq__dividend__iff,axiom,
% 5.64/5.89 ! [M: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.89 => ( ( ( divide_divide_nat @ M @ N )
% 5.64/5.89 = M )
% 5.64/5.89 = ( N = one_one_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_eq_dividend_iff
% 5.64/5.89 thf(fact_3273_div__less__dividend,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ one_one_nat @ N )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.89 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_less_dividend
% 5.64/5.89 thf(fact_3274_vebt__insert_Osimps_I3_J,axiom,
% 5.64/5.89 ! [Info: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.64/5.89 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X2 )
% 5.64/5.89 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_insert.simps(3)
% 5.64/5.89 thf(fact_3275_vebt__mint_Ocases,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT] :
% 5.64/5.89 ( ! [A5: $o,B5: $o] :
% 5.64/5.89 ( X2
% 5.64/5.89 != ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.89 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.89 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_mint.cases
% 5.64/5.89 thf(fact_3276_field__le__mult__one__interval,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ! [Z2: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.64/5.89 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X2 ) @ Y4 ) ) )
% 5.64/5.89 => ( ord_less_eq_rat @ X2 @ Y4 ) ) ).
% 5.64/5.89
% 5.64/5.89 % field_le_mult_one_interval
% 5.64/5.89 thf(fact_3277_field__le__mult__one__interval,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ! [Z2: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.64/5.89 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X2 ) @ Y4 ) ) )
% 5.64/5.89 => ( ord_less_eq_real @ X2 @ Y4 ) ) ).
% 5.64/5.89
% 5.64/5.89 % field_le_mult_one_interval
% 5.64/5.89 thf(fact_3278_mult__less__cancel__right2,axiom,
% 5.64/5.89 ! [A: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.64/5.89 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.64/5.89 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right2
% 5.64/5.89 thf(fact_3279_mult__less__cancel__right2,axiom,
% 5.64/5.89 ! [A: int,C: int] :
% 5.64/5.89 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.64/5.89 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ A @ one_one_int ) )
% 5.64/5.89 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right2
% 5.64/5.89 thf(fact_3280_mult__less__cancel__right2,axiom,
% 5.64/5.89 ! [A: real,C: real] :
% 5.64/5.89 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.64/5.89 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ A @ one_one_real ) )
% 5.64/5.89 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right2
% 5.64/5.89 thf(fact_3281_mult__less__cancel__right1,axiom,
% 5.64/5.89 ! [C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right1
% 5.64/5.89 thf(fact_3282_mult__less__cancel__right1,axiom,
% 5.64/5.89 ! [C: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ one_one_int @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right1
% 5.64/5.89 thf(fact_3283_mult__less__cancel__right1,axiom,
% 5.64/5.89 ! [C: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ one_one_real @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_right1
% 5.64/5.89 thf(fact_3284_mult__less__cancel__left2,axiom,
% 5.64/5.89 ! [C: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.64/5.89 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.64/5.89 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_left2
% 5.64/5.89 thf(fact_3285_mult__less__cancel__left2,axiom,
% 5.64/5.89 ! [C: int,A: int] :
% 5.64/5.89 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.64/5.89 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ A @ one_one_int ) )
% 5.64/5.89 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_left2
% 5.64/5.89 thf(fact_3286_mult__less__cancel__left2,axiom,
% 5.64/5.89 ! [C: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.64/5.89 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ A @ one_one_real ) )
% 5.64/5.89 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_left2
% 5.64/5.89 thf(fact_3287_mult__less__cancel__left1,axiom,
% 5.64/5.89 ! [C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.64/5.89 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_left1
% 5.64/5.89 thf(fact_3288_mult__less__cancel__left1,axiom,
% 5.64/5.89 ! [C: int,B: int] :
% 5.64/5.89 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.64/5.89 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_int @ one_one_int @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_left1
% 5.64/5.89 thf(fact_3289_mult__less__cancel__left1,axiom,
% 5.64/5.89 ! [C: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.64/5.89 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ one_one_real @ B ) )
% 5.64/5.89 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_less_cancel_left1
% 5.64/5.89 thf(fact_3290_mult__le__cancel__right2,axiom,
% 5.64/5.89 ! [A: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.64/5.89 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_right2
% 5.64/5.89 thf(fact_3291_mult__le__cancel__right2,axiom,
% 5.64/5.89 ! [A: int,C: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.64/5.89 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.64/5.89 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_right2
% 5.64/5.89 thf(fact_3292_mult__le__cancel__right2,axiom,
% 5.64/5.89 ! [A: real,C: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.64/5.89 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_right2
% 5.64/5.89 thf(fact_3293_mult__le__cancel__right1,axiom,
% 5.64/5.89 ! [C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.64/5.89 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_right1
% 5.64/5.89 thf(fact_3294_mult__le__cancel__right1,axiom,
% 5.64/5.89 ! [C: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.64/5.89 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_right1
% 5.64/5.89 thf(fact_3295_mult__le__cancel__right1,axiom,
% 5.64/5.89 ! [C: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.64/5.89 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_right1
% 5.64/5.89 thf(fact_3296_mult__le__cancel__left2,axiom,
% 5.64/5.89 ! [C: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.64/5.89 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left2
% 5.64/5.89 thf(fact_3297_mult__le__cancel__left2,axiom,
% 5.64/5.89 ! [C: int,A: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.64/5.89 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.64/5.89 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left2
% 5.64/5.89 thf(fact_3298_mult__le__cancel__left2,axiom,
% 5.64/5.89 ! [C: real,A: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.64/5.89 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left2
% 5.64/5.89 thf(fact_3299_mult__le__cancel__left1,axiom,
% 5.64/5.89 ! [C: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.64/5.89 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left1
% 5.64/5.89 thf(fact_3300_mult__le__cancel__left1,axiom,
% 5.64/5.89 ! [C: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.64/5.89 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.64/5.89 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.64/5.89 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.64/5.89 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left1
% 5.64/5.89 thf(fact_3301_mult__le__cancel__left1,axiom,
% 5.64/5.89 ! [C: real,B: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.64/5.89 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_le_cancel_left1
% 5.64/5.89 thf(fact_3302_divide__le__eq,axiom,
% 5.64/5.89 ! [B: rat,C: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_eq
% 5.64/5.89 thf(fact_3303_divide__le__eq,axiom,
% 5.64/5.89 ! [B: real,C: real,A: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_eq
% 5.64/5.89 thf(fact_3304_le__divide__eq,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % le_divide_eq
% 5.64/5.89 thf(fact_3305_le__divide__eq,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % le_divide_eq
% 5.64/5.89 thf(fact_3306_divide__left__mono,axiom,
% 5.64/5.89 ! [B: rat,A: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.89 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_left_mono
% 5.64/5.89 thf(fact_3307_divide__left__mono,axiom,
% 5.64/5.89 ! [B: real,A: real,C: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.89 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_left_mono
% 5.64/5.89 thf(fact_3308_neg__divide__le__eq,axiom,
% 5.64/5.89 ! [C: rat,B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_divide_le_eq
% 5.64/5.89 thf(fact_3309_neg__divide__le__eq,axiom,
% 5.64/5.89 ! [C: real,B: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_divide_le_eq
% 5.64/5.89 thf(fact_3310_neg__le__divide__eq,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_le_divide_eq
% 5.64/5.89 thf(fact_3311_neg__le__divide__eq,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % neg_le_divide_eq
% 5.64/5.89 thf(fact_3312_pos__divide__le__eq,axiom,
% 5.64/5.89 ! [C: rat,B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_divide_le_eq
% 5.64/5.89 thf(fact_3313_pos__divide__le__eq,axiom,
% 5.64/5.89 ! [C: real,B: real,A: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.64/5.89 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_divide_le_eq
% 5.64/5.89 thf(fact_3314_pos__le__divide__eq,axiom,
% 5.64/5.89 ! [C: rat,A: rat,B: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_le_divide_eq
% 5.64/5.89 thf(fact_3315_pos__le__divide__eq,axiom,
% 5.64/5.89 ! [C: real,A: real,B: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos_le_divide_eq
% 5.64/5.89 thf(fact_3316_mult__imp__div__pos__le,axiom,
% 5.64/5.89 ! [Y4: rat,X2: rat,Z: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y4 ) )
% 5.64/5.89 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_div_pos_le
% 5.64/5.89 thf(fact_3317_mult__imp__div__pos__le,axiom,
% 5.64/5.89 ! [Y4: real,X2: real,Z: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y4 ) )
% 5.64/5.89 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y4 ) @ Z ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_div_pos_le
% 5.64/5.89 thf(fact_3318_mult__imp__le__div__pos,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y4 ) @ X2 )
% 5.64/5.89 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_le_div_pos
% 5.64/5.89 thf(fact_3319_mult__imp__le__div__pos,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y4 ) @ X2 )
% 5.64/5.89 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_imp_le_div_pos
% 5.64/5.89 thf(fact_3320_divide__left__mono__neg,axiom,
% 5.64/5.89 ! [A: rat,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.89 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.89 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_left_mono_neg
% 5.64/5.89 thf(fact_3321_divide__left__mono__neg,axiom,
% 5.64/5.89 ! [A: real,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.89 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.64/5.89 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_left_mono_neg
% 5.64/5.89 thf(fact_3322_le__divide__eq__1,axiom,
% 5.64/5.89 ! [B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 & ( ord_less_eq_rat @ A @ B ) )
% 5.64/5.89 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.89 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % le_divide_eq_1
% 5.64/5.89 thf(fact_3323_le__divide__eq__1,axiom,
% 5.64/5.89 ! [B: real,A: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 & ( ord_less_eq_real @ A @ B ) )
% 5.64/5.89 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.89 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % le_divide_eq_1
% 5.64/5.89 thf(fact_3324_divide__le__eq__1,axiom,
% 5.64/5.89 ! [B: rat,A: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 & ( ord_less_eq_rat @ B @ A ) )
% 5.64/5.89 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.89 & ( ord_less_eq_rat @ A @ B ) )
% 5.64/5.89 | ( A = zero_zero_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_eq_1
% 5.64/5.89 thf(fact_3325_divide__le__eq__1,axiom,
% 5.64/5.89 ! [B: real,A: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 & ( ord_less_eq_real @ B @ A ) )
% 5.64/5.89 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.89 & ( ord_less_eq_real @ A @ B ) )
% 5.64/5.89 | ( A = zero_zero_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_eq_1
% 5.64/5.89 thf(fact_3326_convex__bound__le,axiom,
% 5.64/5.89 ! [X2: rat,A: rat,Y4: rat,U: rat,V: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ X2 @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ Y4 @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.64/5.89 => ( ( ( plus_plus_rat @ U @ V )
% 5.64/5.89 = one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % convex_bound_le
% 5.64/5.89 thf(fact_3327_convex__bound__le,axiom,
% 5.64/5.89 ! [X2: int,A: int,Y4: int,U: int,V: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ X2 @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ Y4 @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.64/5.89 => ( ( ( plus_plus_int @ U @ V )
% 5.64/5.89 = one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % convex_bound_le
% 5.64/5.89 thf(fact_3328_convex__bound__le,axiom,
% 5.64/5.89 ! [X2: real,A: real,Y4: real,U: real,V: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ X2 @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ Y4 @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.64/5.89 => ( ( ( plus_plus_real @ U @ V )
% 5.64/5.89 = one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % convex_bound_le
% 5.64/5.89 thf(fact_3329_divide__less__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: real,C: real,W: num] :
% 5.64/5.89 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_less_eq_numeral(1)
% 5.64/5.89 thf(fact_3330_divide__less__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: rat,C: rat,W: num] :
% 5.64/5.89 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_less_eq_numeral(1)
% 5.64/5.89 thf(fact_3331_less__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3332_less__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3333_frac__le__eq,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat,W: rat] :
% 5.64/5.89 ( ( Y4 != zero_zero_rat )
% 5.64/5.89 => ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.64/5.89 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_le_eq
% 5.64/5.89 thf(fact_3334_frac__le__eq,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real,W: real] :
% 5.64/5.89 ( ( Y4 != zero_zero_real )
% 5.64/5.89 => ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.64/5.89 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_le_eq
% 5.64/5.89 thf(fact_3335_divmod__digit__1_I1_J,axiom,
% 5.64/5.89 ! [A: code_integer,B: code_integer] :
% 5.64/5.89 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.89 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.89 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.89 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.64/5.89 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divmod_digit_1(1)
% 5.64/5.89 thf(fact_3336_divmod__digit__1_I1_J,axiom,
% 5.64/5.89 ! [A: nat,B: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.64/5.89 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.89 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 5.64/5.89 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divmod_digit_1(1)
% 5.64/5.89 thf(fact_3337_divmod__digit__1_I1_J,axiom,
% 5.64/5.89 ! [A: int,B: int] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.89 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.64/5.89 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 5.64/5.89 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divmod_digit_1(1)
% 5.64/5.89 thf(fact_3338_frac__less__eq,axiom,
% 5.64/5.89 ! [Y4: real,Z: real,X2: real,W: real] :
% 5.64/5.89 ( ( Y4 != zero_zero_real )
% 5.64/5.89 => ( ( Z != zero_zero_real )
% 5.64/5.89 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y4 ) @ ( divide_divide_real @ W @ Z ) )
% 5.64/5.89 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y4 ) ) @ ( times_times_real @ Y4 @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_less_eq
% 5.64/5.89 thf(fact_3339_frac__less__eq,axiom,
% 5.64/5.89 ! [Y4: rat,Z: rat,X2: rat,W: rat] :
% 5.64/5.89 ( ( Y4 != zero_zero_rat )
% 5.64/5.89 => ( ( Z != zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y4 ) @ ( divide_divide_rat @ W @ Z ) )
% 5.64/5.89 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y4 ) ) @ ( times_times_rat @ Y4 @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % frac_less_eq
% 5.64/5.89 thf(fact_3340_power__Suc__less,axiom,
% 5.64/5.89 ! [A: real,N: nat] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_real @ A @ one_one_real )
% 5.64/5.89 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less
% 5.64/5.89 thf(fact_3341_power__Suc__less,axiom,
% 5.64/5.89 ! [A: rat,N: nat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less
% 5.64/5.89 thf(fact_3342_power__Suc__less,axiom,
% 5.64/5.89 ! [A: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less
% 5.64/5.89 thf(fact_3343_power__Suc__less,axiom,
% 5.64/5.89 ! [A: int,N: nat] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ A @ one_one_int )
% 5.64/5.89 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less
% 5.64/5.89 thf(fact_3344_vebt__mint_Oelims,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Y4: option_nat] :
% 5.64/5.89 ( ( ( vEBT_vebt_mint @ X2 )
% 5.64/5.89 = Y4 )
% 5.64/5.89 => ( ! [A5: $o,B5: $o] :
% 5.64/5.89 ( ( X2
% 5.64/5.89 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.89 => ~ ( ( A5
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.89 & ( ~ A5
% 5.64/5.89 => ( ( B5
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.89 & ( ~ B5
% 5.64/5.89 => ( Y4 = none_nat ) ) ) ) ) )
% 5.64/5.89 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.89 => ( Y4 != none_nat ) )
% 5.64/5.89 => ~ ! [Mi2: nat] :
% 5.64/5.89 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_mint.elims
% 5.64/5.89 thf(fact_3345_power__Suc__le__self,axiom,
% 5.64/5.89 ! [A: rat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_le_self
% 5.64/5.89 thf(fact_3346_power__Suc__le__self,axiom,
% 5.64/5.89 ! [A: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_le_self
% 5.64/5.89 thf(fact_3347_power__Suc__le__self,axiom,
% 5.64/5.89 ! [A: int,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_le_self
% 5.64/5.89 thf(fact_3348_power__Suc__le__self,axiom,
% 5.64/5.89 ! [A: real,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_le_self
% 5.64/5.89 thf(fact_3349_power__Suc__less__one,axiom,
% 5.64/5.89 ! [A: real,N: nat] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_real @ A @ one_one_real )
% 5.64/5.89 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less_one
% 5.64/5.89 thf(fact_3350_power__Suc__less__one,axiom,
% 5.64/5.89 ! [A: rat,N: nat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less_one
% 5.64/5.89 thf(fact_3351_power__Suc__less__one,axiom,
% 5.64/5.89 ! [A: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less_one
% 5.64/5.89 thf(fact_3352_power__Suc__less__one,axiom,
% 5.64/5.89 ! [A: int,N: nat] :
% 5.64/5.89 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ A @ one_one_int )
% 5.64/5.89 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_Suc_less_one
% 5.64/5.89 thf(fact_3353_vebt__maxt_Oelims,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Y4: option_nat] :
% 5.64/5.89 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.64/5.89 = Y4 )
% 5.64/5.89 => ( ! [A5: $o,B5: $o] :
% 5.64/5.89 ( ( X2
% 5.64/5.89 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.89 => ~ ( ( B5
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.89 & ( ~ B5
% 5.64/5.89 => ( ( A5
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.89 & ( ~ A5
% 5.64/5.89 => ( Y4 = none_nat ) ) ) ) ) )
% 5.64/5.89 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.89 => ( Y4 != none_nat ) )
% 5.64/5.89 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.64/5.89 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_maxt.elims
% 5.64/5.89 thf(fact_3354_power__strict__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: real] :
% 5.64/5.89 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_real @ A @ one_one_real )
% 5.64/5.89 => ( ord_less_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_strict_decreasing
% 5.64/5.89 thf(fact_3355_power__strict__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: rat] :
% 5.64/5.89 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ord_less_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_strict_decreasing
% 5.64/5.89 thf(fact_3356_power__strict__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: nat] :
% 5.64/5.89 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ord_less_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_strict_decreasing
% 5.64/5.89 thf(fact_3357_power__strict__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: int] :
% 5.64/5.89 ( ( ord_less_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_int @ A @ one_one_int )
% 5.64/5.89 => ( ord_less_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_strict_decreasing
% 5.64/5.89 thf(fact_3358_power__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: rat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N5 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_decreasing
% 5.64/5.89 thf(fact_3359_power__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.64/5.89 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.64/5.89 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N5 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_decreasing
% 5.64/5.89 thf(fact_3360_power__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: int] :
% 5.64/5.89 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.64/5.89 => ( ord_less_eq_int @ ( power_power_int @ A @ N5 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_decreasing
% 5.64/5.89 thf(fact_3361_power__decreasing,axiom,
% 5.64/5.89 ! [N: nat,N5: nat,A: real] :
% 5.64/5.89 ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( power_power_real @ A @ N5 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_decreasing
% 5.64/5.89 thf(fact_3362_zero__power2,axiom,
% 5.64/5.89 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = zero_zero_rat ) ).
% 5.64/5.89
% 5.64/5.89 % zero_power2
% 5.64/5.89 thf(fact_3363_zero__power2,axiom,
% 5.64/5.89 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = zero_zero_nat ) ).
% 5.64/5.89
% 5.64/5.89 % zero_power2
% 5.64/5.89 thf(fact_3364_zero__power2,axiom,
% 5.64/5.89 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = zero_zero_real ) ).
% 5.64/5.89
% 5.64/5.89 % zero_power2
% 5.64/5.89 thf(fact_3365_zero__power2,axiom,
% 5.64/5.89 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = zero_zero_int ) ).
% 5.64/5.89
% 5.64/5.89 % zero_power2
% 5.64/5.89 thf(fact_3366_zero__power2,axiom,
% 5.64/5.89 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = zero_zero_complex ) ).
% 5.64/5.89
% 5.64/5.89 % zero_power2
% 5.64/5.89 thf(fact_3367_self__le__power,axiom,
% 5.64/5.89 ! [A: rat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % self_le_power
% 5.64/5.89 thf(fact_3368_self__le__power,axiom,
% 5.64/5.89 ! [A: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % self_le_power
% 5.64/5.89 thf(fact_3369_self__le__power,axiom,
% 5.64/5.89 ! [A: int,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % self_le_power
% 5.64/5.89 thf(fact_3370_self__le__power,axiom,
% 5.64/5.89 ! [A: real,N: nat] :
% 5.64/5.89 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % self_le_power
% 5.64/5.89 thf(fact_3371_one__less__power,axiom,
% 5.64/5.89 ! [A: real,N: nat] :
% 5.64/5.89 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % one_less_power
% 5.64/5.89 thf(fact_3372_one__less__power,axiom,
% 5.64/5.89 ! [A: rat,N: nat] :
% 5.64/5.89 ( ( ord_less_rat @ one_one_rat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % one_less_power
% 5.64/5.89 thf(fact_3373_one__less__power,axiom,
% 5.64/5.89 ! [A: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ one_one_nat @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % one_less_power
% 5.64/5.89 thf(fact_3374_one__less__power,axiom,
% 5.64/5.89 ! [A: int,N: nat] :
% 5.64/5.89 ( ( ord_less_int @ one_one_int @ A )
% 5.64/5.89 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % one_less_power
% 5.64/5.89 thf(fact_3375_numeral__2__eq__2,axiom,
% 5.64/5.89 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.64/5.89 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % numeral_2_eq_2
% 5.64/5.89 thf(fact_3376_pos2,axiom,
% 5.64/5.89 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.64/5.89
% 5.64/5.89 % pos2
% 5.64/5.89 thf(fact_3377_power__diff,axiom,
% 5.64/5.89 ! [A: complex,N: nat,M: nat] :
% 5.64/5.89 ( ( A != zero_zero_complex )
% 5.64/5.89 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.89 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.89 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_diff
% 5.64/5.89 thf(fact_3378_power__diff,axiom,
% 5.64/5.89 ! [A: real,N: nat,M: nat] :
% 5.64/5.89 ( ( A != zero_zero_real )
% 5.64/5.89 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.89 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.89 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_diff
% 5.64/5.89 thf(fact_3379_power__diff,axiom,
% 5.64/5.89 ! [A: rat,N: nat,M: nat] :
% 5.64/5.89 ( ( A != zero_zero_rat )
% 5.64/5.89 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.89 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.89 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_diff
% 5.64/5.89 thf(fact_3380_power__diff,axiom,
% 5.64/5.89 ! [A: nat,N: nat,M: nat] :
% 5.64/5.89 ( ( A != zero_zero_nat )
% 5.64/5.89 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.89 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.89 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_diff
% 5.64/5.89 thf(fact_3381_power__diff,axiom,
% 5.64/5.89 ! [A: int,N: nat,M: nat] :
% 5.64/5.89 ( ( A != zero_zero_int )
% 5.64/5.89 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.89 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.89 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power_diff
% 5.64/5.89 thf(fact_3382_Suc__diff__eq__diff__pred,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.64/5.89 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % Suc_diff_eq_diff_pred
% 5.64/5.89 thf(fact_3383_Suc__pred_H,axiom,
% 5.64/5.89 ! [N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( N
% 5.64/5.89 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % Suc_pred'
% 5.64/5.89 thf(fact_3384_div__if,axiom,
% 5.64/5.89 ( divide_divide_nat
% 5.64/5.89 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.89 ( if_nat
% 5.64/5.89 @ ( ( ord_less_nat @ M2 @ N2 )
% 5.64/5.89 | ( N2 = zero_zero_nat ) )
% 5.64/5.89 @ zero_zero_nat
% 5.64/5.89 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_if
% 5.64/5.89 thf(fact_3385_div__geq,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ~ ( ord_less_nat @ M @ N )
% 5.64/5.89 => ( ( divide_divide_nat @ M @ N )
% 5.64/5.89 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % div_geq
% 5.64/5.89 thf(fact_3386_add__eq__if,axiom,
% 5.64/5.89 ( plus_plus_nat
% 5.64/5.89 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % add_eq_if
% 5.64/5.89 thf(fact_3387_less__eq__div__iff__mult__less__eq,axiom,
% 5.64/5.89 ! [Q3: nat,M: nat,N: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.64/5.89 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q3 ) )
% 5.64/5.89 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % less_eq_div_iff_mult_less_eq
% 5.64/5.89 thf(fact_3388_dividend__less__times__div,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % dividend_less_times_div
% 5.64/5.89 thf(fact_3389_dividend__less__div__times,axiom,
% 5.64/5.89 ! [N: nat,M: nat] :
% 5.64/5.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.89 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % dividend_less_div_times
% 5.64/5.89 thf(fact_3390_split__div,axiom,
% 5.64/5.89 ! [P: nat > $o,M: nat,N: nat] :
% 5.64/5.89 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.89 = ( ( ( N = zero_zero_nat )
% 5.64/5.89 => ( P @ zero_zero_nat ) )
% 5.64/5.89 & ( ( N != zero_zero_nat )
% 5.64/5.89 => ! [I4: nat,J3: nat] :
% 5.64/5.89 ( ( ord_less_nat @ J3 @ N )
% 5.64/5.89 => ( ( M
% 5.64/5.89 = ( plus_plus_nat @ ( times_times_nat @ N @ I4 ) @ J3 ) )
% 5.64/5.89 => ( P @ I4 ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % split_div
% 5.64/5.89 thf(fact_3391_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.89 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.64/5.89 => ( ! [A5: $o,B5: $o] :
% 5.64/5.89 ( ( X2
% 5.64/5.89 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.89 => ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.89 => A5 )
% 5.64/5.89 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.89 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.89 => B5 )
% 5.64/5.89 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.64/5.89 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 != ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.64/5.89 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [S: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.64/5.89 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % VEBT_internal.naive_member.elims(3)
% 5.64/5.89 thf(fact_3392_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.89 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.64/5.89 => ( ! [A5: $o,B5: $o] :
% 5.64/5.89 ( ( X2
% 5.64/5.89 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.89 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.89 => A5 )
% 5.64/5.89 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.89 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.89 => B5 )
% 5.64/5.89 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.64/5.89 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [S: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.64/5.89 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % VEBT_internal.naive_member.elims(2)
% 5.64/5.89 thf(fact_3393_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/5.89 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.64/5.89 = Y4 )
% 5.64/5.89 => ( ! [A5: $o,B5: $o] :
% 5.64/5.89 ( ( X2
% 5.64/5.89 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.89 => A5 )
% 5.64/5.89 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.89 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.89 => B5 )
% 5.64/5.89 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.64/5.89 => ( ( ? [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.64/5.89 => Y4 )
% 5.64/5.89 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [S: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % VEBT_internal.naive_member.elims(1)
% 5.64/5.89 thf(fact_3394_mult__eq__if,axiom,
% 5.64/5.89 ( times_times_nat
% 5.64/5.89 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % mult_eq_if
% 5.64/5.89 thf(fact_3395_vebt__succ_Osimps_I4_J,axiom,
% 5.64/5.89 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve2: nat] :
% 5.64/5.89 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve2 )
% 5.64/5.89 = none_nat ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_succ.simps(4)
% 5.64/5.89 thf(fact_3396_vebt__pred_Osimps_I5_J,axiom,
% 5.64/5.89 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.64/5.89 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve2 ) @ Vf2 )
% 5.64/5.89 = none_nat ) ).
% 5.64/5.89
% 5.64/5.89 % vebt_pred.simps(5)
% 5.64/5.89 thf(fact_3397_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I3_J,axiom,
% 5.64/5.89 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.64/5.89 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.64/5.89 = one_one_nat ) ).
% 5.64/5.89
% 5.64/5.89 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(3)
% 5.64/5.89 thf(fact_3398_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/5.89 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.64/5.89 = Y4 )
% 5.64/5.89 => ( ( ? [Uu: $o,Uv: $o] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/5.89 => Y4 )
% 5.64/5.89 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.64/5.89 => Y4 )
% 5.64/5.89 => ( ! [Mi2: nat,Ma2: nat] :
% 5.64/5.89 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( ~ ( ( Xa2 = Mi2 )
% 5.64/5.89 | ( Xa2 = Ma2 ) ) ) ) )
% 5.64/5.89 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [Vc2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( ~ ( ( Xa2 = Mi2 )
% 5.64/5.89 | ( Xa2 = Ma2 )
% 5.64/5.89 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.64/5.89 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [Vd2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.64/5.89 => ( Y4
% 5.64/5.89 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % VEBT_internal.membermima.elims(1)
% 5.64/5.89 thf(fact_3399_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.64/5.89 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.89 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.64/5.89 => ( ! [Uu: $o,Uv: $o] :
% 5.64/5.89 ( X2
% 5.64/5.89 != ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/5.89 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.64/5.89 => ( ! [Mi2: nat,Ma2: nat] :
% 5.64/5.89 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.64/5.89 => ( ( Xa2 = Mi2 )
% 5.64/5.89 | ( Xa2 = Ma2 ) ) )
% 5.64/5.89 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [Vc2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.64/5.89 => ( ( Xa2 = Mi2 )
% 5.64/5.89 | ( Xa2 = Ma2 )
% 5.64/5.89 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.64/5.89 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.89 ( ? [Vd2: vEBT_VEBT] :
% 5.64/5.89 ( X2
% 5.64/5.89 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.64/5.89 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.89 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.89 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % VEBT_internal.membermima.elims(3)
% 5.64/5.89 thf(fact_3400_convex__bound__lt,axiom,
% 5.64/5.89 ! [X2: rat,A: rat,Y4: rat,U: rat,V: rat] :
% 5.64/5.89 ( ( ord_less_rat @ X2 @ A )
% 5.64/5.89 => ( ( ord_less_rat @ Y4 @ A )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.64/5.89 => ( ( ( plus_plus_rat @ U @ V )
% 5.64/5.89 = one_one_rat )
% 5.64/5.89 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % convex_bound_lt
% 5.64/5.89 thf(fact_3401_convex__bound__lt,axiom,
% 5.64/5.89 ! [X2: int,A: int,Y4: int,U: int,V: int] :
% 5.64/5.89 ( ( ord_less_int @ X2 @ A )
% 5.64/5.89 => ( ( ord_less_int @ Y4 @ A )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.64/5.89 => ( ( ( plus_plus_int @ U @ V )
% 5.64/5.89 = one_one_int )
% 5.64/5.89 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % convex_bound_lt
% 5.64/5.89 thf(fact_3402_convex__bound__lt,axiom,
% 5.64/5.89 ! [X2: real,A: real,Y4: real,U: real,V: real] :
% 5.64/5.89 ( ( ord_less_real @ X2 @ A )
% 5.64/5.89 => ( ( ord_less_real @ Y4 @ A )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.64/5.89 => ( ( ( plus_plus_real @ U @ V )
% 5.64/5.89 = one_one_real )
% 5.64/5.89 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y4 ) ) @ A ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % convex_bound_lt
% 5.64/5.89 thf(fact_3403_le__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: rat,C: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % le_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3404_le__divide__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [W: num,B: real,C: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % le_divide_eq_numeral(1)
% 5.64/5.89 thf(fact_3405_divide__le__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: rat,C: rat,W: num] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.64/5.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.89 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.89 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_eq_numeral(1)
% 5.64/5.89 thf(fact_3406_divide__le__eq__numeral_I1_J,axiom,
% 5.64/5.89 ! [B: real,C: real,W: num] :
% 5.64/5.89 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.64/5.89 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.89 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.64/5.89 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.89 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % divide_le_eq_numeral(1)
% 5.64/5.89 thf(fact_3407_half__gt__zero,axiom,
% 5.64/5.89 ! [A: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.89 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % half_gt_zero
% 5.64/5.89 thf(fact_3408_half__gt__zero,axiom,
% 5.64/5.89 ! [A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.89 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % half_gt_zero
% 5.64/5.89 thf(fact_3409_half__gt__zero__iff,axiom,
% 5.64/5.89 ! [A: real] :
% 5.64/5.89 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.89 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.64/5.89
% 5.64/5.89 % half_gt_zero_iff
% 5.64/5.89 thf(fact_3410_half__gt__zero__iff,axiom,
% 5.64/5.89 ! [A: rat] :
% 5.64/5.89 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.64/5.89 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.89
% 5.64/5.89 % half_gt_zero_iff
% 5.64/5.89 thf(fact_3411_scaling__mono,axiom,
% 5.64/5.89 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ U @ V )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.64/5.89 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % scaling_mono
% 5.64/5.89 thf(fact_3412_scaling__mono,axiom,
% 5.64/5.89 ! [U: real,V: real,R2: real,S2: real] :
% 5.64/5.89 ( ( ord_less_eq_real @ U @ V )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.64/5.89 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.64/5.89 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % scaling_mono
% 5.64/5.89 thf(fact_3413_zero__le__power2,axiom,
% 5.64/5.89 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % zero_le_power2
% 5.64/5.89 thf(fact_3414_zero__le__power2,axiom,
% 5.64/5.89 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % zero_le_power2
% 5.64/5.89 thf(fact_3415_zero__le__power2,axiom,
% 5.64/5.89 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % zero_le_power2
% 5.64/5.89 thf(fact_3416_power2__eq__imp__eq,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( X2 = Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power2_eq_imp_eq
% 5.64/5.89 thf(fact_3417_power2__eq__imp__eq,axiom,
% 5.64/5.89 ! [X2: nat,Y4: nat] :
% 5.64/5.89 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.64/5.89 => ( X2 = Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power2_eq_imp_eq
% 5.64/5.89 thf(fact_3418_power2__eq__imp__eq,axiom,
% 5.64/5.89 ! [X2: int,Y4: int] :
% 5.64/5.89 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.89 => ( X2 = Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power2_eq_imp_eq
% 5.64/5.89 thf(fact_3419_power2__eq__imp__eq,axiom,
% 5.64/5.89 ! [X2: real,Y4: real] :
% 5.64/5.89 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.89 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.89 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.89 => ( X2 = Y4 ) ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power2_eq_imp_eq
% 5.64/5.89 thf(fact_3420_power2__le__imp__le,axiom,
% 5.64/5.89 ! [X2: rat,Y4: rat] :
% 5.64/5.89 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.89 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.89 => ( ord_less_eq_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.89
% 5.64/5.89 % power2_le_imp_le
% 5.64/5.89 thf(fact_3421_power2__le__imp__le,axiom,
% 5.64/5.89 ! [X2: nat,Y4: nat] :
% 5.64/5.89 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.64/5.90 => ( ord_less_eq_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_le_imp_le
% 5.64/5.90 thf(fact_3422_power2__le__imp__le,axiom,
% 5.64/5.90 ! [X2: int,Y4: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.90 => ( ord_less_eq_int @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_le_imp_le
% 5.64/5.90 thf(fact_3423_power2__le__imp__le,axiom,
% 5.64/5.90 ! [X2: real,Y4: real] :
% 5.64/5.90 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.90 => ( ord_less_eq_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_le_imp_le
% 5.64/5.90 thf(fact_3424_power2__less__0,axiom,
% 5.64/5.90 ! [A: real] :
% 5.64/5.90 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_0
% 5.64/5.90 thf(fact_3425_power2__less__0,axiom,
% 5.64/5.90 ! [A: rat] :
% 5.64/5.90 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_0
% 5.64/5.90 thf(fact_3426_power2__less__0,axiom,
% 5.64/5.90 ! [A: int] :
% 5.64/5.90 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_0
% 5.64/5.90 thf(fact_3427_exp__add__not__zero__imp__left,axiom,
% 5.64/5.90 ! [M: nat,N: nat] :
% 5.64/5.90 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.90 != zero_zero_nat )
% 5.64/5.90 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.64/5.90 != zero_zero_nat ) ) ).
% 5.64/5.90
% 5.64/5.90 % exp_add_not_zero_imp_left
% 5.64/5.90 thf(fact_3428_exp__add__not__zero__imp__left,axiom,
% 5.64/5.90 ! [M: nat,N: nat] :
% 5.64/5.90 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.90 != zero_zero_int )
% 5.64/5.90 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.64/5.90 != zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % exp_add_not_zero_imp_left
% 5.64/5.90 thf(fact_3429_exp__add__not__zero__imp__right,axiom,
% 5.64/5.90 ! [M: nat,N: nat] :
% 5.64/5.90 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.90 != zero_zero_nat )
% 5.64/5.90 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.90 != zero_zero_nat ) ) ).
% 5.64/5.90
% 5.64/5.90 % exp_add_not_zero_imp_right
% 5.64/5.90 thf(fact_3430_exp__add__not__zero__imp__right,axiom,
% 5.64/5.90 ! [M: nat,N: nat] :
% 5.64/5.90 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.90 != zero_zero_int )
% 5.64/5.90 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.64/5.90 != zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % exp_add_not_zero_imp_right
% 5.64/5.90 thf(fact_3431_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.64/5.90 ! [N: nat,M: nat] :
% 5.64/5.90 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.90 != zero_zero_nat )
% 5.64/5.90 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.64/5.90 != zero_zero_nat ) ) ).
% 5.64/5.90
% 5.64/5.90 % exp_not_zero_imp_exp_diff_not_zero
% 5.64/5.90 thf(fact_3432_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.64/5.90 ! [N: nat,M: nat] :
% 5.64/5.90 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.64/5.90 != zero_zero_int )
% 5.64/5.90 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.64/5.90 != zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % exp_not_zero_imp_exp_diff_not_zero
% 5.64/5.90 thf(fact_3433_power__diff__power__eq,axiom,
% 5.64/5.90 ! [A: nat,N: nat,M: nat] :
% 5.64/5.90 ( ( A != zero_zero_nat )
% 5.64/5.90 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.90 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.64/5.90 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.64/5.90 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.90 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.64/5.90 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_diff_power_eq
% 5.64/5.90 thf(fact_3434_power__diff__power__eq,axiom,
% 5.64/5.90 ! [A: int,N: nat,M: nat] :
% 5.64/5.90 ( ( A != zero_zero_int )
% 5.64/5.90 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.90 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.64/5.90 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.64/5.90 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.90 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.64/5.90 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_diff_power_eq
% 5.64/5.90 thf(fact_3435_less__2__cases,axiom,
% 5.64/5.90 ! [N: nat] :
% 5.64/5.90 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.90 => ( ( N = zero_zero_nat )
% 5.64/5.90 | ( N
% 5.64/5.90 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % less_2_cases
% 5.64/5.90 thf(fact_3436_less__2__cases__iff,axiom,
% 5.64/5.90 ! [N: nat] :
% 5.64/5.90 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.90 = ( ( N = zero_zero_nat )
% 5.64/5.90 | ( N
% 5.64/5.90 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % less_2_cases_iff
% 5.64/5.90 thf(fact_3437_nat__induct2,axiom,
% 5.64/5.90 ! [P: nat > $o,N: nat] :
% 5.64/5.90 ( ( P @ zero_zero_nat )
% 5.64/5.90 => ( ( P @ one_one_nat )
% 5.64/5.90 => ( ! [N3: nat] :
% 5.64/5.90 ( ( P @ N3 )
% 5.64/5.90 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.90 => ( P @ N ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % nat_induct2
% 5.64/5.90 thf(fact_3438_power__eq__if,axiom,
% 5.64/5.90 ( power_power_complex
% 5.64/5.90 = ( ^ [P5: complex,M2: nat] : ( if_complex @ ( M2 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_eq_if
% 5.64/5.90 thf(fact_3439_power__eq__if,axiom,
% 5.64/5.90 ( power_power_real
% 5.64/5.90 = ( ^ [P5: real,M2: nat] : ( if_real @ ( M2 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_eq_if
% 5.64/5.90 thf(fact_3440_power__eq__if,axiom,
% 5.64/5.90 ( power_power_rat
% 5.64/5.90 = ( ^ [P5: rat,M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_eq_if
% 5.64/5.90 thf(fact_3441_power__eq__if,axiom,
% 5.64/5.90 ( power_power_nat
% 5.64/5.90 = ( ^ [P5: nat,M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_eq_if
% 5.64/5.90 thf(fact_3442_power__eq__if,axiom,
% 5.64/5.90 ( power_power_int
% 5.64/5.90 = ( ^ [P5: int,M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_eq_if
% 5.64/5.90 thf(fact_3443_power__minus__mult,axiom,
% 5.64/5.90 ! [N: nat,A: complex] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.64/5.90 = ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_minus_mult
% 5.64/5.90 thf(fact_3444_power__minus__mult,axiom,
% 5.64/5.90 ! [N: nat,A: real] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.64/5.90 = ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_minus_mult
% 5.64/5.90 thf(fact_3445_power__minus__mult,axiom,
% 5.64/5.90 ! [N: nat,A: rat] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.64/5.90 = ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_minus_mult
% 5.64/5.90 thf(fact_3446_power__minus__mult,axiom,
% 5.64/5.90 ! [N: nat,A: nat] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.64/5.90 = ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_minus_mult
% 5.64/5.90 thf(fact_3447_power__minus__mult,axiom,
% 5.64/5.90 ! [N: nat,A: int] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.64/5.90 = ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power_minus_mult
% 5.64/5.90 thf(fact_3448_le__div__geq,axiom,
% 5.64/5.90 ! [N: nat,M: nat] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.90 => ( ( divide_divide_nat @ M @ N )
% 5.64/5.90 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % le_div_geq
% 5.64/5.90 thf(fact_3449_split__div_H,axiom,
% 5.64/5.90 ! [P: nat > $o,M: nat,N: nat] :
% 5.64/5.90 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.90 = ( ( ( N = zero_zero_nat )
% 5.64/5.90 & ( P @ zero_zero_nat ) )
% 5.64/5.90 | ? [Q4: nat] :
% 5.64/5.90 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q4 ) @ M )
% 5.64/5.90 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q4 ) ) )
% 5.64/5.90 & ( P @ Q4 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % split_div'
% 5.64/5.90 thf(fact_3450_div__exp__mod__exp__eq,axiom,
% 5.64/5.90 ! [A: nat,N: nat,M: nat] :
% 5.64/5.90 ( ( 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 ) )
% 5.64/5.90 = ( 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 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_exp_mod_exp_eq
% 5.64/5.90 thf(fact_3451_div__exp__mod__exp__eq,axiom,
% 5.64/5.90 ! [A: int,N: nat,M: nat] :
% 5.64/5.90 ( ( 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 ) )
% 5.64/5.90 = ( 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 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_exp_mod_exp_eq
% 5.64/5.90 thf(fact_3452_div__exp__mod__exp__eq,axiom,
% 5.64/5.90 ! [A: code_integer,N: nat,M: nat] :
% 5.64/5.90 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.64/5.90 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_exp_mod_exp_eq
% 5.64/5.90 thf(fact_3453_vebt__succ_Osimps_I5_J,axiom,
% 5.64/5.90 ! [V: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.64/5.90 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 5.64/5.90 = none_nat ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_succ.simps(5)
% 5.64/5.90 thf(fact_3454_vebt__pred_Osimps_I6_J,axiom,
% 5.64/5.90 ! [V: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.64/5.90 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 5.64/5.90 = none_nat ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_pred.simps(6)
% 5.64/5.90 thf(fact_3455_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Osimps_I4_J,axiom,
% 5.64/5.90 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.64/5.90 ( ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.64/5.90 = one_one_nat ) ).
% 5.64/5.90
% 5.64/5.90 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.simps(4)
% 5.64/5.90 thf(fact_3456_power2__less__imp__less,axiom,
% 5.64/5.90 ! [X2: rat,Y4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.90 => ( ord_less_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_imp_less
% 5.64/5.90 thf(fact_3457_power2__less__imp__less,axiom,
% 5.64/5.90 ! [X2: nat,Y4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y4 )
% 5.64/5.90 => ( ord_less_nat @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_imp_less
% 5.64/5.90 thf(fact_3458_power2__less__imp__less,axiom,
% 5.64/5.90 ! [X2: int,Y4: int] :
% 5.64/5.90 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.90 => ( ord_less_int @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_imp_less
% 5.64/5.90 thf(fact_3459_power2__less__imp__less,axiom,
% 5.64/5.90 ! [X2: real,Y4: real] :
% 5.64/5.90 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.90 => ( ord_less_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % power2_less_imp_less
% 5.64/5.90 thf(fact_3460_sum__power2__le__zero__iff,axiom,
% 5.64/5.90 ! [X2: rat,Y4: rat] :
% 5.64/5.90 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.64/5.90 = ( ( X2 = zero_zero_rat )
% 5.64/5.90 & ( Y4 = zero_zero_rat ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_le_zero_iff
% 5.64/5.90 thf(fact_3461_sum__power2__le__zero__iff,axiom,
% 5.64/5.90 ! [X2: int,Y4: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.64/5.90 = ( ( X2 = zero_zero_int )
% 5.64/5.90 & ( Y4 = zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_le_zero_iff
% 5.64/5.90 thf(fact_3462_sum__power2__le__zero__iff,axiom,
% 5.64/5.90 ! [X2: real,Y4: real] :
% 5.64/5.90 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.64/5.90 = ( ( X2 = zero_zero_real )
% 5.64/5.90 & ( Y4 = zero_zero_real ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_le_zero_iff
% 5.64/5.90 thf(fact_3463_sum__power2__ge__zero,axiom,
% 5.64/5.90 ! [X2: rat,Y4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_ge_zero
% 5.64/5.90 thf(fact_3464_sum__power2__ge__zero,axiom,
% 5.64/5.90 ! [X2: int,Y4: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_ge_zero
% 5.64/5.90 thf(fact_3465_sum__power2__ge__zero,axiom,
% 5.64/5.90 ! [X2: real,Y4: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_ge_zero
% 5.64/5.90 thf(fact_3466_not__sum__power2__lt__zero,axiom,
% 5.64/5.90 ! [X2: real,Y4: real] :
% 5.64/5.90 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.64/5.90
% 5.64/5.90 % not_sum_power2_lt_zero
% 5.64/5.90 thf(fact_3467_not__sum__power2__lt__zero,axiom,
% 5.64/5.90 ! [X2: rat,Y4: rat] :
% 5.64/5.90 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.64/5.90
% 5.64/5.90 % not_sum_power2_lt_zero
% 5.64/5.90 thf(fact_3468_not__sum__power2__lt__zero,axiom,
% 5.64/5.90 ! [X2: int,Y4: int] :
% 5.64/5.90 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.64/5.90
% 5.64/5.90 % not_sum_power2_lt_zero
% 5.64/5.90 thf(fact_3469_sum__power2__gt__zero__iff,axiom,
% 5.64/5.90 ! [X2: real,Y4: real] :
% 5.64/5.90 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.90 = ( ( X2 != zero_zero_real )
% 5.64/5.90 | ( Y4 != zero_zero_real ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_gt_zero_iff
% 5.64/5.90 thf(fact_3470_sum__power2__gt__zero__iff,axiom,
% 5.64/5.90 ! [X2: rat,Y4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.90 = ( ( X2 != zero_zero_rat )
% 5.64/5.90 | ( Y4 != zero_zero_rat ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_gt_zero_iff
% 5.64/5.90 thf(fact_3471_sum__power2__gt__zero__iff,axiom,
% 5.64/5.90 ! [X2: int,Y4: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.90 = ( ( X2 != zero_zero_int )
% 5.64/5.90 | ( Y4 != zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % sum_power2_gt_zero_iff
% 5.64/5.90 thf(fact_3472_zero__le__even__power_H,axiom,
% 5.64/5.90 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zero_le_even_power'
% 5.64/5.90 thf(fact_3473_zero__le__even__power_H,axiom,
% 5.64/5.90 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zero_le_even_power'
% 5.64/5.90 thf(fact_3474_zero__le__even__power_H,axiom,
% 5.64/5.90 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zero_le_even_power'
% 5.64/5.90 thf(fact_3475_nat__bit__induct,axiom,
% 5.64/5.90 ! [P: nat > $o,N: nat] :
% 5.64/5.90 ( ( P @ zero_zero_nat )
% 5.64/5.90 => ( ! [N3: nat] :
% 5.64/5.90 ( ( P @ N3 )
% 5.64/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.90 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.64/5.90 => ( ! [N3: nat] :
% 5.64/5.90 ( ( P @ N3 )
% 5.64/5.90 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.64/5.90 => ( P @ N ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % nat_bit_induct
% 5.64/5.90 thf(fact_3476_div__2__gt__zero,axiom,
% 5.64/5.90 ! [N: nat] :
% 5.64/5.90 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.90 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_2_gt_zero
% 5.64/5.90 thf(fact_3477_Suc__n__div__2__gt__zero,axiom,
% 5.64/5.90 ! [N: nat] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Suc_n_div_2_gt_zero
% 5.64/5.90 thf(fact_3478_mult__exp__mod__exp__eq,axiom,
% 5.64/5.90 ! [M: nat,N: nat,A: nat] :
% 5.64/5.90 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.90 => ( ( 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 ) )
% 5.64/5.90 = ( 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 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mult_exp_mod_exp_eq
% 5.64/5.90 thf(fact_3479_mult__exp__mod__exp__eq,axiom,
% 5.64/5.90 ! [M: nat,N: nat,A: int] :
% 5.64/5.90 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.90 => ( ( 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 ) )
% 5.64/5.90 = ( 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 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mult_exp_mod_exp_eq
% 5.64/5.90 thf(fact_3480_mult__exp__mod__exp__eq,axiom,
% 5.64/5.90 ! [M: nat,N: nat,A: code_integer] :
% 5.64/5.90 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.90 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.90 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mult_exp_mod_exp_eq
% 5.64/5.90 thf(fact_3481_vebt__member_Oelims_I2_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.90 ( ? [Summary2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ~ ( ( Xa2 != Mi2 )
% 5.64/5.90 => ( ( Xa2 != Ma2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.elims(2)
% 5.64/5.90 thf(fact_3482_vebt__member_Oelims_I1_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/5.90 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.64/5.90 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.90 => Y4 )
% 5.64/5.90 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.90 => Y4 )
% 5.64/5.90 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.90 => Y4 )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.90 ( ? [Summary2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( ~ ( ( Xa2 != Mi2 )
% 5.64/5.90 => ( ( Xa2 != Ma2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.elims(1)
% 5.64/5.90 thf(fact_3483_vebt__member_Oelims_I3_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.64/5.90 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.90 ( ? [Summary2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( Xa2 != Mi2 )
% 5.64/5.90 => ( ( Xa2 != Ma2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.elims(3)
% 5.64/5.90 thf(fact_3484_odd__0__le__power__imp__0__le,axiom,
% 5.64/5.90 ! [A: rat,N: nat] :
% 5.64/5.90 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.90 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_0_le_power_imp_0_le
% 5.64/5.90 thf(fact_3485_odd__0__le__power__imp__0__le,axiom,
% 5.64/5.90 ! [A: int,N: nat] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.90 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_0_le_power_imp_0_le
% 5.64/5.90 thf(fact_3486_odd__0__le__power__imp__0__le,axiom,
% 5.64/5.90 ! [A: real,N: nat] :
% 5.64/5.90 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.90 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_0_le_power_imp_0_le
% 5.64/5.90 thf(fact_3487_odd__power__less__zero,axiom,
% 5.64/5.90 ! [A: real,N: nat] :
% 5.64/5.90 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.90 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_power_less_zero
% 5.64/5.90 thf(fact_3488_odd__power__less__zero,axiom,
% 5.64/5.90 ! [A: rat,N: nat] :
% 5.64/5.90 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.90 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_power_less_zero
% 5.64/5.90 thf(fact_3489_odd__power__less__zero,axiom,
% 5.64/5.90 ! [A: int,N: nat] :
% 5.64/5.90 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.90 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_power_less_zero
% 5.64/5.90 thf(fact_3490_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.64/5.90 ! [X2: nat,N: nat,M: nat] :
% 5.64/5.90 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.64/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.90 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.exp_split_high_low(1)
% 5.64/5.90 thf(fact_3491_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.64/5.90 ! [X2: nat,N: nat,M: nat] :
% 5.64/5.90 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.64/5.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.90 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.exp_split_high_low(2)
% 5.64/5.90 thf(fact_3492_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat] :
% 5.64/5.90 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.64/5.90 => ~ ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 ) ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.90 ( ? [Vc2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.64/5.90 => ~ ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 )
% 5.64/5.90 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.64/5.90 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.90 ( ? [Vd2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.64/5.90 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.membermima.elims(2)
% 5.64/5.90 thf(fact_3493_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Oelims,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: nat] :
% 5.64/5.90 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( ? [A5: $o,B5: $o] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( Y4 != one_one_nat ) )
% 5.64/5.90 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.90 => ( Y4 != one_one_nat ) )
% 5.64/5.90 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.90 => ( Y4 != one_one_nat ) )
% 5.64/5.90 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.90 => ( Y4 != one_one_nat ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.90 ( ? [Summary2: vEBT_VEBT] :
% 5.64/5.90 ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( Y4
% 5.64/5.90 != ( plus_plus_nat @ one_one_nat
% 5.64/5.90 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat
% 5.64/5.90 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.64/5.90 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.64/5.90 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.64/5.90 @ zero_zero_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.elims
% 5.64/5.90 thf(fact_3494_arith__geo__mean,axiom,
% 5.64/5.90 ! [U: rat,X2: rat,Y4: rat] :
% 5.64/5.90 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.90 = ( times_times_rat @ X2 @ Y4 ) )
% 5.64/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.90 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.90 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % arith_geo_mean
% 5.64/5.90 thf(fact_3495_arith__geo__mean,axiom,
% 5.64/5.90 ! [U: real,X2: real,Y4: real] :
% 5.64/5.90 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.90 = ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.90 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.90 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % arith_geo_mean
% 5.64/5.90 thf(fact_3496_invar__vebt_Ocases,axiom,
% 5.64/5.90 ! [A1: vEBT_VEBT,A22: nat] :
% 5.64/5.90 ( ( vEBT_invar_vebt @ A1 @ A22 )
% 5.64/5.90 => ( ( ? [A5: $o,B5: $o] :
% 5.64/5.90 ( A1
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( A22
% 5.64/5.90 != ( suc @ zero_zero_nat ) ) )
% 5.64/5.90 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.64/5.90 ( ( A1
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( A22 = Deg2 )
% 5.64/5.90 => ( ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X3 @ N3 ) )
% 5.64/5.90 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.64/5.90 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( M4 = N3 )
% 5.64/5.90 => ( ( Deg2
% 5.64/5.90 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.64/5.90 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 5.64/5.90 => ~ ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.64/5.90 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.64/5.90 ( ( A1
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( A22 = Deg2 )
% 5.64/5.90 => ( ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X3 @ N3 ) )
% 5.64/5.90 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.64/5.90 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( M4
% 5.64/5.90 = ( suc @ N3 ) )
% 5.64/5.90 => ( ( Deg2
% 5.64/5.90 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.64/5.90 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 5.64/5.90 => ~ ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.64/5.90 => ( ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.64/5.90 ( ( A1
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( A22 = Deg2 )
% 5.64/5.90 => ( ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X3 @ N3 ) )
% 5.64/5.90 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.64/5.90 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( M4 = N3 )
% 5.64/5.90 => ( ( Deg2
% 5.64/5.90 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.64/5.90 => ( ! [I2: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X5 ) )
% 5.64/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.64/5.90 => ( ( ( Mi2 = Ma2 )
% 5.64/5.90 => ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.64/5.90 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.64/5.90 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/5.90 => ~ ( ( Mi2 != Ma2 )
% 5.64/5.90 => ! [I2: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.64/5.90 = I2 )
% 5.64/5.90 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.64/5.90 & ! [X3: nat] :
% 5.64/5.90 ( ( ( ( vEBT_VEBT_high @ X3 @ N3 )
% 5.64/5.90 = I2 )
% 5.64/5.90 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N3 ) ) )
% 5.64/5.90 => ( ( ord_less_nat @ Mi2 @ X3 )
% 5.64/5.90 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.90 => ~ ! [TreeList2: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.64/5.90 ( ( A1
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( A22 = Deg2 )
% 5.64/5.90 => ( ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X3 @ N3 ) )
% 5.64/5.90 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.64/5.90 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( M4
% 5.64/5.90 = ( suc @ N3 ) )
% 5.64/5.90 => ( ( Deg2
% 5.64/5.90 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.64/5.90 => ( ! [I2: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ X5 ) )
% 5.64/5.90 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.64/5.90 => ( ( ( Mi2 = Ma2 )
% 5.64/5.90 => ! [X3: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/5.90 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 5.64/5.90 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.64/5.90 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/5.90 => ~ ( ( Mi2 != Ma2 )
% 5.64/5.90 => ! [I2: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.64/5.90 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.64/5.90 = I2 )
% 5.64/5.90 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.64/5.90 & ! [X3: nat] :
% 5.64/5.90 ( ( ( ( vEBT_VEBT_high @ X3 @ N3 )
% 5.64/5.90 = I2 )
% 5.64/5.90 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I2 ) @ ( vEBT_VEBT_low @ X3 @ N3 ) ) )
% 5.64/5.90 => ( ( ord_less_nat @ Mi2 @ X3 )
% 5.64/5.90 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % invar_vebt.cases
% 5.64/5.90 thf(fact_3497_invar__vebt_Osimps,axiom,
% 5.64/5.90 ( vEBT_invar_vebt
% 5.64/5.90 = ( ^ [A12: vEBT_VEBT,A23: nat] :
% 5.64/5.90 ( ( ? [A3: $o,B3: $o] :
% 5.64/5.90 ( A12
% 5.64/5.90 = ( vEBT_Leaf @ A3 @ B3 ) )
% 5.64/5.90 & ( A23
% 5.64/5.90 = ( suc @ zero_zero_nat ) ) )
% 5.64/5.90 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.64/5.90 ( ( A12
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.64/5.90 & ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.64/5.90 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.64/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.64/5.90 & ( A23
% 5.64/5.90 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.64/5.90 & ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X5 )
% 5.64/5.90 & ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/5.90 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.64/5.90 ( ( A12
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A23 @ TreeList3 @ Summary3 ) )
% 5.64/5.90 & ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.64/5.90 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.64/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.64/5.90 & ( A23
% 5.64/5.90 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.64/5.90 & ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X5 )
% 5.64/5.90 & ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/5.90 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.64/5.90 ( ( A12
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.64/5.90 & ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.64/5.90 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.64/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.64/5.90 & ( A23
% 5.64/5.90 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.64/5.90 & ! [I4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.64/5.90 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X5 ) )
% 5.64/5.90 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.64/5.90 & ( ( Mi3 = Ma3 )
% 5.64/5.90 => ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/5.90 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.64/5.90 & ( ( Mi3 != Ma3 )
% 5.64/5.90 => ! [I4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.64/5.90 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.64/5.90 = I4 )
% 5.64/5.90 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.64/5.90 & ! [X: nat] :
% 5.64/5.90 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.64/5.90 = I4 )
% 5.64/5.90 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.64/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 5.64/5.90 | ? [TreeList3: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.64/5.90 ( ( A12
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A23 @ TreeList3 @ Summary3 ) )
% 5.64/5.90 & ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ( vEBT_invar_vebt @ X @ N2 ) )
% 5.64/5.90 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.64/5.90 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.64/5.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.64/5.90 & ( A23
% 5.64/5.90 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.64/5.90 & ! [I4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.64/5.90 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ X5 ) )
% 5.64/5.90 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I4 ) ) )
% 5.64/5.90 & ( ( Mi3 = Ma3 )
% 5.64/5.90 => ! [X: vEBT_VEBT] :
% 5.64/5.90 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.64/5.90 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/5.90 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/5.90 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A23 ) )
% 5.64/5.90 & ( ( Mi3 != Ma3 )
% 5.64/5.90 => ! [I4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.64/5.90 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.64/5.90 = I4 )
% 5.64/5.90 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.64/5.90 & ! [X: nat] :
% 5.64/5.90 ( ( ( ( vEBT_VEBT_high @ X @ N2 )
% 5.64/5.90 = I4 )
% 5.64/5.90 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I4 ) @ ( vEBT_VEBT_low @ X @ N2 ) ) )
% 5.64/5.90 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/5.90 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % invar_vebt.simps
% 5.64/5.90 thf(fact_3498_vebt__member_Osimps_I2_J,axiom,
% 5.64/5.90 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X2: nat] :
% 5.64/5.90 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X2 ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.simps(2)
% 5.64/5.90 thf(fact_3499_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.64/5.90 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.64/5.90 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.minNull.simps(5)
% 5.64/5.90 thf(fact_3500_inrange,axiom,
% 5.64/5.90 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.90 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.90 => ( 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 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % inrange
% 5.64/5.90 thf(fact_3501_set__bit__0,axiom,
% 5.64/5.90 ! [A: int] :
% 5.64/5.90 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.64/5.90 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % set_bit_0
% 5.64/5.90 thf(fact_3502_set__bit__0,axiom,
% 5.64/5.90 ! [A: nat] :
% 5.64/5.90 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.64/5.90 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % set_bit_0
% 5.64/5.90 thf(fact_3503_vebt__succ_Opelims,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: option_nat] :
% 5.64/5.90 ( ( ( vEBT_vebt_succ @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [Uu: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ Uu @ B5 ) )
% 5.64/5.90 => ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => ( ( ( B5
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.90 & ( ~ B5
% 5.64/5.90 => ( Y4 = none_nat ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ B5 ) @ zero_zero_nat ) ) ) ) )
% 5.64/5.90 => ( ! [Uv: $o,Uw: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ Uv @ Uw ) )
% 5.64/5.90 => ! [N3: nat] :
% 5.64/5.90 ( ( Xa2
% 5.64/5.90 = ( suc @ N3 ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N3 ) ) ) ) ) )
% 5.64/5.90 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( some_nat @ Mi2 ) ) )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 @ ( if_option_nat
% 5.64/5.90 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 != none_nat )
% 5.64/5.90 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.90 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 @ ( if_option_nat
% 5.64/5.90 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.90 = none_nat )
% 5.64/5.90 @ none_nat
% 5.64/5.90 @ ( 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 @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.90 @ none_nat ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_succ.pelims
% 5.64/5.90 thf(fact_3504_vebt__pred_Opelims,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: option_nat] :
% 5.64/5.90 ( ( ( vEBT_vebt_pred @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [Uu: $o,Uv: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/5.90 => ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat ) ) ) ) )
% 5.64/5.90 => ( ! [A5: $o,Uw: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ Uw ) )
% 5.64/5.90 => ( ( Xa2
% 5.64/5.90 = ( suc @ zero_zero_nat ) )
% 5.64/5.90 => ( ( ( A5
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.90 & ( ~ A5
% 5.64/5.90 => ( Y4 = none_nat ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ! [Va2: nat] :
% 5.64/5.90 ( ( Xa2
% 5.64/5.90 = ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.90 => ( ( ( B5
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( some_nat @ one_one_nat ) ) )
% 5.64/5.90 & ( ~ B5
% 5.64/5.90 => ( ( A5
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/5.90 & ( ~ A5
% 5.64/5.90 => ( Y4 = none_nat ) ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 5.64/5.90 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 5.64/5.90 => ( ( Y4 = none_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( some_nat @ Ma2 ) ) )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( Y4
% 5.64/5.90 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 @ ( if_option_nat
% 5.64/5.90 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 != none_nat )
% 5.64/5.90 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.64/5.90 @ ( 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 @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 @ ( if_option_nat
% 5.64/5.90 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.90 = none_nat )
% 5.64/5.90 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.64/5.90 @ ( 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_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.90 @ none_nat ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_pred.pelims
% 5.64/5.90 thf(fact_3505_double__eq__0__iff,axiom,
% 5.64/5.90 ! [A: real] :
% 5.64/5.90 ( ( ( plus_plus_real @ A @ A )
% 5.64/5.90 = zero_zero_real )
% 5.64/5.90 = ( A = zero_zero_real ) ) ).
% 5.64/5.90
% 5.64/5.90 % double_eq_0_iff
% 5.64/5.90 thf(fact_3506_double__eq__0__iff,axiom,
% 5.64/5.90 ! [A: rat] :
% 5.64/5.90 ( ( ( plus_plus_rat @ A @ A )
% 5.64/5.90 = zero_zero_rat )
% 5.64/5.90 = ( A = zero_zero_rat ) ) ).
% 5.64/5.90
% 5.64/5.90 % double_eq_0_iff
% 5.64/5.90 thf(fact_3507_double__eq__0__iff,axiom,
% 5.64/5.90 ! [A: int] :
% 5.64/5.90 ( ( ( plus_plus_int @ A @ A )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 = ( A = zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % double_eq_0_iff
% 5.64/5.90 thf(fact_3508_unset__bit__0,axiom,
% 5.64/5.90 ! [A: nat] :
% 5.64/5.90 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.64/5.90 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unset_bit_0
% 5.64/5.90 thf(fact_3509_unset__bit__0,axiom,
% 5.64/5.90 ! [A: int] :
% 5.64/5.90 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.64/5.90 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unset_bit_0
% 5.64/5.90 thf(fact_3510_set__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: code_integer] :
% 5.64/5.90 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.64/5.90 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % set_bit_Suc
% 5.64/5.90 thf(fact_3511_set__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: int] :
% 5.64/5.90 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.64/5.90 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % set_bit_Suc
% 5.64/5.90 thf(fact_3512_set__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: nat] :
% 5.64/5.90 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.64/5.90 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % set_bit_Suc
% 5.64/5.90 thf(fact_3513_flip__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: code_integer] :
% 5.64/5.90 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.64/5.90 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % flip_bit_Suc
% 5.64/5.90 thf(fact_3514_flip__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: int] :
% 5.64/5.90 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.64/5.90 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % flip_bit_Suc
% 5.64/5.90 thf(fact_3515_flip__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: nat] :
% 5.64/5.90 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.64/5.90 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % flip_bit_Suc
% 5.64/5.90 thf(fact_3516_unset__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: nat] :
% 5.64/5.90 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.64/5.90 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unset_bit_Suc
% 5.64/5.90 thf(fact_3517_unset__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: code_integer] :
% 5.64/5.90 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.64/5.90 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unset_bit_Suc
% 5.64/5.90 thf(fact_3518_unset__bit__Suc,axiom,
% 5.64/5.90 ! [N: nat,A: int] :
% 5.64/5.90 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.64/5.90 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unset_bit_Suc
% 5.64/5.90 thf(fact_3519_div__pos__pos__trivial,axiom,
% 5.64/5.90 ! [K: int,L: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ( ord_less_int @ K @ L )
% 5.64/5.90 => ( ( divide_divide_int @ K @ L )
% 5.64/5.90 = zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_pos_pos_trivial
% 5.64/5.90 thf(fact_3520_div__neg__neg__trivial,axiom,
% 5.64/5.90 ! [K: int,L: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ L @ K )
% 5.64/5.90 => ( ( divide_divide_int @ K @ L )
% 5.64/5.90 = zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_neg_neg_trivial
% 5.64/5.90 thf(fact_3521_i0__less,axiom,
% 5.64/5.90 ! [N: extended_enat] :
% 5.64/5.90 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.64/5.90 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.64/5.90
% 5.64/5.90 % i0_less
% 5.64/5.90 thf(fact_3522_idiff__0,axiom,
% 5.64/5.90 ! [N: extended_enat] :
% 5.64/5.90 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.64/5.90 = zero_z5237406670263579293d_enat ) ).
% 5.64/5.90
% 5.64/5.90 % idiff_0
% 5.64/5.90 thf(fact_3523_idiff__0__right,axiom,
% 5.64/5.90 ! [N: extended_enat] :
% 5.64/5.90 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.64/5.90 = N ) ).
% 5.64/5.90
% 5.64/5.90 % idiff_0_right
% 5.64/5.90 thf(fact_3524_not__real__square__gt__zero,axiom,
% 5.64/5.90 ! [X2: real] :
% 5.64/5.90 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X2 @ X2 ) ) )
% 5.64/5.90 = ( X2 = zero_zero_real ) ) ).
% 5.64/5.90
% 5.64/5.90 % not_real_square_gt_zero
% 5.64/5.90 thf(fact_3525_zmod__numeral__Bit0,axiom,
% 5.64/5.90 ! [V: num,W: num] :
% 5.64/5.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.64/5.90 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zmod_numeral_Bit0
% 5.64/5.90 thf(fact_3526_half__negative__int__iff,axiom,
% 5.64/5.90 ! [K: int] :
% 5.64/5.90 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % half_negative_int_iff
% 5.64/5.90 thf(fact_3527_half__nonnegative__int__iff,axiom,
% 5.64/5.90 ! [K: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.64/5.90 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.64/5.90
% 5.64/5.90 % half_nonnegative_int_iff
% 5.64/5.90 thf(fact_3528_zdiv__mono__strict,axiom,
% 5.64/5.90 ! [A4: int,B4: int,N: int] :
% 5.64/5.90 ( ( ord_less_int @ A4 @ B4 )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.64/5.90 => ( ( ( modulo_modulo_int @ A4 @ N )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 => ( ( ( modulo_modulo_int @ B4 @ N )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 => ( ord_less_int @ ( divide_divide_int @ A4 @ N ) @ ( divide_divide_int @ B4 @ N ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono_strict
% 5.64/5.90 thf(fact_3529_zmod__zmult2__eq,axiom,
% 5.64/5.90 ! [C: int,A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.90 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zmod_zmult2_eq
% 5.64/5.90 thf(fact_3530_verit__le__mono__div__int,axiom,
% 5.64/5.90 ! [A4: int,B4: int,N: int] :
% 5.64/5.90 ( ( ord_less_int @ A4 @ B4 )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.64/5.90 => ( ord_less_eq_int
% 5.64/5.90 @ ( plus_plus_int @ ( divide_divide_int @ A4 @ N )
% 5.64/5.90 @ ( if_int
% 5.64/5.90 @ ( ( modulo_modulo_int @ B4 @ N )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 @ one_one_int
% 5.64/5.90 @ zero_zero_int ) )
% 5.64/5.90 @ ( divide_divide_int @ B4 @ N ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % verit_le_mono_div_int
% 5.64/5.90 thf(fact_3531_split__pos__lemma,axiom,
% 5.64/5.90 ! [K: int,P: int > int > $o,N: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.64/5.90 = ( ! [I4: int,J3: int] :
% 5.64/5.90 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.64/5.90 & ( ord_less_int @ J3 @ K )
% 5.64/5.90 & ( N
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.64/5.90 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % split_pos_lemma
% 5.64/5.90 thf(fact_3532_split__neg__lemma,axiom,
% 5.64/5.90 ! [K: int,P: int > int > $o,N: int] :
% 5.64/5.90 ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.90 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.64/5.90 = ( ! [I4: int,J3: int] :
% 5.64/5.90 ( ( ( ord_less_int @ K @ J3 )
% 5.64/5.90 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.64/5.90 & ( N
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.64/5.90 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % split_neg_lemma
% 5.64/5.90 thf(fact_3533_div__mod__decomp__int,axiom,
% 5.64/5.90 ! [A4: int,N: int] :
% 5.64/5.90 ( A4
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N ) @ N ) @ ( modulo_modulo_int @ A4 @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_mod_decomp_int
% 5.64/5.90 thf(fact_3534_div__neg__pos__less0,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.90 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_neg_pos_less0
% 5.64/5.90 thf(fact_3535_neg__imp__zdiv__neg__iff,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_imp_zdiv_neg_iff
% 5.64/5.90 thf(fact_3536_pos__imp__zdiv__neg__iff,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.90 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_imp_zdiv_neg_iff
% 5.64/5.90 thf(fact_3537_int__div__less__self,axiom,
% 5.64/5.90 ! [X2: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.64/5.90 => ( ( ord_less_int @ one_one_int @ K )
% 5.64/5.90 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_div_less_self
% 5.64/5.90 thf(fact_3538_zdiv__zmult2__eq,axiom,
% 5.64/5.90 ! [C: int,A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.64/5.90 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.90 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_zmult2_eq
% 5.64/5.90 thf(fact_3539_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.64/5.90 = ( ( ord_less_eq_int @ B @ A )
% 5.64/5.90 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % nonneg1_imp_zdiv_pos_iff
% 5.64/5.90 thf(fact_3540_pos__imp__zdiv__nonneg__iff,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.64/5.90 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_imp_zdiv_nonneg_iff
% 5.64/5.90 thf(fact_3541_neg__imp__zdiv__nonneg__iff,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.64/5.90 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_imp_zdiv_nonneg_iff
% 5.64/5.90 thf(fact_3542_pos__imp__zdiv__pos__iff,axiom,
% 5.64/5.90 ! [K: int,I: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.64/5.90 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_imp_zdiv_pos_iff
% 5.64/5.90 thf(fact_3543_div__nonpos__pos__le0,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.90 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_nonpos_pos_le0
% 5.64/5.90 thf(fact_3544_div__nonneg__neg__le0,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.90 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.90 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_nonneg_neg_le0
% 5.64/5.90 thf(fact_3545_div__positive__int,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ L @ K )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.90 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_positive_int
% 5.64/5.90 thf(fact_3546_div__int__pos__iff,axiom,
% 5.64/5.90 ! [K: int,L: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.64/5.90 = ( ( K = zero_zero_int )
% 5.64/5.90 | ( L = zero_zero_int )
% 5.64/5.90 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.90 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.64/5.90 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.90 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_int_pos_iff
% 5.64/5.90 thf(fact_3547_zdiv__mono2__neg,axiom,
% 5.64/5.90 ! [A: int,B2: int,B: int] :
% 5.64/5.90 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.64/5.90 => ( ( ord_less_eq_int @ B2 @ B )
% 5.64/5.90 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono2_neg
% 5.64/5.90 thf(fact_3548_zdiv__mono1__neg,axiom,
% 5.64/5.90 ! [A: int,A2: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ A @ A2 )
% 5.64/5.90 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.90 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono1_neg
% 5.64/5.90 thf(fact_3549_int__div__pos__eq,axiom,
% 5.64/5.90 ! [A: int,B: int,Q3: int,R2: int] :
% 5.64/5.90 ( ( A
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.64/5.90 => ( ( ord_less_int @ R2 @ B )
% 5.64/5.90 => ( ( divide_divide_int @ A @ B )
% 5.64/5.90 = Q3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_div_pos_eq
% 5.64/5.90 thf(fact_3550_int__div__neg__eq,axiom,
% 5.64/5.90 ! [A: int,B: int,Q3: int,R2: int] :
% 5.64/5.90 ( ( A
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ B @ R2 )
% 5.64/5.90 => ( ( divide_divide_int @ A @ B )
% 5.64/5.90 = Q3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_div_neg_eq
% 5.64/5.90 thf(fact_3551_zdiv__eq__0__iff,axiom,
% 5.64/5.90 ! [I: int,K: int] :
% 5.64/5.90 ( ( ( divide_divide_int @ I @ K )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 = ( ( K = zero_zero_int )
% 5.64/5.90 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.64/5.90 & ( ord_less_int @ I @ K ) )
% 5.64/5.90 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.64/5.90 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_eq_0_iff
% 5.64/5.90 thf(fact_3552_div__pos__geq,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.90 => ( ( ord_less_eq_int @ L @ K )
% 5.64/5.90 => ( ( divide_divide_int @ K @ L )
% 5.64/5.90 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % div_pos_geq
% 5.64/5.90 thf(fact_3553_zdiv__mono2,axiom,
% 5.64/5.90 ! [A: int,B2: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.64/5.90 => ( ( ord_less_eq_int @ B2 @ B )
% 5.64/5.90 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono2
% 5.64/5.90 thf(fact_3554_zdiv__mono1,axiom,
% 5.64/5.90 ! [A: int,A2: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ A @ A2 )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.90 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono1
% 5.64/5.90 thf(fact_3555_split__zdiv,axiom,
% 5.64/5.90 ! [P: int > $o,N: int,K: int] :
% 5.64/5.90 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.64/5.90 = ( ( ( K = zero_zero_int )
% 5.64/5.90 => ( P @ zero_zero_int ) )
% 5.64/5.90 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ! [I4: int,J3: int] :
% 5.64/5.90 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.64/5.90 & ( ord_less_int @ J3 @ K )
% 5.64/5.90 & ( N
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.64/5.90 => ( P @ I4 ) ) )
% 5.64/5.90 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.90 => ! [I4: int,J3: int] :
% 5.64/5.90 ( ( ( ord_less_int @ K @ J3 )
% 5.64/5.90 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.64/5.90 & ( N
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.64/5.90 => ( P @ I4 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % split_zdiv
% 5.64/5.90 thf(fact_3556_pos__zmod__mult__2,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.90 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.90 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_zmod_mult_2
% 5.64/5.90 thf(fact_3557_neg__zmod__mult__2,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.90 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.90 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_zmod_mult_2
% 5.64/5.90 thf(fact_3558_enat__0__less__mult__iff,axiom,
% 5.64/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.64/5.90 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.64/5.90 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.64/5.90 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % enat_0_less_mult_iff
% 5.64/5.90 thf(fact_3559_not__iless0,axiom,
% 5.64/5.90 ! [N: extended_enat] :
% 5.64/5.90 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.64/5.90
% 5.64/5.90 % not_iless0
% 5.64/5.90 thf(fact_3560_iadd__is__0,axiom,
% 5.64/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.64/5.90 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.64/5.90 = zero_z5237406670263579293d_enat )
% 5.64/5.90 = ( ( M = zero_z5237406670263579293d_enat )
% 5.64/5.90 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % iadd_is_0
% 5.64/5.90 thf(fact_3561_ile0__eq,axiom,
% 5.64/5.90 ! [N: extended_enat] :
% 5.64/5.90 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.64/5.90 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.64/5.90
% 5.64/5.90 % ile0_eq
% 5.64/5.90 thf(fact_3562_i0__lb,axiom,
% 5.64/5.90 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.64/5.90
% 5.64/5.90 % i0_lb
% 5.64/5.90 thf(fact_3563_ex__nat__less,axiom,
% 5.64/5.90 ! [N: nat,P: nat > $o] :
% 5.64/5.90 ( ( ? [M2: nat] :
% 5.64/5.90 ( ( ord_less_eq_nat @ M2 @ N )
% 5.64/5.90 & ( P @ M2 ) ) )
% 5.64/5.90 = ( ? [X: nat] :
% 5.64/5.90 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.90 & ( P @ X ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % ex_nat_less
% 5.64/5.90 thf(fact_3564_all__nat__less,axiom,
% 5.64/5.90 ! [N: nat,P: nat > $o] :
% 5.64/5.90 ( ( ! [M2: nat] :
% 5.64/5.90 ( ( ord_less_eq_nat @ M2 @ N )
% 5.64/5.90 => ( P @ M2 ) ) )
% 5.64/5.90 = ( ! [X: nat] :
% 5.64/5.90 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.90 => ( P @ X ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % all_nat_less
% 5.64/5.90 thf(fact_3565_not__exp__less__eq__0__int,axiom,
% 5.64/5.90 ! [N: nat] :
% 5.64/5.90 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.64/5.90
% 5.64/5.90 % not_exp_less_eq_0_int
% 5.64/5.90 thf(fact_3566_realpow__pos__nth2,axiom,
% 5.64/5.90 ! [A: real,N: nat] :
% 5.64/5.90 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.90 => ? [R3: real] :
% 5.64/5.90 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.64/5.90 & ( ( power_power_real @ R3 @ ( suc @ N ) )
% 5.64/5.90 = A ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % realpow_pos_nth2
% 5.64/5.90 thf(fact_3567_real__arch__pow__inv,axiom,
% 5.64/5.90 ! [Y4: real,X2: real] :
% 5.64/5.90 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.90 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/5.90 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N3 ) @ Y4 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % real_arch_pow_inv
% 5.64/5.90 thf(fact_3568_realpow__pos__nth,axiom,
% 5.64/5.90 ! [N: nat,A: real] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.90 => ? [R3: real] :
% 5.64/5.90 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.64/5.90 & ( ( power_power_real @ R3 @ N )
% 5.64/5.90 = A ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % realpow_pos_nth
% 5.64/5.90 thf(fact_3569_realpow__pos__nth__unique,axiom,
% 5.64/5.90 ! [N: nat,A: real] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.90 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.90 => ? [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.64/5.90 & ( ( power_power_real @ X4 @ N )
% 5.64/5.90 = A )
% 5.64/5.90 & ! [Y5: real] :
% 5.64/5.90 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 5.64/5.90 & ( ( power_power_real @ Y5 @ N )
% 5.64/5.90 = A ) )
% 5.64/5.90 => ( Y5 = X4 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % realpow_pos_nth_unique
% 5.64/5.90 thf(fact_3570_neg__zdiv__mult__2,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.90 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.90 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_zdiv_mult_2
% 5.64/5.90 thf(fact_3571_pos__zdiv__mult__2,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.90 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.90 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_zdiv_mult_2
% 5.64/5.90 thf(fact_3572_int__power__div__base,axiom,
% 5.64/5.90 ! [M: nat,K: int] :
% 5.64/5.90 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.64/5.90 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_power_div_base
% 5.64/5.90 thf(fact_3573_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_H_Opelims,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: nat] :
% 5.64/5.90 ( ( ( vEBT_T_m_e_m_b_e_r2 @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( Y4 = one_one_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.90 => ( ( Y4 = one_one_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.90 => ( ( Y4 = one_one_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.90 => ( ( Y4 = one_one_nat )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( plus_plus_nat @ one_one_nat
% 5.64/5.90 @ ( if_nat @ ( Xa2 = Mi2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat @ ( Xa2 = Ma2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ zero_zero_nat
% 5.64/5.90 @ ( if_nat
% 5.64/5.90 @ ( ( ord_less_nat @ Mi2 @ Xa2 )
% 5.64/5.90 & ( ord_less_nat @ Xa2 @ Ma2 ) )
% 5.64/5.90 @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( vEBT_T_m_e_m_b_e_r2 @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ zero_zero_nat )
% 5.64/5.90 @ zero_zero_nat ) ) ) ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T8099345112685741742_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r'.pelims
% 5.64/5.90 thf(fact_3574_vebt__member_Opelims_I1_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/5.90 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.90 => ( ~ Y4
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.90 => ( ~ Y4
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.90 => ( ~ Y4
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( Xa2 != Mi2 )
% 5.64/5.90 => ( ( Xa2 != Ma2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.pelims(1)
% 5.64/5.90 thf(fact_3575_vebt__member_Opelims_I3_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.64/5.90 => ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.64/5.90 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.64/5.90 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.64/5.90 => ( ( Xa2 != Mi2 )
% 5.64/5.90 => ( ( Xa2 != Ma2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.pelims(3)
% 5.64/5.90 thf(fact_3576_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/5.90 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.64/5.90 => ( ~ Y4
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) ) )
% 5.64/5.90 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.naive_member.pelims(1)
% 5.64/5.90 thf(fact_3577_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.64/5.90 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.naive_member.pelims(2)
% 5.64/5.90 thf(fact_3578_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.64/5.90 => ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.64/5.90 => ( ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Xa2 ) ) )
% 5.64/5.90 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.naive_member.pelims(3)
% 5.64/5.90 thf(fact_3579_vebt__member_Opelims_I2_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [A5: $o,B5: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.90 => A5 )
% 5.64/5.90 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.90 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.90 => B5 )
% 5.64/5.90 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.64/5.90 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( Xa2 != Mi2 )
% 5.64/5.90 => ( ( Xa2 != Ma2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.64/5.90 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % vebt_member.pelims(2)
% 5.64/5.90 thf(fact_3580_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/5.90 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.64/5.90 = Y4 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [Uu: $o,Uv: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/5.90 => ( ~ Y4
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.64/5.90 => ( ~ Y4
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 )
% 5.64/5.90 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.64/5.90 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.64/5.90 => ( ( Y4
% 5.64/5.90 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.membermima.pelims(1)
% 5.64/5.90 thf(fact_3581_unset__bit__negative__int__iff,axiom,
% 5.64/5.90 ! [N: nat,K: int] :
% 5.64/5.90 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % unset_bit_negative_int_iff
% 5.64/5.90 thf(fact_3582_flip__bit__negative__int__iff,axiom,
% 5.64/5.90 ! [N: nat,K: int] :
% 5.64/5.90 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % flip_bit_negative_int_iff
% 5.64/5.90 thf(fact_3583_set__bit__negative__int__iff,axiom,
% 5.64/5.90 ! [N: nat,K: int] :
% 5.64/5.90 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % set_bit_negative_int_iff
% 5.64/5.90 thf(fact_3584_zle__add1__eq__le,axiom,
% 5.64/5.90 ! [W: int,Z: int] :
% 5.64/5.90 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.64/5.90 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.64/5.90
% 5.64/5.90 % zle_add1_eq_le
% 5.64/5.90 thf(fact_3585_zle__diff1__eq,axiom,
% 5.64/5.90 ! [W: int,Z: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.64/5.90 = ( ord_less_int @ W @ Z ) ) ).
% 5.64/5.90
% 5.64/5.90 % zle_diff1_eq
% 5.64/5.90 thf(fact_3586_mod__neg__neg__trivial,axiom,
% 5.64/5.90 ! [K: int,L: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ L @ K )
% 5.64/5.90 => ( ( modulo_modulo_int @ K @ L )
% 5.64/5.90 = K ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mod_neg_neg_trivial
% 5.64/5.90 thf(fact_3587_mod__pos__pos__trivial,axiom,
% 5.64/5.90 ! [K: int,L: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ( ord_less_int @ K @ L )
% 5.64/5.90 => ( ( modulo_modulo_int @ K @ L )
% 5.64/5.90 = K ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mod_pos_pos_trivial
% 5.64/5.90 thf(fact_3588_le__imp__0__less,axiom,
% 5.64/5.90 ! [Z: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.90 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % le_imp_0_less
% 5.64/5.90 thf(fact_3589_split__zmod,axiom,
% 5.64/5.90 ! [P: int > $o,N: int,K: int] :
% 5.64/5.90 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.64/5.90 = ( ( ( K = zero_zero_int )
% 5.64/5.90 => ( P @ N ) )
% 5.64/5.90 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ! [I4: int,J3: int] :
% 5.64/5.90 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.64/5.90 & ( ord_less_int @ J3 @ K )
% 5.64/5.90 & ( N
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.64/5.90 => ( P @ J3 ) ) )
% 5.64/5.90 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.90 => ! [I4: int,J3: int] :
% 5.64/5.90 ( ( ( ord_less_int @ K @ J3 )
% 5.64/5.90 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.64/5.90 & ( N
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.64/5.90 => ( P @ J3 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % split_zmod
% 5.64/5.90 thf(fact_3590_mod__pos__geq,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.90 => ( ( ord_less_eq_int @ L @ K )
% 5.64/5.90 => ( ( modulo_modulo_int @ K @ L )
% 5.64/5.90 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mod_pos_geq
% 5.64/5.90 thf(fact_3591_q__pos__lemma,axiom,
% 5.64/5.90 ! [B2: int,Q5: int,R4: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 5.64/5.90 => ( ( ord_less_int @ R4 @ B2 )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.64/5.90 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % q_pos_lemma
% 5.64/5.90 thf(fact_3592_neg__mod__conj,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ B @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.64/5.90 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_mod_conj
% 5.64/5.90 thf(fact_3593_pos__mod__conj,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.64/5.90 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_mod_conj
% 5.64/5.90 thf(fact_3594_int__mod__neg__eq,axiom,
% 5.64/5.90 ! [A: int,B: int,Q3: int,R2: int] :
% 5.64/5.90 ( ( A
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ B @ R2 )
% 5.64/5.90 => ( ( modulo_modulo_int @ A @ B )
% 5.64/5.90 = R2 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_mod_neg_eq
% 5.64/5.90 thf(fact_3595_int__mod__pos__eq,axiom,
% 5.64/5.90 ! [A: int,B: int,Q3: int,R2: int] :
% 5.64/5.90 ( ( A
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.64/5.90 => ( ( ord_less_int @ R2 @ B )
% 5.64/5.90 => ( ( modulo_modulo_int @ A @ B )
% 5.64/5.90 = R2 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_mod_pos_eq
% 5.64/5.90 thf(fact_3596_zdiv__mono2__lemma,axiom,
% 5.64/5.90 ! [B: int,Q3: int,R2: int,B2: int,Q5: int,R4: int] :
% 5.64/5.90 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 5.64/5.90 => ( ( ord_less_int @ R4 @ B2 )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.64/5.90 => ( ( ord_less_eq_int @ B2 @ B )
% 5.64/5.90 => ( ord_less_eq_int @ Q3 @ Q5 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono2_lemma
% 5.64/5.90 thf(fact_3597_zmod__trivial__iff,axiom,
% 5.64/5.90 ! [I: int,K: int] :
% 5.64/5.90 ( ( ( modulo_modulo_int @ I @ K )
% 5.64/5.90 = I )
% 5.64/5.90 = ( ( K = zero_zero_int )
% 5.64/5.90 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.64/5.90 & ( ord_less_int @ I @ K ) )
% 5.64/5.90 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.64/5.90 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zmod_trivial_iff
% 5.64/5.90 thf(fact_3598_zdiv__mono2__neg__lemma,axiom,
% 5.64/5.90 ! [B: int,Q3: int,R2: int,B2: int,Q5: int,R4: int] :
% 5.64/5.90 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 )
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 5.64/5.90 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ R2 @ B )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.64/5.90 => ( ( ord_less_eq_int @ B2 @ B )
% 5.64/5.90 => ( ord_less_eq_int @ Q5 @ Q3 ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zdiv_mono2_neg_lemma
% 5.64/5.90 thf(fact_3599_int__one__le__iff__zero__less,axiom,
% 5.64/5.90 ! [Z: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.64/5.90 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_one_le_iff_zero_less
% 5.64/5.90 thf(fact_3600_unique__quotient__lemma,axiom,
% 5.64/5.90 ! [B: int,Q5: int,R4: int,Q3: int,R2: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.64/5.90 => ( ( ord_less_int @ R4 @ B )
% 5.64/5.90 => ( ( ord_less_int @ R2 @ B )
% 5.64/5.90 => ( ord_less_eq_int @ Q5 @ Q3 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unique_quotient_lemma
% 5.64/5.90 thf(fact_3601_neg__mod__sign,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ L @ zero_zero_int )
% 5.64/5.90 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_mod_sign
% 5.64/5.90 thf(fact_3602_Euclidean__Division_Opos__mod__sign,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.90 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Euclidean_Division.pos_mod_sign
% 5.64/5.90 thf(fact_3603_unique__quotient__lemma__neg,axiom,
% 5.64/5.90 ! [B: int,Q5: int,R4: int,Q3: int,R2: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R2 ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 5.64/5.90 => ( ( ord_less_int @ B @ R2 )
% 5.64/5.90 => ( ( ord_less_int @ B @ R4 )
% 5.64/5.90 => ( ord_less_eq_int @ Q3 @ Q5 ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % unique_quotient_lemma_neg
% 5.64/5.90 thf(fact_3604_mod__pos__neg__trivial,axiom,
% 5.64/5.90 ! [K: int,L: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.64/5.90 => ( ( modulo_modulo_int @ K @ L )
% 5.64/5.90 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % mod_pos_neg_trivial
% 5.64/5.90 thf(fact_3605_zmult__zless__mono2,axiom,
% 5.64/5.90 ! [I: int,J: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ I @ J )
% 5.64/5.90 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.90 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zmult_zless_mono2
% 5.64/5.90 thf(fact_3606_pos__zmult__eq__1__iff,axiom,
% 5.64/5.90 ! [M: int,N: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ M )
% 5.64/5.90 => ( ( ( times_times_int @ M @ N )
% 5.64/5.90 = one_one_int )
% 5.64/5.90 = ( ( M = one_one_int )
% 5.64/5.90 & ( N = one_one_int ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pos_zmult_eq_1_iff
% 5.64/5.90 thf(fact_3607_zmod__eq__0D,axiom,
% 5.64/5.90 ! [M: int,D: int] :
% 5.64/5.90 ( ( ( modulo_modulo_int @ M @ D )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 => ? [Q2: int] :
% 5.64/5.90 ( M
% 5.64/5.90 = ( times_times_int @ D @ Q2 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zmod_eq_0D
% 5.64/5.90 thf(fact_3608_zmod__eq__0__iff,axiom,
% 5.64/5.90 ! [M: int,D: int] :
% 5.64/5.90 ( ( ( modulo_modulo_int @ M @ D )
% 5.64/5.90 = zero_zero_int )
% 5.64/5.90 = ( ? [Q4: int] :
% 5.64/5.90 ( M
% 5.64/5.90 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zmod_eq_0_iff
% 5.64/5.90 thf(fact_3609_odd__less__0__iff,axiom,
% 5.64/5.90 ! [Z: int] :
% 5.64/5.90 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.64/5.90 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % odd_less_0_iff
% 5.64/5.90 thf(fact_3610_less__int__code_I1_J,axiom,
% 5.64/5.90 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.64/5.90
% 5.64/5.90 % less_int_code(1)
% 5.64/5.90 thf(fact_3611_bot__enat__def,axiom,
% 5.64/5.90 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.64/5.90
% 5.64/5.90 % bot_enat_def
% 5.64/5.90 thf(fact_3612_Euclidean__Division_Opos__mod__bound,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.90 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.64/5.90
% 5.64/5.90 % Euclidean_Division.pos_mod_bound
% 5.64/5.90 thf(fact_3613_neg__mod__bound,axiom,
% 5.64/5.90 ! [L: int,K: int] :
% 5.64/5.90 ( ( ord_less_int @ L @ zero_zero_int )
% 5.64/5.90 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % neg_mod_bound
% 5.64/5.90 thf(fact_3614_zero__one__enat__neq_I1_J,axiom,
% 5.64/5.90 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.64/5.90
% 5.64/5.90 % zero_one_enat_neq(1)
% 5.64/5.90 thf(fact_3615_imult__is__0,axiom,
% 5.64/5.90 ! [M: extended_enat,N: extended_enat] :
% 5.64/5.90 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.64/5.90 = zero_z5237406670263579293d_enat )
% 5.64/5.90 = ( ( M = zero_z5237406670263579293d_enat )
% 5.64/5.90 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % imult_is_0
% 5.64/5.90 thf(fact_3616_times__int__code_I1_J,axiom,
% 5.64/5.90 ! [K: int] :
% 5.64/5.90 ( ( times_times_int @ K @ zero_zero_int )
% 5.64/5.90 = zero_zero_int ) ).
% 5.64/5.90
% 5.64/5.90 % times_int_code(1)
% 5.64/5.90 thf(fact_3617_times__int__code_I2_J,axiom,
% 5.64/5.90 ! [L: int] :
% 5.64/5.90 ( ( times_times_int @ zero_zero_int @ L )
% 5.64/5.90 = zero_zero_int ) ).
% 5.64/5.90
% 5.64/5.90 % times_int_code(2)
% 5.64/5.90 thf(fact_3618_int__gr__induct,axiom,
% 5.64/5.90 ! [K: int,I: int,P: int > $o] :
% 5.64/5.90 ( ( ord_less_int @ K @ I )
% 5.64/5.90 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.64/5.90 => ( ! [I3: int] :
% 5.64/5.90 ( ( ord_less_int @ K @ I3 )
% 5.64/5.90 => ( ( P @ I3 )
% 5.64/5.90 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.64/5.90 => ( P @ I ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_gr_induct
% 5.64/5.90 thf(fact_3619_zless__add1__eq,axiom,
% 5.64/5.90 ! [W: int,Z: int] :
% 5.64/5.90 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.64/5.90 = ( ( ord_less_int @ W @ Z )
% 5.64/5.90 | ( W = Z ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % zless_add1_eq
% 5.64/5.90 thf(fact_3620_int__distrib_I3_J,axiom,
% 5.64/5.90 ! [Z1: int,Z22: int,W: int] :
% 5.64/5.90 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.64/5.90 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_distrib(3)
% 5.64/5.90 thf(fact_3621_int__distrib_I4_J,axiom,
% 5.64/5.90 ! [W: int,Z1: int,Z22: int] :
% 5.64/5.90 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.64/5.90 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_distrib(4)
% 5.64/5.90 thf(fact_3622_int__distrib_I1_J,axiom,
% 5.64/5.90 ! [Z1: int,Z22: int,W: int] :
% 5.64/5.90 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_distrib(1)
% 5.64/5.90 thf(fact_3623_int__distrib_I2_J,axiom,
% 5.64/5.90 ! [W: int,Z1: int,Z22: int] :
% 5.64/5.90 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.64/5.90 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_distrib(2)
% 5.64/5.90 thf(fact_3624_int__less__induct,axiom,
% 5.64/5.90 ! [I: int,K: int,P: int > $o] :
% 5.64/5.90 ( ( ord_less_int @ I @ K )
% 5.64/5.90 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.64/5.90 => ( ! [I3: int] :
% 5.64/5.90 ( ( ord_less_int @ I3 @ K )
% 5.64/5.90 => ( ( P @ I3 )
% 5.64/5.90 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.64/5.90 => ( P @ I ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % int_less_induct
% 5.64/5.90 thf(fact_3625_zless__imp__add1__zle,axiom,
% 5.64/5.90 ! [W: int,Z: int] :
% 5.64/5.90 ( ( ord_less_int @ W @ Z )
% 5.64/5.90 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.64/5.90
% 5.64/5.90 % zless_imp_add1_zle
% 5.64/5.90 thf(fact_3626_add1__zle__eq,axiom,
% 5.64/5.90 ! [W: int,Z: int] :
% 5.64/5.90 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.64/5.90 = ( ord_less_int @ W @ Z ) ) ).
% 5.64/5.90
% 5.64/5.90 % add1_zle_eq
% 5.64/5.90 thf(fact_3627_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 ) ) ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 )
% 5.64/5.90 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.64/5.90 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 5.64/5.90 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.membermima.pelims(2)
% 5.64/5.90 thf(fact_3628_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.64/5.90 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/5.90 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.90 => ( ! [Uu: $o,Uv: $o] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) )
% 5.64/5.90 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.64/5.90 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.64/5.90 => ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 ) ) ) )
% 5.64/5.90 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.64/5.90 => ( ( Xa2 = Mi2 )
% 5.64/5.90 | ( Xa2 = Ma2 )
% 5.64/5.90 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.64/5.90 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.64/5.90 ( ( X2
% 5.64/5.90 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) )
% 5.64/5.90 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ Xa2 ) )
% 5.64/5.90 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.90 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.90 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % VEBT_internal.membermima.pelims(3)
% 5.64/5.90 thf(fact_3629_atLeastatMost__empty,axiom,
% 5.64/5.90 ! [B: rat,A: rat] :
% 5.64/5.90 ( ( ord_less_rat @ B @ A )
% 5.64/5.90 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.64/5.90 = bot_bot_set_rat ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty
% 5.64/5.90 thf(fact_3630_atLeastatMost__empty,axiom,
% 5.64/5.90 ! [B: num,A: num] :
% 5.64/5.90 ( ( ord_less_num @ B @ A )
% 5.64/5.90 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.64/5.90 = bot_bot_set_num ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty
% 5.64/5.90 thf(fact_3631_atLeastatMost__empty,axiom,
% 5.64/5.90 ! [B: nat,A: nat] :
% 5.64/5.90 ( ( ord_less_nat @ B @ A )
% 5.64/5.90 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.64/5.90 = bot_bot_set_nat ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty
% 5.64/5.90 thf(fact_3632_atLeastatMost__empty,axiom,
% 5.64/5.90 ! [B: int,A: int] :
% 5.64/5.90 ( ( ord_less_int @ B @ A )
% 5.64/5.90 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.64/5.90 = bot_bot_set_int ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty
% 5.64/5.90 thf(fact_3633_atLeastatMost__empty,axiom,
% 5.64/5.90 ! [B: real,A: real] :
% 5.64/5.90 ( ( ord_less_real @ B @ A )
% 5.64/5.90 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.64/5.90 = bot_bot_set_real ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty
% 5.64/5.90 thf(fact_3634_atLeastatMost__subset__iff,axiom,
% 5.64/5.90 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.64/5.90 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.90 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.64/5.90 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_subset_iff
% 5.64/5.90 thf(fact_3635_atLeastatMost__subset__iff,axiom,
% 5.64/5.90 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.90 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.64/5.90 | ( ( ord_less_eq_rat @ C @ A )
% 5.64/5.90 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_subset_iff
% 5.64/5.90 thf(fact_3636_atLeastatMost__subset__iff,axiom,
% 5.64/5.90 ! [A: num,B: num,C: num,D: num] :
% 5.64/5.90 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.64/5.90 | ( ( ord_less_eq_num @ C @ A )
% 5.64/5.90 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_subset_iff
% 5.64/5.90 thf(fact_3637_atLeastatMost__subset__iff,axiom,
% 5.64/5.90 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.90 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.64/5.90 | ( ( ord_less_eq_nat @ C @ A )
% 5.64/5.90 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_subset_iff
% 5.64/5.90 thf(fact_3638_atLeastatMost__subset__iff,axiom,
% 5.64/5.90 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.90 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.64/5.90 | ( ( ord_less_eq_int @ C @ A )
% 5.64/5.90 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_subset_iff
% 5.64/5.90 thf(fact_3639_atLeastatMost__subset__iff,axiom,
% 5.64/5.90 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.90 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.64/5.90 | ( ( ord_less_eq_real @ C @ A )
% 5.64/5.90 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_subset_iff
% 5.64/5.90 thf(fact_3640_atLeastatMost__empty__iff,axiom,
% 5.64/5.90 ! [A: set_nat,B: set_nat] :
% 5.64/5.90 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.64/5.90 = bot_bot_set_set_nat )
% 5.64/5.90 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff
% 5.64/5.90 thf(fact_3641_atLeastatMost__empty__iff,axiom,
% 5.64/5.90 ! [A: rat,B: rat] :
% 5.64/5.90 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.64/5.90 = bot_bot_set_rat )
% 5.64/5.90 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff
% 5.64/5.90 thf(fact_3642_atLeastatMost__empty__iff,axiom,
% 5.64/5.90 ! [A: num,B: num] :
% 5.64/5.90 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.64/5.90 = bot_bot_set_num )
% 5.64/5.90 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff
% 5.64/5.90 thf(fact_3643_atLeastatMost__empty__iff,axiom,
% 5.64/5.90 ! [A: nat,B: nat] :
% 5.64/5.90 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.64/5.90 = bot_bot_set_nat )
% 5.64/5.90 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff
% 5.64/5.90 thf(fact_3644_atLeastatMost__empty__iff,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.64/5.90 = bot_bot_set_int )
% 5.64/5.90 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff
% 5.64/5.90 thf(fact_3645_atLeastatMost__empty__iff,axiom,
% 5.64/5.90 ! [A: real,B: real] :
% 5.64/5.90 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.64/5.90 = bot_bot_set_real )
% 5.64/5.90 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff
% 5.64/5.90 thf(fact_3646_atLeastatMost__empty__iff2,axiom,
% 5.64/5.90 ! [A: set_nat,B: set_nat] :
% 5.64/5.90 ( ( bot_bot_set_set_nat
% 5.64/5.90 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff2
% 5.64/5.90 thf(fact_3647_atLeastatMost__empty__iff2,axiom,
% 5.64/5.90 ! [A: rat,B: rat] :
% 5.64/5.90 ( ( bot_bot_set_rat
% 5.64/5.90 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff2
% 5.64/5.90 thf(fact_3648_atLeastatMost__empty__iff2,axiom,
% 5.64/5.90 ! [A: num,B: num] :
% 5.64/5.90 ( ( bot_bot_set_num
% 5.64/5.90 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff2
% 5.64/5.90 thf(fact_3649_atLeastatMost__empty__iff2,axiom,
% 5.64/5.90 ! [A: nat,B: nat] :
% 5.64/5.90 ( ( bot_bot_set_nat
% 5.64/5.90 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff2
% 5.64/5.90 thf(fact_3650_atLeastatMost__empty__iff2,axiom,
% 5.64/5.90 ! [A: int,B: int] :
% 5.64/5.90 ( ( bot_bot_set_int
% 5.64/5.90 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff2
% 5.64/5.90 thf(fact_3651_atLeastatMost__empty__iff2,axiom,
% 5.64/5.90 ! [A: real,B: real] :
% 5.64/5.90 ( ( bot_bot_set_real
% 5.64/5.90 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.64/5.90 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastatMost_empty_iff2
% 5.64/5.90 thf(fact_3652_decr__mult__lemma,axiom,
% 5.64/5.90 ! [D: int,P: int > $o,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.90 => ( ! [X4: int] :
% 5.64/5.90 ( ( P @ X4 )
% 5.64/5.90 => ( P @ ( minus_minus_int @ X4 @ D ) ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.90 => ! [X3: int] :
% 5.64/5.90 ( ( P @ X3 )
% 5.64/5.90 => ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % decr_mult_lemma
% 5.64/5.90 thf(fact_3653_incr__mult__lemma,axiom,
% 5.64/5.90 ! [D: int,P: int > $o,K: int] :
% 5.64/5.90 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.90 => ( ! [X4: int] :
% 5.64/5.90 ( ( P @ X4 )
% 5.64/5.90 => ( P @ ( plus_plus_int @ X4 @ D ) ) )
% 5.64/5.90 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.90 => ! [X3: int] :
% 5.64/5.90 ( ( P @ X3 )
% 5.64/5.90 => ( P @ ( plus_plus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % incr_mult_lemma
% 5.64/5.90 thf(fact_3654_atLeastAtMost__iff,axiom,
% 5.64/5.90 ! [I: set_nat,L: set_nat,U: set_nat] :
% 5.64/5.90 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.64/5.90 = ( ( ord_less_eq_set_nat @ L @ I )
% 5.64/5.90 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastAtMost_iff
% 5.64/5.90 thf(fact_3655_atLeastAtMost__iff,axiom,
% 5.64/5.90 ! [I: rat,L: rat,U: rat] :
% 5.64/5.90 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.64/5.90 = ( ( ord_less_eq_rat @ L @ I )
% 5.64/5.90 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastAtMost_iff
% 5.64/5.90 thf(fact_3656_atLeastAtMost__iff,axiom,
% 5.64/5.90 ! [I: num,L: num,U: num] :
% 5.64/5.90 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.64/5.90 = ( ( ord_less_eq_num @ L @ I )
% 5.64/5.90 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastAtMost_iff
% 5.64/5.90 thf(fact_3657_atLeastAtMost__iff,axiom,
% 5.64/5.90 ! [I: nat,L: nat,U: nat] :
% 5.64/5.90 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.64/5.90 = ( ( ord_less_eq_nat @ L @ I )
% 5.64/5.90 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastAtMost_iff
% 5.64/5.90 thf(fact_3658_atLeastAtMost__iff,axiom,
% 5.64/5.90 ! [I: int,L: int,U: int] :
% 5.64/5.90 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.64/5.90 = ( ( ord_less_eq_int @ L @ I )
% 5.64/5.90 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastAtMost_iff
% 5.64/5.90 thf(fact_3659_atLeastAtMost__iff,axiom,
% 5.64/5.90 ! [I: real,L: real,U: real] :
% 5.64/5.90 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.64/5.90 = ( ( ord_less_eq_real @ L @ I )
% 5.64/5.90 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % atLeastAtMost_iff
% 5.64/5.90 thf(fact_3660_Icc__eq__Icc,axiom,
% 5.64/5.90 ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.64/5.90 ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 5.64/5.90 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.64/5.90 = ( ( ( L = L3 )
% 5.64/5.90 & ( H2 = H3 ) )
% 5.64/5.90 | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.64/5.90 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Icc_eq_Icc
% 5.64/5.90 thf(fact_3661_Icc__eq__Icc,axiom,
% 5.64/5.90 ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 5.64/5.90 ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 5.64/5.90 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.64/5.90 = ( ( ( L = L3 )
% 5.64/5.90 & ( H2 = H3 ) )
% 5.64/5.90 | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.64/5.90 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Icc_eq_Icc
% 5.64/5.90 thf(fact_3662_Icc__eq__Icc,axiom,
% 5.64/5.90 ! [L: num,H2: num,L3: num,H3: num] :
% 5.64/5.90 ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 5.64/5.90 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.64/5.90 = ( ( ( L = L3 )
% 5.64/5.90 & ( H2 = H3 ) )
% 5.64/5.90 | ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.64/5.90 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Icc_eq_Icc
% 5.64/5.90 thf(fact_3663_Icc__eq__Icc,axiom,
% 5.64/5.90 ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 5.64/5.90 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 5.64/5.90 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.64/5.90 = ( ( ( L = L3 )
% 5.64/5.90 & ( H2 = H3 ) )
% 5.64/5.90 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.64/5.90 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Icc_eq_Icc
% 5.64/5.90 thf(fact_3664_Icc__eq__Icc,axiom,
% 5.64/5.90 ! [L: int,H2: int,L3: int,H3: int] :
% 5.64/5.90 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 5.64/5.90 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.64/5.90 = ( ( ( L = L3 )
% 5.64/5.90 & ( H2 = H3 ) )
% 5.64/5.90 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.64/5.90 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Icc_eq_Icc
% 5.64/5.90 thf(fact_3665_Icc__eq__Icc,axiom,
% 5.64/5.90 ! [L: real,H2: real,L3: real,H3: real] :
% 5.64/5.90 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 5.64/5.90 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.64/5.90 = ( ( ( L = L3 )
% 5.64/5.90 & ( H2 = H3 ) )
% 5.64/5.90 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.64/5.90 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % Icc_eq_Icc
% 5.64/5.90 thf(fact_3666_pinf_I1_J,axiom,
% 5.64/5.90 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.64/5.90 ( ? [Z5: real] :
% 5.64/5.90 ! [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: real] :
% 5.64/5.90 ! [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(1)
% 5.64/5.90 thf(fact_3667_pinf_I1_J,axiom,
% 5.64/5.90 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.64/5.90 ( ? [Z5: rat] :
% 5.64/5.90 ! [X4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: rat] :
% 5.64/5.90 ! [X4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(1)
% 5.64/5.90 thf(fact_3668_pinf_I1_J,axiom,
% 5.64/5.90 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.64/5.90 ( ? [Z5: num] :
% 5.64/5.90 ! [X4: num] :
% 5.64/5.90 ( ( ord_less_num @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: num] :
% 5.64/5.90 ! [X4: num] :
% 5.64/5.90 ( ( ord_less_num @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(1)
% 5.64/5.90 thf(fact_3669_pinf_I1_J,axiom,
% 5.64/5.90 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.64/5.90 ( ? [Z5: nat] :
% 5.64/5.90 ! [X4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: nat] :
% 5.64/5.90 ! [X4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(1)
% 5.64/5.90 thf(fact_3670_pinf_I1_J,axiom,
% 5.64/5.90 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.64/5.90 ( ? [Z5: int] :
% 5.64/5.90 ! [X4: int] :
% 5.64/5.90 ( ( ord_less_int @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: int] :
% 5.64/5.90 ! [X4: int] :
% 5.64/5.90 ( ( ord_less_int @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: int] :
% 5.64/5.90 ! [X3: int] :
% 5.64/5.90 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(1)
% 5.64/5.90 thf(fact_3671_pinf_I2_J,axiom,
% 5.64/5.90 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.64/5.90 ( ? [Z5: real] :
% 5.64/5.90 ! [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: real] :
% 5.64/5.90 ! [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 | ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(2)
% 5.64/5.90 thf(fact_3672_pinf_I2_J,axiom,
% 5.64/5.90 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.64/5.90 ( ? [Z5: rat] :
% 5.64/5.90 ! [X4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: rat] :
% 5.64/5.90 ! [X4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 | ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(2)
% 5.64/5.90 thf(fact_3673_pinf_I2_J,axiom,
% 5.64/5.90 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.64/5.90 ( ? [Z5: num] :
% 5.64/5.90 ! [X4: num] :
% 5.64/5.90 ( ( ord_less_num @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: num] :
% 5.64/5.90 ! [X4: num] :
% 5.64/5.90 ( ( ord_less_num @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 | ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(2)
% 5.64/5.90 thf(fact_3674_pinf_I2_J,axiom,
% 5.64/5.90 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.64/5.90 ( ? [Z5: nat] :
% 5.64/5.90 ! [X4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: nat] :
% 5.64/5.90 ! [X4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 | ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(2)
% 5.64/5.90 thf(fact_3675_pinf_I2_J,axiom,
% 5.64/5.90 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.64/5.90 ( ? [Z5: int] :
% 5.64/5.90 ! [X4: int] :
% 5.64/5.90 ( ( ord_less_int @ Z5 @ X4 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: int] :
% 5.64/5.90 ! [X4: int] :
% 5.64/5.90 ( ( ord_less_int @ Z5 @ X4 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: int] :
% 5.64/5.90 ! [X3: int] :
% 5.64/5.90 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 | ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(2)
% 5.64/5.90 thf(fact_3676_pinf_I3_J,axiom,
% 5.64/5.90 ! [T: real] :
% 5.64/5.90 ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(3)
% 5.64/5.90 thf(fact_3677_pinf_I3_J,axiom,
% 5.64/5.90 ! [T: rat] :
% 5.64/5.90 ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(3)
% 5.64/5.90 thf(fact_3678_pinf_I3_J,axiom,
% 5.64/5.90 ! [T: num] :
% 5.64/5.90 ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(3)
% 5.64/5.90 thf(fact_3679_pinf_I3_J,axiom,
% 5.64/5.90 ! [T: nat] :
% 5.64/5.90 ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(3)
% 5.64/5.90 thf(fact_3680_pinf_I3_J,axiom,
% 5.64/5.90 ! [T: int] :
% 5.64/5.90 ? [Z2: int] :
% 5.64/5.90 ! [X3: int] :
% 5.64/5.90 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(3)
% 5.64/5.90 thf(fact_3681_pinf_I4_J,axiom,
% 5.64/5.90 ! [T: real] :
% 5.64/5.90 ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(4)
% 5.64/5.90 thf(fact_3682_pinf_I4_J,axiom,
% 5.64/5.90 ! [T: rat] :
% 5.64/5.90 ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(4)
% 5.64/5.90 thf(fact_3683_pinf_I4_J,axiom,
% 5.64/5.90 ! [T: num] :
% 5.64/5.90 ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(4)
% 5.64/5.90 thf(fact_3684_pinf_I4_J,axiom,
% 5.64/5.90 ! [T: nat] :
% 5.64/5.90 ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(4)
% 5.64/5.90 thf(fact_3685_pinf_I4_J,axiom,
% 5.64/5.90 ! [T: int] :
% 5.64/5.90 ? [Z2: int] :
% 5.64/5.90 ! [X3: int] :
% 5.64/5.90 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.90 => ( X3 != T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(4)
% 5.64/5.90 thf(fact_3686_pinf_I5_J,axiom,
% 5.64/5.90 ! [T: real] :
% 5.64/5.90 ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.90 => ~ ( ord_less_real @ X3 @ T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(5)
% 5.64/5.90 thf(fact_3687_pinf_I5_J,axiom,
% 5.64/5.90 ! [T: rat] :
% 5.64/5.90 ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.90 => ~ ( ord_less_rat @ X3 @ T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(5)
% 5.64/5.90 thf(fact_3688_pinf_I5_J,axiom,
% 5.64/5.90 ! [T: num] :
% 5.64/5.90 ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.90 => ~ ( ord_less_num @ X3 @ T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(5)
% 5.64/5.90 thf(fact_3689_pinf_I5_J,axiom,
% 5.64/5.90 ! [T: nat] :
% 5.64/5.90 ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.90 => ~ ( ord_less_nat @ X3 @ T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(5)
% 5.64/5.90 thf(fact_3690_pinf_I5_J,axiom,
% 5.64/5.90 ! [T: int] :
% 5.64/5.90 ? [Z2: int] :
% 5.64/5.90 ! [X3: int] :
% 5.64/5.90 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.90 => ~ ( ord_less_int @ X3 @ T ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(5)
% 5.64/5.90 thf(fact_3691_pinf_I7_J,axiom,
% 5.64/5.90 ! [T: real] :
% 5.64/5.90 ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.90 => ( ord_less_real @ T @ X3 ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(7)
% 5.64/5.90 thf(fact_3692_pinf_I7_J,axiom,
% 5.64/5.90 ! [T: rat] :
% 5.64/5.90 ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.90 => ( ord_less_rat @ T @ X3 ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(7)
% 5.64/5.90 thf(fact_3693_pinf_I7_J,axiom,
% 5.64/5.90 ! [T: num] :
% 5.64/5.90 ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.90 => ( ord_less_num @ T @ X3 ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(7)
% 5.64/5.90 thf(fact_3694_pinf_I7_J,axiom,
% 5.64/5.90 ! [T: nat] :
% 5.64/5.90 ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.90 => ( ord_less_nat @ T @ X3 ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(7)
% 5.64/5.90 thf(fact_3695_pinf_I7_J,axiom,
% 5.64/5.90 ! [T: int] :
% 5.64/5.90 ? [Z2: int] :
% 5.64/5.90 ! [X3: int] :
% 5.64/5.90 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.90 => ( ord_less_int @ T @ X3 ) ) ).
% 5.64/5.90
% 5.64/5.90 % pinf(7)
% 5.64/5.90 thf(fact_3696_minf_I1_J,axiom,
% 5.64/5.90 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.64/5.90 ( ? [Z5: real] :
% 5.64/5.90 ! [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ X4 @ Z5 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: real] :
% 5.64/5.90 ! [X4: real] :
% 5.64/5.90 ( ( ord_less_real @ X4 @ Z5 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: real] :
% 5.64/5.90 ! [X3: real] :
% 5.64/5.90 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % minf(1)
% 5.64/5.90 thf(fact_3697_minf_I1_J,axiom,
% 5.64/5.90 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.64/5.90 ( ? [Z5: rat] :
% 5.64/5.90 ! [X4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ X4 @ Z5 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: rat] :
% 5.64/5.90 ! [X4: rat] :
% 5.64/5.90 ( ( ord_less_rat @ X4 @ Z5 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: rat] :
% 5.64/5.90 ! [X3: rat] :
% 5.64/5.90 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % minf(1)
% 5.64/5.90 thf(fact_3698_minf_I1_J,axiom,
% 5.64/5.90 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.64/5.90 ( ? [Z5: num] :
% 5.64/5.90 ! [X4: num] :
% 5.64/5.90 ( ( ord_less_num @ X4 @ Z5 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: num] :
% 5.64/5.90 ! [X4: num] :
% 5.64/5.90 ( ( ord_less_num @ X4 @ Z5 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: num] :
% 5.64/5.90 ! [X3: num] :
% 5.64/5.90 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.90 & ( Q @ X3 ) )
% 5.64/5.90 = ( ( P6 @ X3 )
% 5.64/5.90 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.90
% 5.64/5.90 % minf(1)
% 5.64/5.90 thf(fact_3699_minf_I1_J,axiom,
% 5.64/5.90 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.64/5.90 ( ? [Z5: nat] :
% 5.64/5.90 ! [X4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ X4 @ Z5 )
% 5.64/5.90 => ( ( P @ X4 )
% 5.64/5.90 = ( P6 @ X4 ) ) )
% 5.64/5.90 => ( ? [Z5: nat] :
% 5.64/5.90 ! [X4: nat] :
% 5.64/5.90 ( ( ord_less_nat @ X4 @ Z5 )
% 5.64/5.90 => ( ( Q @ X4 )
% 5.64/5.90 = ( Q6 @ X4 ) ) )
% 5.64/5.90 => ? [Z2: nat] :
% 5.64/5.90 ! [X3: nat] :
% 5.64/5.90 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.90 => ( ( ( P @ X3 )
% 5.64/5.91 & ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(1)
% 5.64/5.91 thf(fact_3700_minf_I1_J,axiom,
% 5.64/5.91 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.64/5.91 ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ X4 @ Z5 )
% 5.64/5.91 => ( ( Q @ X4 )
% 5.64/5.91 = ( Q6 @ X4 ) ) )
% 5.64/5.91 => ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ( ( ( P @ X3 )
% 5.64/5.91 & ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(1)
% 5.64/5.91 thf(fact_3701_minf_I2_J,axiom,
% 5.64/5.91 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.64/5.91 ( ? [Z5: real] :
% 5.64/5.91 ! [X4: real] :
% 5.64/5.91 ( ( ord_less_real @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [Z5: real] :
% 5.64/5.91 ! [X4: real] :
% 5.64/5.91 ( ( ord_less_real @ X4 @ Z5 )
% 5.64/5.91 => ( ( Q @ X4 )
% 5.64/5.91 = ( Q6 @ X4 ) ) )
% 5.64/5.91 => ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(2)
% 5.64/5.91 thf(fact_3702_minf_I2_J,axiom,
% 5.64/5.91 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.64/5.91 ( ? [Z5: rat] :
% 5.64/5.91 ! [X4: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [Z5: rat] :
% 5.64/5.91 ! [X4: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X4 @ Z5 )
% 5.64/5.91 => ( ( Q @ X4 )
% 5.64/5.91 = ( Q6 @ X4 ) ) )
% 5.64/5.91 => ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(2)
% 5.64/5.91 thf(fact_3703_minf_I2_J,axiom,
% 5.64/5.91 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.64/5.91 ( ? [Z5: num] :
% 5.64/5.91 ! [X4: num] :
% 5.64/5.91 ( ( ord_less_num @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [Z5: num] :
% 5.64/5.91 ! [X4: num] :
% 5.64/5.91 ( ( ord_less_num @ X4 @ Z5 )
% 5.64/5.91 => ( ( Q @ X4 )
% 5.64/5.91 = ( Q6 @ X4 ) ) )
% 5.64/5.91 => ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(2)
% 5.64/5.91 thf(fact_3704_minf_I2_J,axiom,
% 5.64/5.91 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.64/5.91 ( ? [Z5: nat] :
% 5.64/5.91 ! [X4: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [Z5: nat] :
% 5.64/5.91 ! [X4: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X4 @ Z5 )
% 5.64/5.91 => ( ( Q @ X4 )
% 5.64/5.91 = ( Q6 @ X4 ) ) )
% 5.64/5.91 => ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(2)
% 5.64/5.91 thf(fact_3705_minf_I2_J,axiom,
% 5.64/5.91 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.64/5.91 ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ X4 @ Z5 )
% 5.64/5.91 => ( ( Q @ X4 )
% 5.64/5.91 = ( Q6 @ X4 ) ) )
% 5.64/5.91 => ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P6 @ X3 )
% 5.64/5.91 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(2)
% 5.64/5.91 thf(fact_3706_minf_I3_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(3)
% 5.64/5.91 thf(fact_3707_minf_I3_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(3)
% 5.64/5.91 thf(fact_3708_minf_I3_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(3)
% 5.64/5.91 thf(fact_3709_minf_I3_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(3)
% 5.64/5.91 thf(fact_3710_minf_I3_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(3)
% 5.64/5.91 thf(fact_3711_minf_I4_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(4)
% 5.64/5.91 thf(fact_3712_minf_I4_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(4)
% 5.64/5.91 thf(fact_3713_minf_I4_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(4)
% 5.64/5.91 thf(fact_3714_minf_I4_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(4)
% 5.64/5.91 thf(fact_3715_minf_I4_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ( X3 != T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(4)
% 5.64/5.91 thf(fact_3716_minf_I5_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_real @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(5)
% 5.64/5.91 thf(fact_3717_minf_I5_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_rat @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(5)
% 5.64/5.91 thf(fact_3718_minf_I5_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_num @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(5)
% 5.64/5.91 thf(fact_3719_minf_I5_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_nat @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(5)
% 5.64/5.91 thf(fact_3720_minf_I5_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_int @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(5)
% 5.64/5.91 thf(fact_3721_minf_I7_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_real @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(7)
% 5.64/5.91 thf(fact_3722_minf_I7_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_rat @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(7)
% 5.64/5.91 thf(fact_3723_minf_I7_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_num @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(7)
% 5.64/5.91 thf(fact_3724_minf_I7_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_nat @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(7)
% 5.64/5.91 thf(fact_3725_minf_I7_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_int @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(7)
% 5.64/5.91 thf(fact_3726_bounded__Max__nat,axiom,
% 5.64/5.91 ! [P: nat > $o,X2: nat,M7: nat] :
% 5.64/5.91 ( ( P @ X2 )
% 5.64/5.91 => ( ! [X4: nat] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 => ( ord_less_eq_nat @ X4 @ M7 ) )
% 5.64/5.91 => ~ ! [M4: nat] :
% 5.64/5.91 ( ( P @ M4 )
% 5.64/5.91 => ~ ! [X3: nat] :
% 5.64/5.91 ( ( P @ X3 )
% 5.64/5.91 => ( ord_less_eq_nat @ X3 @ M4 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bounded_Max_nat
% 5.64/5.91 thf(fact_3727_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.64/5.91 ! [X2: produc3368934014287244435at_num] :
% 5.64/5.91 ~ ! [F2: nat > num > num,A5: nat,B5: nat,Acc: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % fold_atLeastAtMost_nat.cases
% 5.64/5.91 thf(fact_3728_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.64/5.91 ! [X2: produc4471711990508489141at_nat] :
% 5.64/5.91 ~ ! [F2: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % fold_atLeastAtMost_nat.cases
% 5.64/5.91 thf(fact_3729_periodic__finite__ex,axiom,
% 5.64/5.91 ! [D: int,P: int > $o] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.64/5.91 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.64/5.91 = ( ? [X: int] :
% 5.64/5.91 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.64/5.91 & ( P @ X ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % periodic_finite_ex
% 5.64/5.91 thf(fact_3730_bset_I3_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,B4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ B4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( X3 = T )
% 5.64/5.91 => ( ( minus_minus_int @ X3 @ D4 )
% 5.64/5.91 = T ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bset(3)
% 5.64/5.91 thf(fact_3731_bset_I4_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,B4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ T @ B4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ B4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( X3 != T )
% 5.64/5.91 => ( ( minus_minus_int @ X3 @ D4 )
% 5.64/5.91 != T ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bset(4)
% 5.64/5.91 thf(fact_3732_bset_I5_J,axiom,
% 5.64/5.91 ! [D4: int,B4: set_int,T: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ B4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_int @ X3 @ T )
% 5.64/5.91 => ( ord_less_int @ ( minus_minus_int @ X3 @ D4 ) @ T ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bset(5)
% 5.64/5.91 thf(fact_3733_bset_I7_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,B4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ T @ B4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ B4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_int @ T @ X3 )
% 5.64/5.91 => ( ord_less_int @ T @ ( minus_minus_int @ X3 @ D4 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bset(7)
% 5.64/5.91 thf(fact_3734_aset_I3_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,A4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ A4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( X3 = T )
% 5.64/5.91 => ( ( plus_plus_int @ X3 @ D4 )
% 5.64/5.91 = T ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % aset(3)
% 5.64/5.91 thf(fact_3735_aset_I4_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,A4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ T @ A4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ A4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( X3 != T )
% 5.64/5.91 => ( ( plus_plus_int @ X3 @ D4 )
% 5.64/5.91 != T ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % aset(4)
% 5.64/5.91 thf(fact_3736_aset_I5_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,A4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ T @ A4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ A4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_int @ X3 @ T )
% 5.64/5.91 => ( ord_less_int @ ( plus_plus_int @ X3 @ D4 ) @ T ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % aset(5)
% 5.64/5.91 thf(fact_3737_aset_I7_J,axiom,
% 5.64/5.91 ! [D4: int,A4: set_int,T: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ A4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_int @ T @ X3 )
% 5.64/5.91 => ( ord_less_int @ T @ ( plus_plus_int @ X3 @ D4 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % aset(7)
% 5.64/5.91 thf(fact_3738_bset_I6_J,axiom,
% 5.64/5.91 ! [D4: int,B4: set_int,T: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ B4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_eq_int @ X3 @ T )
% 5.64/5.91 => ( ord_less_eq_int @ ( minus_minus_int @ X3 @ D4 ) @ T ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bset(6)
% 5.64/5.91 thf(fact_3739_bset_I8_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,B4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ B4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_eq_int @ T @ X3 )
% 5.64/5.91 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X3 @ D4 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % bset(8)
% 5.64/5.91 thf(fact_3740_aset_I6_J,axiom,
% 5.64/5.91 ! [D4: int,T: int,A4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ A4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_eq_int @ X3 @ T )
% 5.64/5.91 => ( ord_less_eq_int @ ( plus_plus_int @ X3 @ D4 ) @ T ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % aset(6)
% 5.64/5.91 thf(fact_3741_aset_I8_J,axiom,
% 5.64/5.91 ! [D4: int,A4: set_int,T: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ! [X3: int] :
% 5.64/5.91 ( ! [Xa3: int] :
% 5.64/5.91 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb2: int] :
% 5.64/5.91 ( ( member_int @ Xb2 @ A4 )
% 5.64/5.91 => ( X3
% 5.64/5.91 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.64/5.91 => ( ( ord_less_eq_int @ T @ X3 )
% 5.64/5.91 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X3 @ D4 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % aset(8)
% 5.64/5.91 thf(fact_3742_cppi,axiom,
% 5.64/5.91 ! [D4: int,P: int > $o,P6: int > $o,A4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ Z5 @ X4 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ! [X4: int] :
% 5.64/5.91 ( ! [Xa: int] :
% 5.64/5.91 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb3: int] :
% 5.64/5.91 ( ( member_int @ Xb3 @ A4 )
% 5.64/5.91 => ( X4
% 5.64/5.91 != ( minus_minus_int @ Xb3 @ Xa ) ) ) )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 => ( P @ ( plus_plus_int @ X4 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P6 @ X4 )
% 5.64/5.91 = ( P6 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.64/5.91 = ( ? [X: int] :
% 5.64/5.91 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 & ( P6 @ X ) )
% 5.64/5.91 | ? [X: int] :
% 5.64/5.91 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 & ? [Y: int] :
% 5.64/5.91 ( ( member_int @ Y @ A4 )
% 5.64/5.91 & ( P @ ( minus_minus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cppi
% 5.64/5.91 thf(fact_3743_cpmi,axiom,
% 5.64/5.91 ! [D4: int,P: int > $o,P6: int > $o,B4: set_int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.64/5.91 => ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ! [X4: int] :
% 5.64/5.91 ( ! [Xa: int] :
% 5.64/5.91 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 => ! [Xb3: int] :
% 5.64/5.91 ( ( member_int @ Xb3 @ B4 )
% 5.64/5.91 => ( X4
% 5.64/5.91 != ( plus_plus_int @ Xb3 @ Xa ) ) ) )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 => ( P @ ( minus_minus_int @ X4 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P6 @ X4 )
% 5.64/5.91 = ( P6 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ( ? [X5: int] : ( P @ X5 ) )
% 5.64/5.91 = ( ? [X: int] :
% 5.64/5.91 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 & ( P6 @ X ) )
% 5.64/5.91 | ? [X: int] :
% 5.64/5.91 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.64/5.91 & ? [Y: int] :
% 5.64/5.91 ( ( member_int @ Y @ B4 )
% 5.64/5.91 & ( P @ ( plus_plus_int @ Y @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cpmi
% 5.64/5.91 thf(fact_3744_minf_I8_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_eq_rat @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(8)
% 5.64/5.91 thf(fact_3745_minf_I8_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_eq_num @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(8)
% 5.64/5.91 thf(fact_3746_minf_I8_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_eq_nat @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(8)
% 5.64/5.91 thf(fact_3747_minf_I8_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_eq_int @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(8)
% 5.64/5.91 thf(fact_3748_minf_I8_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ~ ( ord_less_eq_real @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(8)
% 5.64/5.91 thf(fact_3749_minf_I6_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_eq_rat @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(6)
% 5.64/5.91 thf(fact_3750_minf_I6_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_eq_num @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(6)
% 5.64/5.91 thf(fact_3751_minf_I6_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_eq_nat @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(6)
% 5.64/5.91 thf(fact_3752_minf_I6_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_eq_int @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(6)
% 5.64/5.91 thf(fact_3753_minf_I6_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.91 => ( ord_less_eq_real @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % minf(6)
% 5.64/5.91 thf(fact_3754_pinf_I8_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.91 => ( ord_less_eq_rat @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(8)
% 5.64/5.91 thf(fact_3755_pinf_I8_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.91 => ( ord_less_eq_num @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(8)
% 5.64/5.91 thf(fact_3756_pinf_I8_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.91 => ( ord_less_eq_nat @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(8)
% 5.64/5.91 thf(fact_3757_pinf_I8_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.91 => ( ord_less_eq_int @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(8)
% 5.64/5.91 thf(fact_3758_pinf_I8_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.91 => ( ord_less_eq_real @ T @ X3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(8)
% 5.64/5.91 thf(fact_3759_pinf_I6_J,axiom,
% 5.64/5.91 ! [T: rat] :
% 5.64/5.91 ? [Z2: rat] :
% 5.64/5.91 ! [X3: rat] :
% 5.64/5.91 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.91 => ~ ( ord_less_eq_rat @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(6)
% 5.64/5.91 thf(fact_3760_pinf_I6_J,axiom,
% 5.64/5.91 ! [T: num] :
% 5.64/5.91 ? [Z2: num] :
% 5.64/5.91 ! [X3: num] :
% 5.64/5.91 ( ( ord_less_num @ Z2 @ X3 )
% 5.64/5.91 => ~ ( ord_less_eq_num @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(6)
% 5.64/5.91 thf(fact_3761_pinf_I6_J,axiom,
% 5.64/5.91 ! [T: nat] :
% 5.64/5.91 ? [Z2: nat] :
% 5.64/5.91 ! [X3: nat] :
% 5.64/5.91 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.91 => ~ ( ord_less_eq_nat @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(6)
% 5.64/5.91 thf(fact_3762_pinf_I6_J,axiom,
% 5.64/5.91 ! [T: int] :
% 5.64/5.91 ? [Z2: int] :
% 5.64/5.91 ! [X3: int] :
% 5.64/5.91 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.91 => ~ ( ord_less_eq_int @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(6)
% 5.64/5.91 thf(fact_3763_pinf_I6_J,axiom,
% 5.64/5.91 ! [T: real] :
% 5.64/5.91 ? [Z2: real] :
% 5.64/5.91 ! [X3: real] :
% 5.64/5.91 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.91 => ~ ( ord_less_eq_real @ X3 @ T ) ) ).
% 5.64/5.91
% 5.64/5.91 % pinf(6)
% 5.64/5.91 thf(fact_3764_inf__period_I1_J,axiom,
% 5.64/5.91 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.64/5.91 ( ! [X4: real,K3: real] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: real,K3: real] :
% 5.64/5.91 ( ( Q @ X4 )
% 5.64/5.91 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ! [X3: real,K4: real] :
% 5.64/5.91 ( ( ( P @ X3 )
% 5.64/5.91 & ( Q @ X3 ) )
% 5.64/5.91 = ( ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.64/5.91 & ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % inf_period(1)
% 5.64/5.91 thf(fact_3765_inf__period_I1_J,axiom,
% 5.64/5.91 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.64/5.91 ( ! [X4: rat,K3: rat] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: rat,K3: rat] :
% 5.64/5.91 ( ( Q @ X4 )
% 5.64/5.91 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ! [X3: rat,K4: rat] :
% 5.64/5.91 ( ( ( P @ X3 )
% 5.64/5.91 & ( Q @ X3 ) )
% 5.64/5.91 = ( ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.64/5.91 & ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % inf_period(1)
% 5.64/5.91 thf(fact_3766_inf__period_I1_J,axiom,
% 5.64/5.91 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.64/5.91 ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( Q @ X4 )
% 5.64/5.91 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ! [X3: int,K4: int] :
% 5.64/5.91 ( ( ( P @ X3 )
% 5.64/5.91 & ( Q @ X3 ) )
% 5.64/5.91 = ( ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.64/5.91 & ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % inf_period(1)
% 5.64/5.91 thf(fact_3767_inf__period_I2_J,axiom,
% 5.64/5.91 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.64/5.91 ( ! [X4: real,K3: real] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: real,K3: real] :
% 5.64/5.91 ( ( Q @ X4 )
% 5.64/5.91 = ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ! [X3: real,K4: real] :
% 5.64/5.91 ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.64/5.91 | ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % inf_period(2)
% 5.64/5.91 thf(fact_3768_inf__period_I2_J,axiom,
% 5.64/5.91 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.64/5.91 ( ! [X4: rat,K3: rat] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: rat,K3: rat] :
% 5.64/5.91 ( ( Q @ X4 )
% 5.64/5.91 = ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ! [X3: rat,K4: rat] :
% 5.64/5.91 ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.64/5.91 | ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % inf_period(2)
% 5.64/5.91 thf(fact_3769_inf__period_I2_J,axiom,
% 5.64/5.91 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.64/5.91 ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P @ X4 )
% 5.64/5.91 = ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( Q @ X4 )
% 5.64/5.91 = ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.64/5.91 => ! [X3: int,K4: int] :
% 5.64/5.91 ( ( ( P @ X3 )
% 5.64/5.91 | ( Q @ X3 ) )
% 5.64/5.91 = ( ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.64/5.91 | ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % inf_period(2)
% 5.64/5.91 thf(fact_3770_atLeastatMost__psubset__iff,axiom,
% 5.64/5.91 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.64/5.91 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.64/5.91 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.64/5.91 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.64/5.91 & ( ord_less_eq_set_nat @ B @ D )
% 5.64/5.91 & ( ( ord_less_set_nat @ C @ A )
% 5.64/5.91 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.64/5.91 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % atLeastatMost_psubset_iff
% 5.64/5.91 thf(fact_3771_atLeastatMost__psubset__iff,axiom,
% 5.64/5.91 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.91 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.64/5.91 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.64/5.91 | ( ( ord_less_eq_rat @ C @ A )
% 5.64/5.91 & ( ord_less_eq_rat @ B @ D )
% 5.64/5.91 & ( ( ord_less_rat @ C @ A )
% 5.64/5.91 | ( ord_less_rat @ B @ D ) ) ) )
% 5.64/5.91 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % atLeastatMost_psubset_iff
% 5.64/5.91 thf(fact_3772_atLeastatMost__psubset__iff,axiom,
% 5.64/5.91 ! [A: num,B: num,C: num,D: num] :
% 5.64/5.91 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.64/5.91 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.64/5.91 | ( ( ord_less_eq_num @ C @ A )
% 5.64/5.91 & ( ord_less_eq_num @ B @ D )
% 5.64/5.91 & ( ( ord_less_num @ C @ A )
% 5.64/5.91 | ( ord_less_num @ B @ D ) ) ) )
% 5.64/5.91 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % atLeastatMost_psubset_iff
% 5.64/5.91 thf(fact_3773_atLeastatMost__psubset__iff,axiom,
% 5.64/5.91 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.64/5.91 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.64/5.91 | ( ( ord_less_eq_nat @ C @ A )
% 5.64/5.91 & ( ord_less_eq_nat @ B @ D )
% 5.64/5.91 & ( ( ord_less_nat @ C @ A )
% 5.64/5.91 | ( ord_less_nat @ B @ D ) ) ) )
% 5.64/5.91 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % atLeastatMost_psubset_iff
% 5.64/5.91 thf(fact_3774_atLeastatMost__psubset__iff,axiom,
% 5.64/5.91 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.91 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.64/5.91 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.64/5.91 | ( ( ord_less_eq_int @ C @ A )
% 5.64/5.91 & ( ord_less_eq_int @ B @ D )
% 5.64/5.91 & ( ( ord_less_int @ C @ A )
% 5.64/5.91 | ( ord_less_int @ B @ D ) ) ) )
% 5.64/5.91 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % atLeastatMost_psubset_iff
% 5.64/5.91 thf(fact_3775_atLeastatMost__psubset__iff,axiom,
% 5.64/5.91 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.91 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.64/5.91 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.64/5.91 | ( ( ord_less_eq_real @ C @ A )
% 5.64/5.91 & ( ord_less_eq_real @ B @ D )
% 5.64/5.91 & ( ( ord_less_real @ C @ A )
% 5.64/5.91 | ( ord_less_real @ B @ D ) ) ) )
% 5.64/5.91 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % atLeastatMost_psubset_iff
% 5.64/5.91 thf(fact_3776_minusinfinity,axiom,
% 5.64/5.91 ! [D: int,P1: int > $o,P: int > $o] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P1 @ X4 )
% 5.64/5.91 = ( P1 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.64/5.91 => ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ X4 @ Z5 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P1 @ X4 ) ) )
% 5.64/5.91 => ( ? [X_1: int] : ( P1 @ X_1 )
% 5.64/5.91 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % minusinfinity
% 5.64/5.91 thf(fact_3777_plusinfinity,axiom,
% 5.64/5.91 ! [D: int,P6: int > $o,P: int > $o] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.91 => ( ! [X4: int,K3: int] :
% 5.64/5.91 ( ( P6 @ X4 )
% 5.64/5.91 = ( P6 @ ( minus_minus_int @ X4 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.64/5.91 => ( ? [Z5: int] :
% 5.64/5.91 ! [X4: int] :
% 5.64/5.91 ( ( ord_less_int @ Z5 @ X4 )
% 5.64/5.91 => ( ( P @ X4 )
% 5.64/5.91 = ( P6 @ X4 ) ) )
% 5.64/5.91 => ( ? [X_1: int] : ( P6 @ X_1 )
% 5.64/5.91 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % plusinfinity
% 5.64/5.91 thf(fact_3778_Bolzano,axiom,
% 5.64/5.91 ! [A: real,B: real,P: real > real > $o] :
% 5.64/5.91 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.91 => ( ! [A5: real,B5: real,C3: real] :
% 5.64/5.91 ( ( P @ A5 @ B5 )
% 5.64/5.91 => ( ( P @ B5 @ C3 )
% 5.64/5.91 => ( ( ord_less_eq_real @ A5 @ B5 )
% 5.64/5.91 => ( ( ord_less_eq_real @ B5 @ C3 )
% 5.64/5.91 => ( P @ A5 @ C3 ) ) ) ) )
% 5.64/5.91 => ( ! [X4: real] :
% 5.64/5.91 ( ( ord_less_eq_real @ A @ X4 )
% 5.64/5.91 => ( ( ord_less_eq_real @ X4 @ B )
% 5.64/5.91 => ? [D5: real] :
% 5.64/5.91 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.64/5.91 & ! [A5: real,B5: real] :
% 5.64/5.91 ( ( ( ord_less_eq_real @ A5 @ X4 )
% 5.64/5.91 & ( ord_less_eq_real @ X4 @ B5 )
% 5.64/5.91 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 5.64/5.91 => ( P @ A5 @ B5 ) ) ) ) )
% 5.64/5.91 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % Bolzano
% 5.64/5.91 thf(fact_3779_mult__le__cancel__iff2,axiom,
% 5.64/5.91 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.91 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.64/5.91 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y4 ) )
% 5.64/5.91 = ( ord_less_eq_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_le_cancel_iff2
% 5.64/5.91 thf(fact_3780_mult__le__cancel__iff2,axiom,
% 5.64/5.91 ! [Z: int,X2: int,Y4: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.91 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y4 ) )
% 5.64/5.91 = ( ord_less_eq_int @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_le_cancel_iff2
% 5.64/5.91 thf(fact_3781_mult__le__cancel__iff2,axiom,
% 5.64/5.91 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.91 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.64/5.91 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y4 ) )
% 5.64/5.91 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_le_cancel_iff2
% 5.64/5.91 thf(fact_3782_mult__le__cancel__iff1,axiom,
% 5.64/5.91 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.91 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.64/5.91 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y4 @ Z ) )
% 5.64/5.91 = ( ord_less_eq_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_le_cancel_iff1
% 5.64/5.91 thf(fact_3783_mult__le__cancel__iff1,axiom,
% 5.64/5.91 ! [Z: int,X2: int,Y4: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.91 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y4 @ Z ) )
% 5.64/5.91 = ( ord_less_eq_int @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_le_cancel_iff1
% 5.64/5.91 thf(fact_3784_mult__le__cancel__iff1,axiom,
% 5.64/5.91 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.91 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.64/5.91 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y4 @ Z ) )
% 5.64/5.91 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_le_cancel_iff1
% 5.64/5.91 thf(fact_3785_divides__aux__eq,axiom,
% 5.64/5.91 ! [Q3: nat,R2: nat] :
% 5.64/5.91 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R2 ) )
% 5.64/5.91 = ( R2 = zero_zero_nat ) ) ).
% 5.64/5.91
% 5.64/5.91 % divides_aux_eq
% 5.64/5.91 thf(fact_3786_divides__aux__eq,axiom,
% 5.64/5.91 ! [Q3: int,R2: int] :
% 5.64/5.91 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.91 = ( R2 = zero_zero_int ) ) ).
% 5.64/5.91
% 5.64/5.91 % divides_aux_eq
% 5.64/5.91 thf(fact_3787_neg__eucl__rel__int__mult__2,axiom,
% 5.64/5.91 ! [B: int,A: int,Q3: int,R2: int] :
% 5.64/5.91 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.64/5.91 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.91 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % neg_eucl_rel_int_mult_2
% 5.64/5.91 thf(fact_3788_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_num,Ys: list_num] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_num @ Xs2 ) @ ( size_size_list_num @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( product_Pair_num_num @ ( nth_num @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3789_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_Code_integer,Ys: list_o] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3790_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3791_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3792_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3793_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3794_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3795_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3796_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3797_product__nth,axiom,
% 5.64/5.91 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 5.64/5.91 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 5.64/5.91 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 5.64/5.91 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % product_nth
% 5.64/5.91 thf(fact_3798_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I1_J,axiom,
% 5.64/5.91 ! [A: $o,B: $o,X2: nat] :
% 5.64/5.91 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 5.64/5.91 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(1)
% 5.64/5.91 thf(fact_3799_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.64/5.91 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3800_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 5.64/5.91 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3801_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 5.64/5.91 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3802_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 5.64/5.91 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3803_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 5.64/5.91 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3804_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_o,Ys: list_o] :
% 5.64/5.91 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3805_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_o,Ys: list_nat] :
% 5.64/5.91 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3806_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_o,Ys: list_int] :
% 5.64/5.91 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3807_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 5.64/5.91 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3808_length__product,axiom,
% 5.64/5.91 ! [Xs2: list_nat,Ys: list_o] :
% 5.64/5.91 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 5.64/5.91 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % length_product
% 5.64/5.91 thf(fact_3809_div__int__unique,axiom,
% 5.64/5.91 ! [K: int,L: int,Q3: int,R2: int] :
% 5.64/5.91 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.91 => ( ( divide_divide_int @ K @ L )
% 5.64/5.91 = Q3 ) ) ).
% 5.64/5.91
% 5.64/5.91 % div_int_unique
% 5.64/5.91 thf(fact_3810_eucl__rel__int__dividesI,axiom,
% 5.64/5.91 ! [L: int,K: int,Q3: int] :
% 5.64/5.91 ( ( L != zero_zero_int )
% 5.64/5.91 => ( ( K
% 5.64/5.91 = ( times_times_int @ Q3 @ L ) )
% 5.64/5.91 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % eucl_rel_int_dividesI
% 5.64/5.91 thf(fact_3811_eucl__rel__int,axiom,
% 5.64/5.91 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % eucl_rel_int
% 5.64/5.91 thf(fact_3812_eucl__rel__int__iff,axiom,
% 5.64/5.91 ! [K: int,L: int,Q3: int,R2: int] :
% 5.64/5.91 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.91 = ( ( K
% 5.64/5.91 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R2 ) )
% 5.64/5.91 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.91 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 5.64/5.91 & ( ord_less_int @ R2 @ L ) ) )
% 5.64/5.91 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.64/5.91 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.64/5.91 => ( ( ord_less_int @ L @ R2 )
% 5.64/5.91 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 5.64/5.91 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.64/5.91 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % eucl_rel_int_iff
% 5.64/5.91 thf(fact_3813_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I2_J,axiom,
% 5.64/5.91 ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X2: nat] :
% 5.64/5.91 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X2 )
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(2)
% 5.64/5.91 thf(fact_3814_mult__less__iff1,axiom,
% 5.64/5.91 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.91 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.64/5.91 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y4 @ Z ) )
% 5.64/5.91 = ( ord_less_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_less_iff1
% 5.64/5.91 thf(fact_3815_mult__less__iff1,axiom,
% 5.64/5.91 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.91 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.64/5.91 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y4 @ Z ) )
% 5.64/5.91 = ( ord_less_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_less_iff1
% 5.64/5.91 thf(fact_3816_mult__less__iff1,axiom,
% 5.64/5.91 ! [Z: int,X2: int,Y4: int] :
% 5.64/5.91 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.91 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y4 @ Z ) )
% 5.64/5.91 = ( ord_less_int @ X2 @ Y4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mult_less_iff1
% 5.64/5.91 thf(fact_3817_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I3_J,axiom,
% 5.64/5.91 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 5.64/5.91 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 )
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(3)
% 5.64/5.91 thf(fact_3818_pos__eucl__rel__int__mult__2,axiom,
% 5.64/5.91 ! [B: int,A: int,Q3: int,R2: int] :
% 5.64/5.91 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.91 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.64/5.91 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % pos_eucl_rel_int_mult_2
% 5.64/5.91 thf(fact_3819_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I4_J,axiom,
% 5.64/5.91 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.64/5.91 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 )
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(4)
% 5.64/5.91 thf(fact_3820_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Oelims,axiom,
% 5.64/5.91 ! [X2: vEBT_VEBT,Xa2: nat,Y4: nat] :
% 5.64/5.91 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa2 )
% 5.64/5.91 = Y4 )
% 5.64/5.91 => ( ( ? [A5: $o,B5: $o] :
% 5.64/5.91 ( X2
% 5.64/5.91 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.91 => ( Y4
% 5.64/5.91 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ) )
% 5.64/5.91 => ( ( ? [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.91 ( X2
% 5.64/5.91 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.91 => ( Y4
% 5.64/5.91 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.91 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.91 ( X2
% 5.64/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.91 => ( Y4
% 5.64/5.91 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.91 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.91 ( X2
% 5.64/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.91 => ( Y4
% 5.64/5.91 != ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.91 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT] :
% 5.64/5.91 ( ? [Summary2: vEBT_VEBT] :
% 5.64/5.91 ( X2
% 5.64/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.91 => ( Y4
% 5.64/5.91 != ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.elims
% 5.64/5.91 thf(fact_3821_psubsetI,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat] :
% 5.64/5.91 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 5.64/5.91 => ( ( A4 != B4 )
% 5.64/5.91 => ( ord_less_set_nat @ A4 @ B4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetI
% 5.64/5.91 thf(fact_3822_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Osimps_I5_J,axiom,
% 5.64/5.91 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.91 ( ( vEBT_T_m_e_m_b_e_r @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.91 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( X2 = Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( X2 = Ma ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma @ X2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.simps(5)
% 5.64/5.91 thf(fact_3823_T_092_060_094sub_062m_092_060_094sub_062e_092_060_094sub_062m_092_060_094sub_062b_092_060_094sub_062e_092_060_094sub_062r_Opelims,axiom,
% 5.64/5.91 ! [X2: vEBT_VEBT,Xa2: nat,Y4: nat] :
% 5.64/5.91 ( ( ( vEBT_T_m_e_m_b_e_r @ X2 @ Xa2 )
% 5.64/5.91 = Y4 )
% 5.64/5.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.91 => ( ! [A5: $o,B5: $o] :
% 5.64/5.91 ( ( X2
% 5.64/5.91 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.91 => ( ( Y4
% 5.64/5.91 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = zero_zero_nat ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) )
% 5.64/5.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.64/5.91 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/5.91 ( ( X2
% 5.64/5.91 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/5.91 => ( ( Y4
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ Xa2 ) ) ) )
% 5.64/5.91 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/5.91 ( ( X2
% 5.64/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.64/5.91 => ( ( Y4
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.64/5.91 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/5.91 ( ( X2
% 5.64/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.64/5.91 => ( ( Y4
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.64/5.91 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.91 ( ( X2
% 5.64/5.91 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.91 => ( ( Y4
% 5.64/5.91 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( if_nat @ ( Xa2 = Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( Xa2 = Ma2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ one_one_nat @ ( plus_plus_nat @ one_one_nat @ ( if_nat @ ( ord_less_nat @ Ma2 @ Xa2 ) @ one_one_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) @ ( if_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_T_m_e_m_b_e_r @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_nat ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_T5837161174952499735_r_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % T\<^sub>m\<^sub>e\<^sub>m\<^sub>b\<^sub>e\<^sub>r.pelims
% 5.64/5.91 thf(fact_3824_obtain__set__pred,axiom,
% 5.64/5.91 ! [Z: nat,X2: nat,A4: set_nat] :
% 5.64/5.91 ( ( ord_less_nat @ Z @ X2 )
% 5.64/5.91 => ( ( vEBT_VEBT_min_in_set @ A4 @ Z )
% 5.64/5.91 => ( ( finite_finite_nat @ A4 )
% 5.64/5.91 => ? [X_12: nat] : ( vEBT_is_pred_in_set @ A4 @ X2 @ X_12 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % obtain_set_pred
% 5.64/5.91 thf(fact_3825_obtain__set__succ,axiom,
% 5.64/5.91 ! [X2: nat,Z: nat,A4: set_nat,B4: set_nat] :
% 5.64/5.91 ( ( ord_less_nat @ X2 @ Z )
% 5.64/5.91 => ( ( vEBT_VEBT_max_in_set @ A4 @ Z )
% 5.64/5.91 => ( ( finite_finite_nat @ B4 )
% 5.64/5.91 => ( ( A4 = B4 )
% 5.64/5.91 => ? [X_12: nat] : ( vEBT_is_succ_in_set @ A4 @ X2 @ X_12 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % obtain_set_succ
% 5.64/5.91 thf(fact_3826_VEBT__internal_Oheight_Osimps_I1_J,axiom,
% 5.64/5.91 ! [A: $o,B: $o] :
% 5.64/5.91 ( ( vEBT_VEBT_height @ ( vEBT_Leaf @ A @ B ) )
% 5.64/5.91 = zero_zero_nat ) ).
% 5.64/5.91
% 5.64/5.91 % VEBT_internal.height.simps(1)
% 5.64/5.91 thf(fact_3827_set__vebt__finite,axiom,
% 5.64/5.91 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.91 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % set_vebt_finite
% 5.64/5.91 thf(fact_3828_succ__none__empty,axiom,
% 5.64/5.91 ! [Xs2: set_nat,A: nat] :
% 5.64/5.91 ( ~ ? [X_12: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_12 )
% 5.64/5.91 => ( ( finite_finite_nat @ Xs2 )
% 5.64/5.91 => ~ ? [X3: nat] :
% 5.64/5.91 ( ( member_nat @ X3 @ Xs2 )
% 5.64/5.91 & ( ord_less_nat @ A @ X3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % succ_none_empty
% 5.64/5.91 thf(fact_3829_pred__none__empty,axiom,
% 5.64/5.91 ! [Xs2: set_nat,A: nat] :
% 5.64/5.91 ( ~ ? [X_12: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_12 )
% 5.64/5.91 => ( ( finite_finite_nat @ Xs2 )
% 5.64/5.91 => ~ ? [X3: nat] :
% 5.64/5.91 ( ( member_nat @ X3 @ Xs2 )
% 5.64/5.91 & ( ord_less_nat @ X3 @ A ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % pred_none_empty
% 5.64/5.91 thf(fact_3830_verit__eq__simplify_I9_J,axiom,
% 5.64/5.91 ! [X32: num,Y32: num] :
% 5.64/5.91 ( ( ( bit1 @ X32 )
% 5.64/5.91 = ( bit1 @ Y32 ) )
% 5.64/5.91 = ( X32 = Y32 ) ) ).
% 5.64/5.91
% 5.64/5.91 % verit_eq_simplify(9)
% 5.64/5.91 thf(fact_3831_semiring__norm_I90_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( bit1 @ M )
% 5.64/5.91 = ( bit1 @ N ) )
% 5.64/5.91 = ( M = N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(90)
% 5.64/5.91 thf(fact_3832_semiring__norm_I88_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( bit0 @ M )
% 5.64/5.91 != ( bit1 @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(88)
% 5.64/5.91 thf(fact_3833_semiring__norm_I89_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( bit1 @ M )
% 5.64/5.91 != ( bit0 @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(89)
% 5.64/5.91 thf(fact_3834_semiring__norm_I84_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( one
% 5.64/5.91 != ( bit1 @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(84)
% 5.64/5.91 thf(fact_3835_semiring__norm_I86_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ( ( bit1 @ M )
% 5.64/5.91 != one ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(86)
% 5.64/5.91 thf(fact_3836_List_Ofinite__set,axiom,
% 5.64/5.91 ! [Xs2: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) ).
% 5.64/5.91
% 5.64/5.91 % List.finite_set
% 5.64/5.91 thf(fact_3837_List_Ofinite__set,axiom,
% 5.64/5.91 ! [Xs2: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs2 ) ) ).
% 5.64/5.91
% 5.64/5.91 % List.finite_set
% 5.64/5.91 thf(fact_3838_List_Ofinite__set,axiom,
% 5.64/5.91 ! [Xs2: list_int] : ( finite_finite_int @ ( set_int2 @ Xs2 ) ) ).
% 5.64/5.91
% 5.64/5.91 % List.finite_set
% 5.64/5.91 thf(fact_3839_List_Ofinite__set,axiom,
% 5.64/5.91 ! [Xs2: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs2 ) ) ).
% 5.64/5.91
% 5.64/5.91 % List.finite_set
% 5.64/5.91 thf(fact_3840_semiring__norm_I80_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(80)
% 5.64/5.91 thf(fact_3841_semiring__norm_I73_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(73)
% 5.64/5.91 thf(fact_3842_infinite__Icc__iff,axiom,
% 5.64/5.91 ! [A: rat,B: rat] :
% 5.64/5.91 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.64/5.91 = ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.91
% 5.64/5.91 % infinite_Icc_iff
% 5.64/5.91 thf(fact_3843_infinite__Icc__iff,axiom,
% 5.64/5.91 ! [A: real,B: real] :
% 5.64/5.91 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.64/5.91 = ( ord_less_real @ A @ B ) ) ).
% 5.64/5.91
% 5.64/5.91 % infinite_Icc_iff
% 5.64/5.91 thf(fact_3844_semiring__norm_I7_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(7)
% 5.64/5.91 thf(fact_3845_semiring__norm_I9_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.91 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(9)
% 5.64/5.91 thf(fact_3846_semiring__norm_I15_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.91 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(15)
% 5.64/5.91 thf(fact_3847_semiring__norm_I14_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(14)
% 5.64/5.91 thf(fact_3848_semiring__norm_I81_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.91 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(81)
% 5.64/5.91 thf(fact_3849_semiring__norm_I72_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(72)
% 5.64/5.91 thf(fact_3850_semiring__norm_I77_J,axiom,
% 5.64/5.91 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(77)
% 5.64/5.91 thf(fact_3851_semiring__norm_I70_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(70)
% 5.64/5.91 thf(fact_3852_zdiv__numeral__Bit1,axiom,
% 5.64/5.91 ! [V: num,W: num] :
% 5.64/5.91 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.64/5.91 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % zdiv_numeral_Bit1
% 5.64/5.91 thf(fact_3853_semiring__norm_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.64/5.91 = ( bit1 @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(3)
% 5.64/5.91 thf(fact_3854_semiring__norm_I4_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.64/5.91 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(4)
% 5.64/5.91 thf(fact_3855_semiring__norm_I5_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.64/5.91 = ( bit1 @ M ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(5)
% 5.64/5.91 thf(fact_3856_semiring__norm_I8_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.64/5.91 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(8)
% 5.64/5.91 thf(fact_3857_semiring__norm_I10_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(10)
% 5.64/5.91 thf(fact_3858_semiring__norm_I16_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(16)
% 5.64/5.91 thf(fact_3859_semiring__norm_I79_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(79)
% 5.64/5.91 thf(fact_3860_semiring__norm_I74_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.91 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % semiring_norm(74)
% 5.64/5.91 thf(fact_3861_Suc__div__eq__add3__div__numeral,axiom,
% 5.64/5.91 ! [M: nat,V: num] :
% 5.64/5.91 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.91 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % Suc_div_eq_add3_div_numeral
% 5.64/5.91 thf(fact_3862_div__Suc__eq__div__add3,axiom,
% 5.64/5.91 ! [M: nat,N: nat] :
% 5.64/5.91 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.64/5.91 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % div_Suc_eq_div_add3
% 5.64/5.91 thf(fact_3863_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.64/5.91 ! [M: nat,V: num] :
% 5.64/5.91 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.91 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % Suc_mod_eq_add3_mod_numeral
% 5.64/5.91 thf(fact_3864_mod__Suc__eq__mod__add3,axiom,
% 5.64/5.91 ! [M: nat,N: nat] :
% 5.64/5.91 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.64/5.91 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mod_Suc_eq_mod_add3
% 5.64/5.91 thf(fact_3865_zmod__numeral__Bit1,axiom,
% 5.64/5.91 ! [V: num,W: num] :
% 5.64/5.91 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.64/5.91 = ( 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 ) ) ).
% 5.64/5.91
% 5.64/5.91 % zmod_numeral_Bit1
% 5.64/5.91 thf(fact_3866_verit__eq__simplify_I14_J,axiom,
% 5.64/5.91 ! [X22: num,X32: num] :
% 5.64/5.91 ( ( bit0 @ X22 )
% 5.64/5.91 != ( bit1 @ X32 ) ) ).
% 5.64/5.91
% 5.64/5.91 % verit_eq_simplify(14)
% 5.64/5.91 thf(fact_3867_verit__eq__simplify_I12_J,axiom,
% 5.64/5.91 ! [X32: num] :
% 5.64/5.91 ( one
% 5.64/5.91 != ( bit1 @ X32 ) ) ).
% 5.64/5.91
% 5.64/5.91 % verit_eq_simplify(12)
% 5.64/5.91 thf(fact_3868_finite__nat__set__iff__bounded,axiom,
% 5.64/5.91 ( finite_finite_nat
% 5.64/5.91 = ( ^ [N6: set_nat] :
% 5.64/5.91 ? [M2: nat] :
% 5.64/5.91 ! [X: nat] :
% 5.64/5.91 ( ( member_nat @ X @ N6 )
% 5.64/5.91 => ( ord_less_nat @ X @ M2 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_nat_set_iff_bounded
% 5.64/5.91 thf(fact_3869_bounded__nat__set__is__finite,axiom,
% 5.64/5.91 ! [N5: set_nat,N: nat] :
% 5.64/5.91 ( ! [X4: nat] :
% 5.64/5.91 ( ( member_nat @ X4 @ N5 )
% 5.64/5.91 => ( ord_less_nat @ X4 @ N ) )
% 5.64/5.91 => ( finite_finite_nat @ N5 ) ) ).
% 5.64/5.91
% 5.64/5.91 % bounded_nat_set_is_finite
% 5.64/5.91 thf(fact_3870_finite__nat__set__iff__bounded__le,axiom,
% 5.64/5.91 ( finite_finite_nat
% 5.64/5.91 = ( ^ [N6: set_nat] :
% 5.64/5.91 ? [M2: nat] :
% 5.64/5.91 ! [X: nat] :
% 5.64/5.91 ( ( member_nat @ X @ N6 )
% 5.64/5.91 => ( ord_less_eq_nat @ X @ M2 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_nat_set_iff_bounded_le
% 5.64/5.91 thf(fact_3871_finite__list,axiom,
% 5.64/5.91 ! [A4: set_VEBT_VEBT] :
% 5.64/5.91 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.91 => ? [Xs3: list_VEBT_VEBT] :
% 5.64/5.91 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.64/5.91 = A4 ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_list
% 5.64/5.91 thf(fact_3872_finite__list,axiom,
% 5.64/5.91 ! [A4: set_nat] :
% 5.64/5.91 ( ( finite_finite_nat @ A4 )
% 5.64/5.91 => ? [Xs3: list_nat] :
% 5.64/5.91 ( ( set_nat2 @ Xs3 )
% 5.64/5.91 = A4 ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_list
% 5.64/5.91 thf(fact_3873_finite__list,axiom,
% 5.64/5.91 ! [A4: set_int] :
% 5.64/5.91 ( ( finite_finite_int @ A4 )
% 5.64/5.91 => ? [Xs3: list_int] :
% 5.64/5.91 ( ( set_int2 @ Xs3 )
% 5.64/5.91 = A4 ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_list
% 5.64/5.91 thf(fact_3874_finite__list,axiom,
% 5.64/5.91 ! [A4: set_complex] :
% 5.64/5.91 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.91 => ? [Xs3: list_complex] :
% 5.64/5.91 ( ( set_complex2 @ Xs3 )
% 5.64/5.91 = A4 ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_list
% 5.64/5.91 thf(fact_3875_finite__M__bounded__by__nat,axiom,
% 5.64/5.91 ! [P: nat > $o,I: nat] :
% 5.64/5.91 ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [K2: nat] :
% 5.64/5.91 ( ( P @ K2 )
% 5.64/5.91 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_M_bounded_by_nat
% 5.64/5.91 thf(fact_3876_finite__less__ub,axiom,
% 5.64/5.91 ! [F: nat > nat,U: nat] :
% 5.64/5.91 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_less_ub
% 5.64/5.91 thf(fact_3877_finite__lists__length__eq,axiom,
% 5.64/5.91 ! [A4: set_complex,N: nat] :
% 5.64/5.91 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.91 => ( finite8712137658972009173omplex
% 5.64/5.91 @ ( collect_list_complex
% 5.64/5.91 @ ^ [Xs: list_complex] :
% 5.64/5.91 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ( size_s3451745648224563538omplex @ Xs )
% 5.64/5.91 = N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_eq
% 5.64/5.91 thf(fact_3878_finite__lists__length__eq,axiom,
% 5.64/5.91 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.64/5.91 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.91 => ( finite3004134309566078307T_VEBT
% 5.64/5.91 @ ( collec5608196760682091941T_VEBT
% 5.64/5.91 @ ^ [Xs: list_VEBT_VEBT] :
% 5.64/5.91 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.64/5.91 = N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_eq
% 5.64/5.91 thf(fact_3879_finite__lists__length__eq,axiom,
% 5.64/5.91 ! [A4: set_o,N: nat] :
% 5.64/5.91 ( ( finite_finite_o @ A4 )
% 5.64/5.91 => ( finite_finite_list_o
% 5.64/5.91 @ ( collect_list_o
% 5.64/5.91 @ ^ [Xs: list_o] :
% 5.64/5.91 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ( size_size_list_o @ Xs )
% 5.64/5.91 = N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_eq
% 5.64/5.91 thf(fact_3880_finite__lists__length__eq,axiom,
% 5.64/5.91 ! [A4: set_int,N: nat] :
% 5.64/5.91 ( ( finite_finite_int @ A4 )
% 5.64/5.91 => ( finite3922522038869484883st_int
% 5.64/5.91 @ ( collect_list_int
% 5.64/5.91 @ ^ [Xs: list_int] :
% 5.64/5.91 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ( size_size_list_int @ Xs )
% 5.64/5.91 = N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_eq
% 5.64/5.91 thf(fact_3881_finite__lists__length__eq,axiom,
% 5.64/5.91 ! [A4: set_nat,N: nat] :
% 5.64/5.91 ( ( finite_finite_nat @ A4 )
% 5.64/5.91 => ( finite8100373058378681591st_nat
% 5.64/5.91 @ ( collect_list_nat
% 5.64/5.91 @ ^ [Xs: list_nat] :
% 5.64/5.91 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ( size_size_list_nat @ Xs )
% 5.64/5.91 = N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_eq
% 5.64/5.91 thf(fact_3882_xor__num_Ocases,axiom,
% 5.64/5.91 ! [X2: product_prod_num_num] :
% 5.64/5.91 ( ( X2
% 5.64/5.91 != ( product_Pair_num_num @ one @ one ) )
% 5.64/5.91 => ( ! [N3: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.64/5.91 => ( ! [N3: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.64/5.91 => ( ! [M4: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.64/5.91 => ( ! [M4: num,N3: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.64/5.91 => ( ! [M4: num,N3: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 5.64/5.91 => ( ! [M4: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.64/5.91 => ( ! [M4: num,N3: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.64/5.91 => ~ ! [M4: num,N3: num] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % xor_num.cases
% 5.64/5.91 thf(fact_3883_num_Oexhaust,axiom,
% 5.64/5.91 ! [Y4: num] :
% 5.64/5.91 ( ( Y4 != one )
% 5.64/5.91 => ( ! [X23: num] :
% 5.64/5.91 ( Y4
% 5.64/5.91 != ( bit0 @ X23 ) )
% 5.64/5.91 => ~ ! [X33: num] :
% 5.64/5.91 ( Y4
% 5.64/5.91 != ( bit1 @ X33 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % num.exhaust
% 5.64/5.91 thf(fact_3884_infinite__Icc,axiom,
% 5.64/5.91 ! [A: rat,B: rat] :
% 5.64/5.91 ( ( ord_less_rat @ A @ B )
% 5.64/5.91 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % infinite_Icc
% 5.64/5.91 thf(fact_3885_infinite__Icc,axiom,
% 5.64/5.91 ! [A: real,B: real] :
% 5.64/5.91 ( ( ord_less_real @ A @ B )
% 5.64/5.91 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % infinite_Icc
% 5.64/5.91 thf(fact_3886_finite__lists__length__le,axiom,
% 5.64/5.91 ! [A4: set_complex,N: nat] :
% 5.64/5.91 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.91 => ( finite8712137658972009173omplex
% 5.64/5.91 @ ( collect_list_complex
% 5.64/5.91 @ ^ [Xs: list_complex] :
% 5.64/5.91 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_le
% 5.64/5.91 thf(fact_3887_finite__lists__length__le,axiom,
% 5.64/5.91 ! [A4: set_VEBT_VEBT,N: nat] :
% 5.64/5.91 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.91 => ( finite3004134309566078307T_VEBT
% 5.64/5.91 @ ( collec5608196760682091941T_VEBT
% 5.64/5.91 @ ^ [Xs: list_VEBT_VEBT] :
% 5.64/5.91 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_le
% 5.64/5.91 thf(fact_3888_finite__lists__length__le,axiom,
% 5.64/5.91 ! [A4: set_o,N: nat] :
% 5.64/5.91 ( ( finite_finite_o @ A4 )
% 5.64/5.91 => ( finite_finite_list_o
% 5.64/5.91 @ ( collect_list_o
% 5.64/5.91 @ ^ [Xs: list_o] :
% 5.64/5.91 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_le
% 5.64/5.91 thf(fact_3889_finite__lists__length__le,axiom,
% 5.64/5.91 ! [A4: set_int,N: nat] :
% 5.64/5.91 ( ( finite_finite_int @ A4 )
% 5.64/5.91 => ( finite3922522038869484883st_int
% 5.64/5.91 @ ( collect_list_int
% 5.64/5.91 @ ^ [Xs: list_int] :
% 5.64/5.91 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_le
% 5.64/5.91 thf(fact_3890_finite__lists__length__le,axiom,
% 5.64/5.91 ! [A4: set_nat,N: nat] :
% 5.64/5.91 ( ( finite_finite_nat @ A4 )
% 5.64/5.91 => ( finite8100373058378681591st_nat
% 5.64/5.91 @ ( collect_list_nat
% 5.64/5.91 @ ^ [Xs: list_nat] :
% 5.64/5.91 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 5.64/5.91 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_lists_length_le
% 5.64/5.91 thf(fact_3891_numeral__Bit1,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1
% 5.64/5.91 thf(fact_3892_numeral__Bit1,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1
% 5.64/5.91 thf(fact_3893_numeral__Bit1,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1
% 5.64/5.91 thf(fact_3894_numeral__Bit1,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1
% 5.64/5.91 thf(fact_3895_numeral__Bit1,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1
% 5.64/5.91 thf(fact_3896_eval__nat__numeral_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.64/5.91 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % eval_nat_numeral(3)
% 5.64/5.91 thf(fact_3897_cong__exp__iff__simps_I10_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(10)
% 5.64/5.91 thf(fact_3898_cong__exp__iff__simps_I10_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(10)
% 5.64/5.91 thf(fact_3899_cong__exp__iff__simps_I10_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(10)
% 5.64/5.91 thf(fact_3900_cong__exp__iff__simps_I12_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(12)
% 5.64/5.91 thf(fact_3901_cong__exp__iff__simps_I12_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(12)
% 5.64/5.91 thf(fact_3902_cong__exp__iff__simps_I12_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(12)
% 5.64/5.91 thf(fact_3903_cong__exp__iff__simps_I13_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.64/5.91 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(13)
% 5.64/5.91 thf(fact_3904_cong__exp__iff__simps_I13_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.64/5.91 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(13)
% 5.64/5.91 thf(fact_3905_cong__exp__iff__simps_I13_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num,N: num] :
% 5.64/5.91 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.64/5.91 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(13)
% 5.64/5.91 thf(fact_3906_numeral__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_code(3)
% 5.64/5.91 thf(fact_3907_numeral__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_code(3)
% 5.64/5.91 thf(fact_3908_numeral__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_code(3)
% 5.64/5.91 thf(fact_3909_numeral__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_code(3)
% 5.64/5.91 thf(fact_3910_numeral__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.64/5.91 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_code(3)
% 5.64/5.91 thf(fact_3911_power__numeral__odd,axiom,
% 5.64/5.91 ! [Z: complex,W: num] :
% 5.64/5.91 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.64/5.91 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % power_numeral_odd
% 5.64/5.91 thf(fact_3912_power__numeral__odd,axiom,
% 5.64/5.91 ! [Z: real,W: num] :
% 5.64/5.91 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.64/5.91 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % power_numeral_odd
% 5.64/5.91 thf(fact_3913_power__numeral__odd,axiom,
% 5.64/5.91 ! [Z: rat,W: num] :
% 5.64/5.91 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.64/5.91 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % power_numeral_odd
% 5.64/5.91 thf(fact_3914_power__numeral__odd,axiom,
% 5.64/5.91 ! [Z: nat,W: num] :
% 5.64/5.91 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.64/5.91 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % power_numeral_odd
% 5.64/5.91 thf(fact_3915_power__numeral__odd,axiom,
% 5.64/5.91 ! [Z: int,W: num] :
% 5.64/5.91 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.64/5.91 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % power_numeral_odd
% 5.64/5.91 thf(fact_3916_psubset__imp__ex__mem,axiom,
% 5.64/5.91 ! [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.64/5.91 ( ( ord_le7866589430770878221at_nat @ A4 @ B4 )
% 5.64/5.91 => ? [B5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B5 @ ( minus_1356011639430497352at_nat @ B4 @ A4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_imp_ex_mem
% 5.64/5.91 thf(fact_3917_psubset__imp__ex__mem,axiom,
% 5.64/5.91 ! [A4: set_complex,B4: set_complex] :
% 5.64/5.91 ( ( ord_less_set_complex @ A4 @ B4 )
% 5.64/5.91 => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B4 @ A4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_imp_ex_mem
% 5.64/5.91 thf(fact_3918_psubset__imp__ex__mem,axiom,
% 5.64/5.91 ! [A4: set_real,B4: set_real] :
% 5.64/5.91 ( ( ord_less_set_real @ A4 @ B4 )
% 5.64/5.91 => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B4 @ A4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_imp_ex_mem
% 5.64/5.91 thf(fact_3919_psubset__imp__ex__mem,axiom,
% 5.64/5.91 ! [A4: set_int,B4: set_int] :
% 5.64/5.91 ( ( ord_less_set_int @ A4 @ B4 )
% 5.64/5.91 => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B4 @ A4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_imp_ex_mem
% 5.64/5.91 thf(fact_3920_psubset__imp__ex__mem,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ A4 @ B4 )
% 5.64/5.91 => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B4 @ A4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_imp_ex_mem
% 5.64/5.91 thf(fact_3921_psubsetD,axiom,
% 5.64/5.91 ! [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.64/5.91 ( ( ord_le7866589430770878221at_nat @ A4 @ B4 )
% 5.64/5.91 => ( ( member8440522571783428010at_nat @ C @ A4 )
% 5.64/5.91 => ( member8440522571783428010at_nat @ C @ B4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetD
% 5.64/5.91 thf(fact_3922_psubsetD,axiom,
% 5.64/5.91 ! [A4: set_complex,B4: set_complex,C: complex] :
% 5.64/5.91 ( ( ord_less_set_complex @ A4 @ B4 )
% 5.64/5.91 => ( ( member_complex @ C @ A4 )
% 5.64/5.91 => ( member_complex @ C @ B4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetD
% 5.64/5.91 thf(fact_3923_psubsetD,axiom,
% 5.64/5.91 ! [A4: set_real,B4: set_real,C: real] :
% 5.64/5.91 ( ( ord_less_set_real @ A4 @ B4 )
% 5.64/5.91 => ( ( member_real @ C @ A4 )
% 5.64/5.91 => ( member_real @ C @ B4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetD
% 5.64/5.91 thf(fact_3924_psubsetD,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat,C: nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ A4 @ B4 )
% 5.64/5.91 => ( ( member_nat @ C @ A4 )
% 5.64/5.91 => ( member_nat @ C @ B4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetD
% 5.64/5.91 thf(fact_3925_psubsetD,axiom,
% 5.64/5.91 ! [A4: set_int,B4: set_int,C: int] :
% 5.64/5.91 ( ( ord_less_set_int @ A4 @ B4 )
% 5.64/5.91 => ( ( member_int @ C @ A4 )
% 5.64/5.91 => ( member_int @ C @ B4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetD
% 5.64/5.91 thf(fact_3926_numeral__Bit1__div__2,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.91 = ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1_div_2
% 5.64/5.91 thf(fact_3927_numeral__Bit1__div__2,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.91 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_Bit1_div_2
% 5.64/5.91 thf(fact_3928_cong__exp__iff__simps_I3_J,axiom,
% 5.64/5.91 ! [N: num,Q3: num] :
% 5.64/5.91 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != zero_zero_nat ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(3)
% 5.64/5.91 thf(fact_3929_cong__exp__iff__simps_I3_J,axiom,
% 5.64/5.91 ! [N: num,Q3: num] :
% 5.64/5.91 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != zero_zero_int ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(3)
% 5.64/5.91 thf(fact_3930_cong__exp__iff__simps_I3_J,axiom,
% 5.64/5.91 ! [N: num,Q3: num] :
% 5.64/5.91 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 != zero_z3403309356797280102nteger ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(3)
% 5.64/5.91 thf(fact_3931_power3__eq__cube,axiom,
% 5.64/5.91 ! [A: complex] :
% 5.64/5.91 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.64/5.91 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.64/5.91
% 5.64/5.91 % power3_eq_cube
% 5.64/5.91 thf(fact_3932_power3__eq__cube,axiom,
% 5.64/5.91 ! [A: real] :
% 5.64/5.91 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.64/5.91 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.64/5.91
% 5.64/5.91 % power3_eq_cube
% 5.64/5.91 thf(fact_3933_power3__eq__cube,axiom,
% 5.64/5.91 ! [A: rat] :
% 5.64/5.91 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.64/5.91 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.64/5.91
% 5.64/5.91 % power3_eq_cube
% 5.64/5.91 thf(fact_3934_power3__eq__cube,axiom,
% 5.64/5.91 ! [A: nat] :
% 5.64/5.91 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.64/5.91 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.64/5.91
% 5.64/5.91 % power3_eq_cube
% 5.64/5.91 thf(fact_3935_power3__eq__cube,axiom,
% 5.64/5.91 ! [A: int] :
% 5.64/5.91 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.64/5.91 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.64/5.91
% 5.64/5.91 % power3_eq_cube
% 5.64/5.91 thf(fact_3936_numeral__3__eq__3,axiom,
% 5.64/5.91 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.64/5.91 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % numeral_3_eq_3
% 5.64/5.91 thf(fact_3937_Suc3__eq__add__3,axiom,
% 5.64/5.91 ! [N: nat] :
% 5.64/5.91 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.64/5.91 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % Suc3_eq_add_3
% 5.64/5.91 thf(fact_3938_num_Osize_I6_J,axiom,
% 5.64/5.91 ! [X32: num] :
% 5.64/5.91 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.64/5.91 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % num.size(6)
% 5.64/5.91 thf(fact_3939_cong__exp__iff__simps_I7_J,axiom,
% 5.64/5.91 ! [Q3: num,N: num] :
% 5.64/5.91 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.64/5.91 = zero_zero_nat ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(7)
% 5.64/5.91 thf(fact_3940_cong__exp__iff__simps_I7_J,axiom,
% 5.64/5.91 ! [Q3: num,N: num] :
% 5.64/5.91 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q3 ) )
% 5.64/5.91 = zero_zero_int ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(7)
% 5.64/5.91 thf(fact_3941_cong__exp__iff__simps_I7_J,axiom,
% 5.64/5.91 ! [Q3: num,N: num] :
% 5.64/5.91 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.64/5.91 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(7)
% 5.64/5.91 thf(fact_3942_cong__exp__iff__simps_I11_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num] :
% 5.64/5.91 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.64/5.91 = zero_zero_nat ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(11)
% 5.64/5.91 thf(fact_3943_cong__exp__iff__simps_I11_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num] :
% 5.64/5.91 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.64/5.91 = zero_zero_int ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(11)
% 5.64/5.91 thf(fact_3944_cong__exp__iff__simps_I11_J,axiom,
% 5.64/5.91 ! [M: num,Q3: num] :
% 5.64/5.91 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.64/5.91 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.64/5.91 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.64/5.91 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.91
% 5.64/5.91 % cong_exp_iff_simps(11)
% 5.64/5.91 thf(fact_3945_less__set__def,axiom,
% 5.64/5.91 ( ord_le7866589430770878221at_nat
% 5.64/5.91 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.64/5.91 ( ord_le549003669493604880_nat_o
% 5.64/5.91 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 5.64/5.91 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % less_set_def
% 5.64/5.91 thf(fact_3946_less__set__def,axiom,
% 5.64/5.91 ( ord_less_set_complex
% 5.64/5.91 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.64/5.91 ( ord_less_complex_o
% 5.64/5.91 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.64/5.91 @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % less_set_def
% 5.64/5.91 thf(fact_3947_less__set__def,axiom,
% 5.64/5.91 ( ord_less_set_real
% 5.64/5.91 = ( ^ [A6: set_real,B6: set_real] :
% 5.64/5.91 ( ord_less_real_o
% 5.64/5.91 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.64/5.91 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % less_set_def
% 5.64/5.91 thf(fact_3948_less__set__def,axiom,
% 5.64/5.91 ( ord_less_set_nat
% 5.64/5.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.64/5.91 ( ord_less_nat_o
% 5.64/5.91 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.64/5.91 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % less_set_def
% 5.64/5.91 thf(fact_3949_less__set__def,axiom,
% 5.64/5.91 ( ord_less_set_int
% 5.64/5.91 = ( ^ [A6: set_int,B6: set_int] :
% 5.64/5.91 ( ord_less_int_o
% 5.64/5.91 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.64/5.91 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % less_set_def
% 5.64/5.91 thf(fact_3950_Suc__div__eq__add3__div,axiom,
% 5.64/5.91 ! [M: nat,N: nat] :
% 5.64/5.91 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.64/5.91 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % Suc_div_eq_add3_div
% 5.64/5.91 thf(fact_3951_Suc__mod__eq__add3__mod,axiom,
% 5.64/5.91 ! [M: nat,N: nat] :
% 5.64/5.91 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.64/5.91 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.64/5.91
% 5.64/5.91 % Suc_mod_eq_add3_mod
% 5.64/5.91 thf(fact_3952_not__psubset__empty,axiom,
% 5.64/5.91 ! [A4: set_nat] :
% 5.64/5.91 ~ ( ord_less_set_nat @ A4 @ bot_bot_set_nat ) ).
% 5.64/5.91
% 5.64/5.91 % not_psubset_empty
% 5.64/5.91 thf(fact_3953_not__psubset__empty,axiom,
% 5.64/5.91 ! [A4: set_int] :
% 5.64/5.91 ~ ( ord_less_set_int @ A4 @ bot_bot_set_int ) ).
% 5.64/5.91
% 5.64/5.91 % not_psubset_empty
% 5.64/5.91 thf(fact_3954_not__psubset__empty,axiom,
% 5.64/5.91 ! [A4: set_real] :
% 5.64/5.91 ~ ( ord_less_set_real @ A4 @ bot_bot_set_real ) ).
% 5.64/5.91
% 5.64/5.91 % not_psubset_empty
% 5.64/5.91 thf(fact_3955_psubsetE,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ A4 @ B4 )
% 5.64/5.91 => ~ ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 5.64/5.91 => ( ord_less_eq_set_nat @ B4 @ A4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubsetE
% 5.64/5.91 thf(fact_3956_psubset__eq,axiom,
% 5.64/5.91 ( ord_less_set_nat
% 5.64/5.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.64/5.91 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 5.64/5.91 & ( A6 != B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_eq
% 5.64/5.91 thf(fact_3957_psubset__imp__subset,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ A4 @ B4 )
% 5.64/5.91 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_imp_subset
% 5.64/5.91 thf(fact_3958_psubset__subset__trans,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat,C4: set_nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ A4 @ B4 )
% 5.64/5.91 => ( ( ord_less_eq_set_nat @ B4 @ C4 )
% 5.64/5.91 => ( ord_less_set_nat @ A4 @ C4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % psubset_subset_trans
% 5.64/5.91 thf(fact_3959_subset__not__subset__eq,axiom,
% 5.64/5.91 ( ord_less_set_nat
% 5.64/5.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.64/5.91 ( ( ord_less_eq_set_nat @ A6 @ B6 )
% 5.64/5.91 & ~ ( ord_less_eq_set_nat @ B6 @ A6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % subset_not_subset_eq
% 5.64/5.91 thf(fact_3960_subset__psubset__trans,axiom,
% 5.64/5.91 ! [A4: set_nat,B4: set_nat,C4: set_nat] :
% 5.64/5.91 ( ( ord_less_eq_set_nat @ A4 @ B4 )
% 5.64/5.91 => ( ( ord_less_set_nat @ B4 @ C4 )
% 5.64/5.91 => ( ord_less_set_nat @ A4 @ C4 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % subset_psubset_trans
% 5.64/5.91 thf(fact_3961_subset__iff__psubset__eq,axiom,
% 5.64/5.91 ( ord_less_eq_set_nat
% 5.64/5.91 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.64/5.91 ( ( ord_less_set_nat @ A6 @ B6 )
% 5.64/5.91 | ( A6 = B6 ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % subset_iff_psubset_eq
% 5.64/5.91 thf(fact_3962_VEBT__internal_Oheight_Ocases,axiom,
% 5.64/5.91 ! [X2: vEBT_VEBT] :
% 5.64/5.91 ( ! [A5: $o,B5: $o] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.91 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.91 ( X2
% 5.64/5.91 != ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % VEBT_internal.height.cases
% 5.64/5.91 thf(fact_3963_member__bound__height,axiom,
% 5.64/5.91 ! [T: vEBT_VEBT,N: nat,X2: nat] :
% 5.64/5.91 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.91 => ( ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r @ T @ X2 ) @ ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ T ) ) @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % member_bound_height
% 5.64/5.91 thf(fact_3964_mod__exhaust__less__4,axiom,
% 5.64/5.91 ! [M: nat] :
% 5.64/5.91 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.91 = zero_zero_nat )
% 5.64/5.91 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.91 = one_one_nat )
% 5.64/5.91 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.91 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.91 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % mod_exhaust_less_4
% 5.64/5.91 thf(fact_3965_finite__Collect__le__nat,axiom,
% 5.64/5.91 ! [K: nat] :
% 5.64/5.91 ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_Collect_le_nat
% 5.64/5.91 thf(fact_3966_finite__Collect__less__nat,axiom,
% 5.64/5.91 ! [K: nat] :
% 5.64/5.91 ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_Collect_less_nat
% 5.64/5.91 thf(fact_3967_finite__roots__unity,axiom,
% 5.64/5.91 ! [N: nat] :
% 5.64/5.91 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [Z4: real] :
% 5.64/5.91 ( ( power_power_real @ Z4 @ N )
% 5.64/5.91 = one_one_real ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_roots_unity
% 5.64/5.91 thf(fact_3968_finite__roots__unity,axiom,
% 5.64/5.91 ! [N: nat] :
% 5.64/5.91 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.64/5.91 => ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [Z4: complex] :
% 5.64/5.91 ( ( power_power_complex @ Z4 @ N )
% 5.64/5.91 = one_one_complex ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_roots_unity
% 5.64/5.91 thf(fact_3969_divmod__algorithm__code_I8_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( ord_less_num @ M @ N )
% 5.64/5.91 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.64/5.91 & ( ~ ( ord_less_num @ M @ N )
% 5.64/5.91 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(8)
% 5.64/5.91 thf(fact_3970_divmod__algorithm__code_I8_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( ord_less_num @ M @ N )
% 5.64/5.91 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.64/5.91 & ( ~ ( ord_less_num @ M @ N )
% 5.64/5.91 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(8)
% 5.64/5.91 thf(fact_3971_divmod__algorithm__code_I8_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( ord_less_num @ M @ N )
% 5.64/5.91 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.64/5.91 & ( ~ ( ord_less_num @ M @ N )
% 5.64/5.91 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(8)
% 5.64/5.91 thf(fact_3972_divmod__algorithm__code_I7_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( ord_less_eq_num @ M @ N )
% 5.64/5.91 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.64/5.91 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.64/5.91 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(7)
% 5.64/5.91 thf(fact_3973_divmod__algorithm__code_I7_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( ord_less_eq_num @ M @ N )
% 5.64/5.91 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.64/5.91 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.64/5.91 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(7)
% 5.64/5.91 thf(fact_3974_divmod__algorithm__code_I7_J,axiom,
% 5.64/5.91 ! [M: num,N: num] :
% 5.64/5.91 ( ( ( ord_less_eq_num @ M @ N )
% 5.64/5.91 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.64/5.91 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.64/5.91 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/5.91 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(7)
% 5.64/5.91 thf(fact_3975_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_real,X2: real > complex,Y4: real > complex] :
% 5.64/5.91 ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3976_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_nat,X2: nat > complex,Y4: nat > complex] :
% 5.64/5.91 ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3977_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_int,X2: int > complex,Y4: int > complex] :
% 5.64/5.91 ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3978_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_complex,X2: complex > complex,Y4: complex > complex] :
% 5.64/5.91 ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_complex ) ) ) )
% 5.64/5.91 => ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3979_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_real,X2: real > real,Y4: real > real] :
% 5.64/5.91 ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3980_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_nat,X2: nat > real,Y4: nat > real] :
% 5.64/5.91 ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3981_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_int,X2: int > real,Y4: int > real] :
% 5.64/5.91 ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3982_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_complex,X2: complex > real,Y4: complex > real] :
% 5.64/5.91 ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_real ) ) ) )
% 5.64/5.91 => ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3983_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_real,X2: real > rat,Y4: real > rat] :
% 5.64/5.91 ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_rat ) ) ) )
% 5.64/5.91 => ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_rat ) ) ) )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_rat @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_rat ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3984_prod_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_nat,X2: nat > rat,Y4: nat > rat] :
% 5.64/5.91 ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != one_one_rat ) ) ) )
% 5.64/5.91 => ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != one_one_rat ) ) ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( times_times_rat @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != one_one_rat ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % prod.finite_Collect_op
% 5.64/5.91 thf(fact_3985_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_real,X2: real > complex,Y4: real > complex] :
% 5.64/5.91 ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3986_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_nat,X2: nat > complex,Y4: nat > complex] :
% 5.64/5.91 ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3987_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_int,X2: int > complex,Y4: int > complex] :
% 5.64/5.91 ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3988_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_complex,X2: complex > complex,Y4: complex > complex] :
% 5.64/5.91 ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_complex ) ) ) )
% 5.64/5.91 => ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_complex @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_complex ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3989_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_real,X2: real > real,Y4: real > real] :
% 5.64/5.91 ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3990_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_nat,X2: nat > real,Y4: nat > real] :
% 5.64/5.91 ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3991_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_int,X2: int > real,Y4: int > real] :
% 5.64/5.91 ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( member_int @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3992_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_complex,X2: complex > real,Y4: complex > real] :
% 5.64/5.91 ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_real ) ) ) )
% 5.64/5.91 => ( finite3207457112153483333omplex
% 5.64/5.91 @ ( collect_complex
% 5.64/5.91 @ ^ [I4: complex] :
% 5.64/5.91 ( ( member_complex @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_real @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3993_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_real,X2: real > rat,Y4: real > rat] :
% 5.64/5.91 ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_rat ) ) ) )
% 5.64/5.91 => ( ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_rat ) ) ) )
% 5.64/5.91 => ( finite_finite_real
% 5.64/5.91 @ ( collect_real
% 5.64/5.91 @ ^ [I4: real] :
% 5.64/5.91 ( ( member_real @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3994_sum_Ofinite__Collect__op,axiom,
% 5.64/5.91 ! [I5: set_nat,X2: nat > rat,Y4: nat > rat] :
% 5.64/5.91 ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( X2 @ I4 )
% 5.64/5.91 != zero_zero_rat ) ) ) )
% 5.64/5.91 => ( ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( Y4 @ I4 )
% 5.64/5.91 != zero_zero_rat ) ) ) )
% 5.64/5.91 => ( finite_finite_nat
% 5.64/5.91 @ ( collect_nat
% 5.64/5.91 @ ^ [I4: nat] :
% 5.64/5.91 ( ( member_nat @ I4 @ I5 )
% 5.64/5.91 & ( ( plus_plus_rat @ ( X2 @ I4 ) @ ( Y4 @ I4 ) )
% 5.64/5.91 != zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % sum.finite_Collect_op
% 5.64/5.91 thf(fact_3995_finite__interval__int4,axiom,
% 5.64/5.91 ! [A: int,B: int] :
% 5.64/5.91 ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( ord_less_int @ A @ I4 )
% 5.64/5.91 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_interval_int4
% 5.64/5.91 thf(fact_3996_finite__interval__int2,axiom,
% 5.64/5.91 ! [A: int,B: int] :
% 5.64/5.91 ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( ord_less_eq_int @ A @ I4 )
% 5.64/5.91 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_interval_int2
% 5.64/5.91 thf(fact_3997_finite__interval__int3,axiom,
% 5.64/5.91 ! [A: int,B: int] :
% 5.64/5.91 ( finite_finite_int
% 5.64/5.91 @ ( collect_int
% 5.64/5.91 @ ^ [I4: int] :
% 5.64/5.91 ( ( ord_less_int @ A @ I4 )
% 5.64/5.91 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_interval_int3
% 5.64/5.91 thf(fact_3998_divmod__algorithm__code_I2_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ( ( unique5052692396658037445od_int @ M @ one )
% 5.64/5.91 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(2)
% 5.64/5.91 thf(fact_3999_divmod__algorithm__code_I2_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.64/5.91 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(2)
% 5.64/5.91 thf(fact_4000_divmod__algorithm__code_I2_J,axiom,
% 5.64/5.91 ! [M: num] :
% 5.64/5.91 ( ( unique3479559517661332726nteger @ M @ one )
% 5.64/5.91 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(2)
% 5.64/5.91 thf(fact_4001_divmod__algorithm__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.64/5.91 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(3)
% 5.64/5.91 thf(fact_4002_divmod__algorithm__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.64/5.91 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(3)
% 5.64/5.91 thf(fact_4003_divmod__algorithm__code_I3_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.64/5.91 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(3)
% 5.64/5.91 thf(fact_4004_divmod__algorithm__code_I4_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.64/5.91 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(4)
% 5.64/5.91 thf(fact_4005_divmod__algorithm__code_I4_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.64/5.91 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(4)
% 5.64/5.91 thf(fact_4006_divmod__algorithm__code_I4_J,axiom,
% 5.64/5.91 ! [N: num] :
% 5.64/5.91 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.64/5.91 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_algorithm_code(4)
% 5.64/5.91 thf(fact_4007_finite__maxlen,axiom,
% 5.64/5.91 ! [M7: set_list_VEBT_VEBT] :
% 5.64/5.91 ( ( finite3004134309566078307T_VEBT @ M7 )
% 5.64/5.91 => ? [N3: nat] :
% 5.64/5.91 ! [X3: list_VEBT_VEBT] :
% 5.64/5.91 ( ( member2936631157270082147T_VEBT @ X3 @ M7 )
% 5.64/5.91 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X3 ) @ N3 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_maxlen
% 5.64/5.91 thf(fact_4008_finite__maxlen,axiom,
% 5.64/5.91 ! [M7: set_list_o] :
% 5.64/5.91 ( ( finite_finite_list_o @ M7 )
% 5.64/5.91 => ? [N3: nat] :
% 5.64/5.91 ! [X3: list_o] :
% 5.64/5.91 ( ( member_list_o @ X3 @ M7 )
% 5.64/5.91 => ( ord_less_nat @ ( size_size_list_o @ X3 ) @ N3 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_maxlen
% 5.64/5.91 thf(fact_4009_finite__maxlen,axiom,
% 5.64/5.91 ! [M7: set_list_nat] :
% 5.64/5.91 ( ( finite8100373058378681591st_nat @ M7 )
% 5.64/5.91 => ? [N3: nat] :
% 5.64/5.91 ! [X3: list_nat] :
% 5.64/5.91 ( ( member_list_nat @ X3 @ M7 )
% 5.64/5.91 => ( ord_less_nat @ ( size_size_list_nat @ X3 ) @ N3 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_maxlen
% 5.64/5.91 thf(fact_4010_finite__maxlen,axiom,
% 5.64/5.91 ! [M7: set_list_int] :
% 5.64/5.91 ( ( finite3922522038869484883st_int @ M7 )
% 5.64/5.91 => ? [N3: nat] :
% 5.64/5.91 ! [X3: list_int] :
% 5.64/5.91 ( ( member_list_int @ X3 @ M7 )
% 5.64/5.91 => ( ord_less_nat @ ( size_size_list_int @ X3 ) @ N3 ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_maxlen
% 5.64/5.91 thf(fact_4011_divmod__int__def,axiom,
% 5.64/5.91 ( unique5052692396658037445od_int
% 5.64/5.91 = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_int_def
% 5.64/5.91 thf(fact_4012_divmod__def,axiom,
% 5.64/5.91 ( unique5052692396658037445od_int
% 5.64/5.91 = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_def
% 5.64/5.91 thf(fact_4013_divmod__def,axiom,
% 5.64/5.91 ( unique5055182867167087721od_nat
% 5.64/5.91 = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_def
% 5.64/5.91 thf(fact_4014_divmod__def,axiom,
% 5.64/5.91 ( unique3479559517661332726nteger
% 5.64/5.91 = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod_def
% 5.64/5.91 thf(fact_4015_divmod_H__nat__def,axiom,
% 5.64/5.91 ( unique5055182867167087721od_nat
% 5.64/5.91 = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % divmod'_nat_def
% 5.64/5.91 thf(fact_4016_finite__has__minimal2,axiom,
% 5.64/5.91 ! [A4: set_set_nat,A: set_nat] :
% 5.64/5.91 ( ( finite1152437895449049373et_nat @ A4 )
% 5.64/5.91 => ( ( member_set_nat @ A @ A4 )
% 5.64/5.91 => ? [X4: set_nat] :
% 5.64/5.91 ( ( member_set_nat @ X4 @ A4 )
% 5.64/5.91 & ( ord_less_eq_set_nat @ X4 @ A )
% 5.64/5.91 & ! [Xa: set_nat] :
% 5.64/5.91 ( ( member_set_nat @ Xa @ A4 )
% 5.64/5.91 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 5.64/5.91 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_has_minimal2
% 5.64/5.91 thf(fact_4017_finite__has__minimal2,axiom,
% 5.64/5.91 ! [A4: set_rat,A: rat] :
% 5.64/5.91 ( ( finite_finite_rat @ A4 )
% 5.64/5.91 => ( ( member_rat @ A @ A4 )
% 5.64/5.91 => ? [X4: rat] :
% 5.64/5.91 ( ( member_rat @ X4 @ A4 )
% 5.64/5.91 & ( ord_less_eq_rat @ X4 @ A )
% 5.64/5.91 & ! [Xa: rat] :
% 5.64/5.91 ( ( member_rat @ Xa @ A4 )
% 5.64/5.91 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 5.64/5.91 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_has_minimal2
% 5.64/5.91 thf(fact_4018_finite__has__minimal2,axiom,
% 5.64/5.91 ! [A4: set_num,A: num] :
% 5.64/5.91 ( ( finite_finite_num @ A4 )
% 5.64/5.91 => ( ( member_num @ A @ A4 )
% 5.64/5.91 => ? [X4: num] :
% 5.64/5.91 ( ( member_num @ X4 @ A4 )
% 5.64/5.91 & ( ord_less_eq_num @ X4 @ A )
% 5.64/5.91 & ! [Xa: num] :
% 5.64/5.91 ( ( member_num @ Xa @ A4 )
% 5.64/5.91 => ( ( ord_less_eq_num @ Xa @ X4 )
% 5.64/5.91 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_has_minimal2
% 5.64/5.91 thf(fact_4019_finite__has__minimal2,axiom,
% 5.64/5.91 ! [A4: set_nat,A: nat] :
% 5.64/5.91 ( ( finite_finite_nat @ A4 )
% 5.64/5.91 => ( ( member_nat @ A @ A4 )
% 5.64/5.91 => ? [X4: nat] :
% 5.64/5.91 ( ( member_nat @ X4 @ A4 )
% 5.64/5.91 & ( ord_less_eq_nat @ X4 @ A )
% 5.64/5.91 & ! [Xa: nat] :
% 5.64/5.91 ( ( member_nat @ Xa @ A4 )
% 5.64/5.91 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.64/5.91 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_has_minimal2
% 5.64/5.91 thf(fact_4020_finite__has__minimal2,axiom,
% 5.64/5.91 ! [A4: set_int,A: int] :
% 5.64/5.91 ( ( finite_finite_int @ A4 )
% 5.64/5.91 => ( ( member_int @ A @ A4 )
% 5.64/5.91 => ? [X4: int] :
% 5.64/5.91 ( ( member_int @ X4 @ A4 )
% 5.64/5.91 & ( ord_less_eq_int @ X4 @ A )
% 5.64/5.91 & ! [Xa: int] :
% 5.64/5.91 ( ( member_int @ Xa @ A4 )
% 5.64/5.91 => ( ( ord_less_eq_int @ Xa @ X4 )
% 5.64/5.91 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.91
% 5.64/5.91 % finite_has_minimal2
% 5.64/5.91 thf(fact_4021_finite__has__minimal2,axiom,
% 5.64/5.92 ! [A4: set_real,A: real] :
% 5.64/5.92 ( ( finite_finite_real @ A4 )
% 5.64/5.92 => ( ( member_real @ A @ A4 )
% 5.64/5.92 => ? [X4: real] :
% 5.64/5.92 ( ( member_real @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_real @ X4 @ A )
% 5.64/5.92 & ! [Xa: real] :
% 5.64/5.92 ( ( member_real @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_real @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal2
% 5.64/5.92 thf(fact_4022_finite__has__maximal2,axiom,
% 5.64/5.92 ! [A4: set_set_nat,A: set_nat] :
% 5.64/5.92 ( ( finite1152437895449049373et_nat @ A4 )
% 5.64/5.92 => ( ( member_set_nat @ A @ A4 )
% 5.64/5.92 => ? [X4: set_nat] :
% 5.64/5.92 ( ( member_set_nat @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_set_nat @ A @ X4 )
% 5.64/5.92 & ! [Xa: set_nat] :
% 5.64/5.92 ( ( member_set_nat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal2
% 5.64/5.92 thf(fact_4023_finite__has__maximal2,axiom,
% 5.64/5.92 ! [A4: set_rat,A: rat] :
% 5.64/5.92 ( ( finite_finite_rat @ A4 )
% 5.64/5.92 => ( ( member_rat @ A @ A4 )
% 5.64/5.92 => ? [X4: rat] :
% 5.64/5.92 ( ( member_rat @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_rat @ A @ X4 )
% 5.64/5.92 & ! [Xa: rat] :
% 5.64/5.92 ( ( member_rat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal2
% 5.64/5.92 thf(fact_4024_finite__has__maximal2,axiom,
% 5.64/5.92 ! [A4: set_num,A: num] :
% 5.64/5.92 ( ( finite_finite_num @ A4 )
% 5.64/5.92 => ( ( member_num @ A @ A4 )
% 5.64/5.92 => ? [X4: num] :
% 5.64/5.92 ( ( member_num @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_num @ A @ X4 )
% 5.64/5.92 & ! [Xa: num] :
% 5.64/5.92 ( ( member_num @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_num @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal2
% 5.64/5.92 thf(fact_4025_finite__has__maximal2,axiom,
% 5.64/5.92 ! [A4: set_nat,A: nat] :
% 5.64/5.92 ( ( finite_finite_nat @ A4 )
% 5.64/5.92 => ( ( member_nat @ A @ A4 )
% 5.64/5.92 => ? [X4: nat] :
% 5.64/5.92 ( ( member_nat @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_nat @ A @ X4 )
% 5.64/5.92 & ! [Xa: nat] :
% 5.64/5.92 ( ( member_nat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal2
% 5.64/5.92 thf(fact_4026_finite__has__maximal2,axiom,
% 5.64/5.92 ! [A4: set_int,A: int] :
% 5.64/5.92 ( ( finite_finite_int @ A4 )
% 5.64/5.92 => ( ( member_int @ A @ A4 )
% 5.64/5.92 => ? [X4: int] :
% 5.64/5.92 ( ( member_int @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_int @ A @ X4 )
% 5.64/5.92 & ! [Xa: int] :
% 5.64/5.92 ( ( member_int @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_int @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal2
% 5.64/5.92 thf(fact_4027_finite__has__maximal2,axiom,
% 5.64/5.92 ! [A4: set_real,A: real] :
% 5.64/5.92 ( ( finite_finite_real @ A4 )
% 5.64/5.92 => ( ( member_real @ A @ A4 )
% 5.64/5.92 => ? [X4: real] :
% 5.64/5.92 ( ( member_real @ X4 @ A4 )
% 5.64/5.92 & ( ord_less_eq_real @ A @ X4 )
% 5.64/5.92 & ! [Xa: real] :
% 5.64/5.92 ( ( member_real @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_real @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal2
% 5.64/5.92 thf(fact_4028_finite__psubset__induct,axiom,
% 5.64/5.92 ! [A4: set_nat,P: set_nat > $o] :
% 5.64/5.92 ( ( finite_finite_nat @ A4 )
% 5.64/5.92 => ( ! [A7: set_nat] :
% 5.64/5.92 ( ( finite_finite_nat @ A7 )
% 5.64/5.92 => ( ! [B7: set_nat] :
% 5.64/5.92 ( ( ord_less_set_nat @ B7 @ A7 )
% 5.64/5.92 => ( P @ B7 ) )
% 5.64/5.92 => ( P @ A7 ) ) )
% 5.64/5.92 => ( P @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_psubset_induct
% 5.64/5.92 thf(fact_4029_finite__psubset__induct,axiom,
% 5.64/5.92 ! [A4: set_int,P: set_int > $o] :
% 5.64/5.92 ( ( finite_finite_int @ A4 )
% 5.64/5.92 => ( ! [A7: set_int] :
% 5.64/5.92 ( ( finite_finite_int @ A7 )
% 5.64/5.92 => ( ! [B7: set_int] :
% 5.64/5.92 ( ( ord_less_set_int @ B7 @ A7 )
% 5.64/5.92 => ( P @ B7 ) )
% 5.64/5.92 => ( P @ A7 ) ) )
% 5.64/5.92 => ( P @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_psubset_induct
% 5.64/5.92 thf(fact_4030_finite__psubset__induct,axiom,
% 5.64/5.92 ! [A4: set_complex,P: set_complex > $o] :
% 5.64/5.92 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.92 => ( ! [A7: set_complex] :
% 5.64/5.92 ( ( finite3207457112153483333omplex @ A7 )
% 5.64/5.92 => ( ! [B7: set_complex] :
% 5.64/5.92 ( ( ord_less_set_complex @ B7 @ A7 )
% 5.64/5.92 => ( P @ B7 ) )
% 5.64/5.92 => ( P @ A7 ) ) )
% 5.64/5.92 => ( P @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_psubset_induct
% 5.64/5.92 thf(fact_4031_divmod__divmod__step,axiom,
% 5.64/5.92 ( unique5055182867167087721od_nat
% 5.64/5.92 = ( ^ [M2: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M2 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_divmod_step
% 5.64/5.92 thf(fact_4032_divmod__divmod__step,axiom,
% 5.64/5.92 ( unique5052692396658037445od_int
% 5.64/5.92 = ( ^ [M2: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M2 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_divmod_step
% 5.64/5.92 thf(fact_4033_divmod__divmod__step,axiom,
% 5.64/5.92 ( unique3479559517661332726nteger
% 5.64/5.92 = ( ^ [M2: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M2 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_divmod_step
% 5.64/5.92 thf(fact_4034_finite__has__maximal,axiom,
% 5.64/5.92 ! [A4: set_set_nat] :
% 5.64/5.92 ( ( finite1152437895449049373et_nat @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_set_nat )
% 5.64/5.92 => ? [X4: set_nat] :
% 5.64/5.92 ( ( member_set_nat @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: set_nat] :
% 5.64/5.92 ( ( member_set_nat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_set_nat @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal
% 5.64/5.92 thf(fact_4035_finite__has__maximal,axiom,
% 5.64/5.92 ! [A4: set_rat] :
% 5.64/5.92 ( ( finite_finite_rat @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_rat )
% 5.64/5.92 => ? [X4: rat] :
% 5.64/5.92 ( ( member_rat @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: rat] :
% 5.64/5.92 ( ( member_rat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_rat @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal
% 5.64/5.92 thf(fact_4036_finite__has__maximal,axiom,
% 5.64/5.92 ! [A4: set_num] :
% 5.64/5.92 ( ( finite_finite_num @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_num )
% 5.64/5.92 => ? [X4: num] :
% 5.64/5.92 ( ( member_num @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: num] :
% 5.64/5.92 ( ( member_num @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_num @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal
% 5.64/5.92 thf(fact_4037_finite__has__maximal,axiom,
% 5.64/5.92 ! [A4: set_nat] :
% 5.64/5.92 ( ( finite_finite_nat @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_nat )
% 5.64/5.92 => ? [X4: nat] :
% 5.64/5.92 ( ( member_nat @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: nat] :
% 5.64/5.92 ( ( member_nat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_nat @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal
% 5.64/5.92 thf(fact_4038_finite__has__maximal,axiom,
% 5.64/5.92 ! [A4: set_int] :
% 5.64/5.92 ( ( finite_finite_int @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_int )
% 5.64/5.92 => ? [X4: int] :
% 5.64/5.92 ( ( member_int @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: int] :
% 5.64/5.92 ( ( member_int @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_int @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal
% 5.64/5.92 thf(fact_4039_finite__has__maximal,axiom,
% 5.64/5.92 ! [A4: set_real] :
% 5.64/5.92 ( ( finite_finite_real @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_real )
% 5.64/5.92 => ? [X4: real] :
% 5.64/5.92 ( ( member_real @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: real] :
% 5.64/5.92 ( ( member_real @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_real @ X4 @ Xa )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_maximal
% 5.64/5.92 thf(fact_4040_finite__has__minimal,axiom,
% 5.64/5.92 ! [A4: set_set_nat] :
% 5.64/5.92 ( ( finite1152437895449049373et_nat @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_set_nat )
% 5.64/5.92 => ? [X4: set_nat] :
% 5.64/5.92 ( ( member_set_nat @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: set_nat] :
% 5.64/5.92 ( ( member_set_nat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_set_nat @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal
% 5.64/5.92 thf(fact_4041_finite__has__minimal,axiom,
% 5.64/5.92 ! [A4: set_rat] :
% 5.64/5.92 ( ( finite_finite_rat @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_rat )
% 5.64/5.92 => ? [X4: rat] :
% 5.64/5.92 ( ( member_rat @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: rat] :
% 5.64/5.92 ( ( member_rat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_rat @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal
% 5.64/5.92 thf(fact_4042_finite__has__minimal,axiom,
% 5.64/5.92 ! [A4: set_num] :
% 5.64/5.92 ( ( finite_finite_num @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_num )
% 5.64/5.92 => ? [X4: num] :
% 5.64/5.92 ( ( member_num @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: num] :
% 5.64/5.92 ( ( member_num @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_num @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal
% 5.64/5.92 thf(fact_4043_finite__has__minimal,axiom,
% 5.64/5.92 ! [A4: set_nat] :
% 5.64/5.92 ( ( finite_finite_nat @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_nat )
% 5.64/5.92 => ? [X4: nat] :
% 5.64/5.92 ( ( member_nat @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: nat] :
% 5.64/5.92 ( ( member_nat @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal
% 5.64/5.92 thf(fact_4044_finite__has__minimal,axiom,
% 5.64/5.92 ! [A4: set_int] :
% 5.64/5.92 ( ( finite_finite_int @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_int )
% 5.64/5.92 => ? [X4: int] :
% 5.64/5.92 ( ( member_int @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: int] :
% 5.64/5.92 ( ( member_int @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_int @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal
% 5.64/5.92 thf(fact_4045_finite__has__minimal,axiom,
% 5.64/5.92 ! [A4: set_real] :
% 5.64/5.92 ( ( finite_finite_real @ A4 )
% 5.64/5.92 => ( ( A4 != bot_bot_set_real )
% 5.64/5.92 => ? [X4: real] :
% 5.64/5.92 ( ( member_real @ X4 @ A4 )
% 5.64/5.92 & ! [Xa: real] :
% 5.64/5.92 ( ( member_real @ Xa @ A4 )
% 5.64/5.92 => ( ( ord_less_eq_real @ Xa @ X4 )
% 5.64/5.92 => ( X4 = Xa ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_has_minimal
% 5.64/5.92 thf(fact_4046_arcosh__1,axiom,
% 5.64/5.92 ( ( arcosh_real @ one_one_real )
% 5.64/5.92 = zero_zero_real ) ).
% 5.64/5.92
% 5.64/5.92 % arcosh_1
% 5.64/5.92 thf(fact_4047_finite__nth__roots,axiom,
% 5.64/5.92 ! [N: nat,C: complex] :
% 5.64/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( finite3207457112153483333omplex
% 5.64/5.92 @ ( collect_complex
% 5.64/5.92 @ ^ [Z4: complex] :
% 5.64/5.92 ( ( power_power_complex @ Z4 @ N )
% 5.64/5.92 = C ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % finite_nth_roots
% 5.64/5.92 thf(fact_4048_dbl__inc__simps_I3_J,axiom,
% 5.64/5.92 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.64/5.92 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(3)
% 5.64/5.92 thf(fact_4049_dbl__inc__simps_I3_J,axiom,
% 5.64/5.92 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.64/5.92 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(3)
% 5.64/5.92 thf(fact_4050_dbl__inc__simps_I3_J,axiom,
% 5.64/5.92 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.64/5.92 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(3)
% 5.64/5.92 thf(fact_4051_dbl__inc__simps_I3_J,axiom,
% 5.64/5.92 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.64/5.92 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(3)
% 5.64/5.92 thf(fact_4052_insert__simp__excp,axiom,
% 5.64/5.92 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.92 => ( ( ord_less_nat @ X2 @ Mi )
% 5.64/5.92 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.92 => ( ( X2 != Ma )
% 5.64/5.92 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( 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 @ TreeList @ ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % insert_simp_excp
% 5.64/5.92 thf(fact_4053_insert__simp__norm,axiom,
% 5.64/5.92 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.92 => ( ( ord_less_nat @ Mi @ X2 )
% 5.64/5.92 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.64/5.92 => ( ( X2 != Ma )
% 5.64/5.92 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 5.64/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X2 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % insert_simp_norm
% 5.64/5.92 thf(fact_4054_gcd__nat__induct,axiom,
% 5.64/5.92 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.64/5.92 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.64/5.92 => ( ! [M4: nat,N3: nat] :
% 5.64/5.92 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.92 => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 5.64/5.92 => ( P @ M4 @ N3 ) ) )
% 5.64/5.92 => ( P @ M @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % gcd_nat_induct
% 5.64/5.92 thf(fact_4055_list__update__overwrite,axiom,
% 5.64/5.92 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT,Y4: vEBT_VEBT] :
% 5.64/5.92 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ I @ Y4 )
% 5.64/5.92 = ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_overwrite
% 5.64/5.92 thf(fact_4056_max__bot,axiom,
% 5.64/5.92 ! [X2: set_nat] :
% 5.64/5.92 ( ( ord_max_set_nat @ bot_bot_set_nat @ X2 )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot
% 5.64/5.92 thf(fact_4057_max__bot,axiom,
% 5.64/5.92 ! [X2: set_int] :
% 5.64/5.92 ( ( ord_max_set_int @ bot_bot_set_int @ X2 )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot
% 5.64/5.92 thf(fact_4058_max__bot,axiom,
% 5.64/5.92 ! [X2: set_real] :
% 5.64/5.92 ( ( ord_max_set_real @ bot_bot_set_real @ X2 )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot
% 5.64/5.92 thf(fact_4059_max__bot,axiom,
% 5.64/5.92 ! [X2: nat] :
% 5.64/5.92 ( ( ord_max_nat @ bot_bot_nat @ X2 )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot
% 5.64/5.92 thf(fact_4060_max__bot,axiom,
% 5.64/5.92 ! [X2: extended_enat] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ bot_bo4199563552545308370d_enat @ X2 )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot
% 5.64/5.92 thf(fact_4061_max__bot2,axiom,
% 5.64/5.92 ! [X2: set_nat] :
% 5.64/5.92 ( ( ord_max_set_nat @ X2 @ bot_bot_set_nat )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot2
% 5.64/5.92 thf(fact_4062_max__bot2,axiom,
% 5.64/5.92 ! [X2: set_int] :
% 5.64/5.92 ( ( ord_max_set_int @ X2 @ bot_bot_set_int )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot2
% 5.64/5.92 thf(fact_4063_max__bot2,axiom,
% 5.64/5.92 ! [X2: set_real] :
% 5.64/5.92 ( ( ord_max_set_real @ X2 @ bot_bot_set_real )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot2
% 5.64/5.92 thf(fact_4064_max__bot2,axiom,
% 5.64/5.92 ! [X2: nat] :
% 5.64/5.92 ( ( ord_max_nat @ X2 @ bot_bot_nat )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot2
% 5.64/5.92 thf(fact_4065_max__bot2,axiom,
% 5.64/5.92 ! [X2: extended_enat] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ X2 @ bot_bo4199563552545308370d_enat )
% 5.64/5.92 = X2 ) ).
% 5.64/5.92
% 5.64/5.92 % max_bot2
% 5.64/5.92 thf(fact_4066_length__list__update,axiom,
% 5.64/5.92 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) )
% 5.64/5.92 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % length_list_update
% 5.64/5.92 thf(fact_4067_length__list__update,axiom,
% 5.64/5.92 ! [Xs2: list_o,I: nat,X2: $o] :
% 5.64/5.92 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I @ X2 ) )
% 5.64/5.92 = ( size_size_list_o @ Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % length_list_update
% 5.64/5.92 thf(fact_4068_length__list__update,axiom,
% 5.64/5.92 ! [Xs2: list_nat,I: nat,X2: nat] :
% 5.64/5.92 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) )
% 5.64/5.92 = ( size_size_list_nat @ Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % length_list_update
% 5.64/5.92 thf(fact_4069_length__list__update,axiom,
% 5.64/5.92 ! [Xs2: list_int,I: nat,X2: int] :
% 5.64/5.92 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I @ X2 ) )
% 5.64/5.92 = ( size_size_list_int @ Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % length_list_update
% 5.64/5.92 thf(fact_4070_max__Suc__Suc,axiom,
% 5.64/5.92 ! [M: nat,N: nat] :
% 5.64/5.92 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.64/5.92 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_Suc_Suc
% 5.64/5.92 thf(fact_4071_max__nat_Oeq__neutr__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( ( ord_max_nat @ A @ B )
% 5.64/5.92 = zero_zero_nat )
% 5.64/5.92 = ( ( A = zero_zero_nat )
% 5.64/5.92 & ( B = zero_zero_nat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_nat.eq_neutr_iff
% 5.64/5.92 thf(fact_4072_max__nat_Oleft__neutral,axiom,
% 5.64/5.92 ! [A: nat] :
% 5.64/5.92 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.64/5.92 = A ) ).
% 5.64/5.92
% 5.64/5.92 % max_nat.left_neutral
% 5.64/5.92 thf(fact_4073_max__nat_Oneutr__eq__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( zero_zero_nat
% 5.64/5.92 = ( ord_max_nat @ A @ B ) )
% 5.64/5.92 = ( ( A = zero_zero_nat )
% 5.64/5.92 & ( B = zero_zero_nat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_nat.neutr_eq_iff
% 5.64/5.92 thf(fact_4074_max__nat_Oright__neutral,axiom,
% 5.64/5.92 ! [A: nat] :
% 5.64/5.92 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.64/5.92 = A ) ).
% 5.64/5.92
% 5.64/5.92 % max_nat.right_neutral
% 5.64/5.92 thf(fact_4075_max__0L,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.64/5.92 = N ) ).
% 5.64/5.92
% 5.64/5.92 % max_0L
% 5.64/5.92 thf(fact_4076_max__0R,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.64/5.92 = N ) ).
% 5.64/5.92
% 5.64/5.92 % max_0R
% 5.64/5.92 thf(fact_4077_nth__list__update__neq,axiom,
% 5.64/5.92 ! [I: nat,J: nat,Xs2: list_int,X2: int] :
% 5.64/5.92 ( ( I != J )
% 5.64/5.92 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( nth_int @ Xs2 @ J ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_neq
% 5.64/5.92 thf(fact_4078_nth__list__update__neq,axiom,
% 5.64/5.92 ! [I: nat,J: nat,Xs2: list_nat,X2: nat] :
% 5.64/5.92 ( ( I != J )
% 5.64/5.92 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( nth_nat @ Xs2 @ J ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_neq
% 5.64/5.92 thf(fact_4079_nth__list__update__neq,axiom,
% 5.64/5.92 ! [I: nat,J: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( I != J )
% 5.64/5.92 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_neq
% 5.64/5.92 thf(fact_4080_list__update__id,axiom,
% 5.64/5.92 ! [Xs2: list_int,I: nat] :
% 5.64/5.92 ( ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ I ) )
% 5.64/5.92 = Xs2 ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_id
% 5.64/5.92 thf(fact_4081_list__update__id,axiom,
% 5.64/5.92 ! [Xs2: list_nat,I: nat] :
% 5.64/5.92 ( ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ I ) )
% 5.64/5.92 = Xs2 ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_id
% 5.64/5.92 thf(fact_4082_list__update__id,axiom,
% 5.64/5.92 ! [Xs2: list_VEBT_VEBT,I: nat] :
% 5.64/5.92 ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 5.64/5.92 = Xs2 ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_id
% 5.64/5.92 thf(fact_4083_max__number__of_I1_J,axiom,
% 5.64/5.92 ! [U: num,V: num] :
% 5.64/5.92 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.64/5.92 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.64/5.92 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.64/5.92 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_number_of(1)
% 5.64/5.92 thf(fact_4084_max__number__of_I1_J,axiom,
% 5.64/5.92 ! [U: num,V: num] :
% 5.64/5.92 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.92 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.92 = ( numeral_numeral_rat @ V ) ) )
% 5.64/5.92 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.92 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.92 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_number_of(1)
% 5.64/5.92 thf(fact_4085_max__number__of_I1_J,axiom,
% 5.64/5.92 ! [U: num,V: num] :
% 5.64/5.92 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.92 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.92 = ( numeral_numeral_nat @ V ) ) )
% 5.64/5.92 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.92 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.64/5.92 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_number_of(1)
% 5.64/5.92 thf(fact_4086_max__number__of_I1_J,axiom,
% 5.64/5.92 ! [U: num,V: num] :
% 5.64/5.92 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.92 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.92 = ( numeral_numeral_int @ V ) ) )
% 5.64/5.92 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.92 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.92 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_number_of(1)
% 5.64/5.92 thf(fact_4087_max__number__of_I1_J,axiom,
% 5.64/5.92 ! [U: num,V: num] :
% 5.64/5.92 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.92 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.92 = ( numeral_numeral_real @ V ) ) )
% 5.64/5.92 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.92 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.92 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_number_of(1)
% 5.64/5.92 thf(fact_4088_max__0__1_I4_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ zero_z5237406670263579293d_enat )
% 5.64/5.92 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(4)
% 5.64/5.92 thf(fact_4089_max__0__1_I4_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ zero_zero_real )
% 5.64/5.92 = ( numeral_numeral_real @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(4)
% 5.64/5.92 thf(fact_4090_max__0__1_I4_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ zero_zero_rat )
% 5.64/5.92 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(4)
% 5.64/5.92 thf(fact_4091_max__0__1_I4_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ zero_zero_nat )
% 5.64/5.92 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(4)
% 5.64/5.92 thf(fact_4092_max__0__1_I4_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ zero_zero_int )
% 5.64/5.92 = ( numeral_numeral_int @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(4)
% 5.64/5.92 thf(fact_4093_max__0__1_I3_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.64/5.92 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(3)
% 5.64/5.92 thf(fact_4094_max__0__1_I3_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_real @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(3)
% 5.64/5.92 thf(fact_4095_max__0__1_I3_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(3)
% 5.64/5.92 thf(fact_4096_max__0__1_I3_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(3)
% 5.64/5.92 thf(fact_4097_max__0__1_I3_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_int @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(3)
% 5.64/5.92 thf(fact_4098_max__0__1_I2_J,axiom,
% 5.64/5.92 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.64/5.92 = one_one_real ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(2)
% 5.64/5.92 thf(fact_4099_max__0__1_I2_J,axiom,
% 5.64/5.92 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.64/5.92 = one_one_rat ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(2)
% 5.64/5.92 thf(fact_4100_max__0__1_I2_J,axiom,
% 5.64/5.92 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.64/5.92 = one_one_nat ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(2)
% 5.64/5.92 thf(fact_4101_max__0__1_I2_J,axiom,
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.64/5.92 = one_on7984719198319812577d_enat ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(2)
% 5.64/5.92 thf(fact_4102_max__0__1_I2_J,axiom,
% 5.64/5.92 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.64/5.92 = one_one_int ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(2)
% 5.64/5.92 thf(fact_4103_max__0__1_I1_J,axiom,
% 5.64/5.92 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.64/5.92 = one_one_real ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(1)
% 5.64/5.92 thf(fact_4104_max__0__1_I1_J,axiom,
% 5.64/5.92 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.64/5.92 = one_one_rat ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(1)
% 5.64/5.92 thf(fact_4105_max__0__1_I1_J,axiom,
% 5.64/5.92 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.64/5.92 = one_one_nat ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(1)
% 5.64/5.92 thf(fact_4106_max__0__1_I1_J,axiom,
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.64/5.92 = one_on7984719198319812577d_enat ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(1)
% 5.64/5.92 thf(fact_4107_max__0__1_I1_J,axiom,
% 5.64/5.92 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.64/5.92 = one_one_int ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(1)
% 5.64/5.92 thf(fact_4108_max__0__1_I6_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X2 ) @ one_on7984719198319812577d_enat )
% 5.64/5.92 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(6)
% 5.64/5.92 thf(fact_4109_max__0__1_I6_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ one_one_real )
% 5.64/5.92 = ( numeral_numeral_real @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(6)
% 5.64/5.92 thf(fact_4110_max__0__1_I6_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat )
% 5.64/5.92 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(6)
% 5.64/5.92 thf(fact_4111_max__0__1_I6_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat )
% 5.64/5.92 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(6)
% 5.64/5.92 thf(fact_4112_max__0__1_I6_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ one_one_int )
% 5.64/5.92 = ( numeral_numeral_int @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(6)
% 5.64/5.92 thf(fact_4113_max__0__1_I5_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X2 ) )
% 5.64/5.92 = ( numera1916890842035813515d_enat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(5)
% 5.64/5.92 thf(fact_4114_max__0__1_I5_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_real @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(5)
% 5.64/5.92 thf(fact_4115_max__0__1_I5_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_rat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(5)
% 5.64/5.92 thf(fact_4116_max__0__1_I5_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_nat @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(5)
% 5.64/5.92 thf(fact_4117_max__0__1_I5_J,axiom,
% 5.64/5.92 ! [X2: num] :
% 5.64/5.92 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 5.64/5.92 = ( numeral_numeral_int @ X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_0_1(5)
% 5.64/5.92 thf(fact_4118_list__update__beyond,axiom,
% 5.64/5.92 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I )
% 5.64/5.92 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_beyond
% 5.64/5.92 thf(fact_4119_list__update__beyond,axiom,
% 5.64/5.92 ! [Xs2: list_o,I: nat,X2: $o] :
% 5.64/5.92 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I )
% 5.64/5.92 => ( ( list_update_o @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_beyond
% 5.64/5.92 thf(fact_4120_list__update__beyond,axiom,
% 5.64/5.92 ! [Xs2: list_nat,I: nat,X2: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I )
% 5.64/5.92 => ( ( list_update_nat @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_beyond
% 5.64/5.92 thf(fact_4121_list__update__beyond,axiom,
% 5.64/5.92 ! [Xs2: list_int,I: nat,X2: int] :
% 5.64/5.92 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I )
% 5.64/5.92 => ( ( list_update_int @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_beyond
% 5.64/5.92 thf(fact_4122_dbl__inc__simps_I2_J,axiom,
% 5.64/5.92 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.64/5.92 = one_one_complex ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(2)
% 5.64/5.92 thf(fact_4123_dbl__inc__simps_I2_J,axiom,
% 5.64/5.92 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.64/5.92 = one_one_real ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(2)
% 5.64/5.92 thf(fact_4124_dbl__inc__simps_I2_J,axiom,
% 5.64/5.92 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.64/5.92 = one_one_rat ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(2)
% 5.64/5.92 thf(fact_4125_dbl__inc__simps_I2_J,axiom,
% 5.64/5.92 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.64/5.92 = one_one_int ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(2)
% 5.64/5.92 thf(fact_4126_dbl__inc__simps_I5_J,axiom,
% 5.64/5.92 ! [K: num] :
% 5.64/5.92 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.64/5.92 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(5)
% 5.64/5.92 thf(fact_4127_dbl__inc__simps_I5_J,axiom,
% 5.64/5.92 ! [K: num] :
% 5.64/5.92 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.64/5.92 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(5)
% 5.64/5.92 thf(fact_4128_dbl__inc__simps_I5_J,axiom,
% 5.64/5.92 ! [K: num] :
% 5.64/5.92 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.64/5.92 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(5)
% 5.64/5.92 thf(fact_4129_dbl__inc__simps_I5_J,axiom,
% 5.64/5.92 ! [K: num] :
% 5.64/5.92 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.64/5.92 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_simps(5)
% 5.64/5.92 thf(fact_4130_nth__list__update__eq,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.92 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ I )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_eq
% 5.64/5.92 thf(fact_4131_nth__list__update__eq,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_o,X2: $o] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.92 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X2 ) @ I )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_eq
% 5.64/5.92 thf(fact_4132_nth__list__update__eq,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_nat,X2: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.92 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ I )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_eq
% 5.64/5.92 thf(fact_4133_nth__list__update__eq,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_int,X2: int] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.92 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ I )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update_eq
% 5.64/5.92 thf(fact_4134_set__swap,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.92 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.92 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) )
% 5.64/5.92 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_swap
% 5.64/5.92 thf(fact_4135_set__swap,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_o,J: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.92 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.92 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I @ ( nth_o @ Xs2 @ J ) ) @ J @ ( nth_o @ Xs2 @ I ) ) )
% 5.64/5.92 = ( set_o2 @ Xs2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_swap
% 5.64/5.92 thf(fact_4136_set__swap,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_nat,J: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.92 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.92 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I @ ( nth_nat @ Xs2 @ J ) ) @ J @ ( nth_nat @ Xs2 @ I ) ) )
% 5.64/5.92 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_swap
% 5.64/5.92 thf(fact_4137_set__swap,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_int,J: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.92 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.92 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I @ ( nth_int @ Xs2 @ J ) ) @ J @ ( nth_int @ Xs2 @ I ) ) )
% 5.64/5.92 = ( set_int2 @ Xs2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_swap
% 5.64/5.92 thf(fact_4138_list__update__swap,axiom,
% 5.64/5.92 ! [I: nat,I6: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT,X7: vEBT_VEBT] :
% 5.64/5.92 ( ( I != I6 )
% 5.64/5.92 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ I6 @ X7 )
% 5.64/5.92 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I6 @ X7 ) @ I @ X2 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_swap
% 5.64/5.92 thf(fact_4139_max__def,axiom,
% 5.64/5.92 ( ord_ma741700101516333627d_enat
% 5.64/5.92 = ( ^ [A3: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4140_max__def,axiom,
% 5.64/5.92 ( ord_max_set_nat
% 5.64/5.92 = ( ^ [A3: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4141_max__def,axiom,
% 5.64/5.92 ( ord_max_rat
% 5.64/5.92 = ( ^ [A3: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4142_max__def,axiom,
% 5.64/5.92 ( ord_max_num
% 5.64/5.92 = ( ^ [A3: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4143_max__def,axiom,
% 5.64/5.92 ( ord_max_nat
% 5.64/5.92 = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4144_max__def,axiom,
% 5.64/5.92 ( ord_max_int
% 5.64/5.92 = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4145_max__def,axiom,
% 5.64/5.92 ( ord_max_real
% 5.64/5.92 = ( ^ [A3: real,B3: real] : ( if_real @ ( ord_less_eq_real @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def
% 5.64/5.92 thf(fact_4146_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: extended_enat,X2: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4147_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: set_nat,X2: set_nat] :
% 5.64/5.92 ( ( ord_less_eq_set_nat @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_max_set_nat @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4148_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: rat,X2: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_max_rat @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4149_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: num,X2: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_max_num @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4150_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: nat,X2: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_max_nat @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4151_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: int,X2: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_max_int @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4152_max__absorb1,axiom,
% 5.64/5.92 ! [Y4: real,X2: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.92 => ( ( ord_max_real @ X2 @ Y4 )
% 5.64/5.92 = X2 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb1
% 5.64/5.92 thf(fact_4153_max__absorb2,axiom,
% 5.64/5.92 ! [X2: extended_enat,Y4: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4154_max__absorb2,axiom,
% 5.64/5.92 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.92 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_max_set_nat @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4155_max__absorb2,axiom,
% 5.64/5.92 ! [X2: rat,Y4: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_max_rat @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4156_max__absorb2,axiom,
% 5.64/5.92 ! [X2: num,Y4: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_max_num @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4157_max__absorb2,axiom,
% 5.64/5.92 ! [X2: nat,Y4: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_max_nat @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4158_max__absorb2,axiom,
% 5.64/5.92 ! [X2: int,Y4: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_max_int @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4159_max__absorb2,axiom,
% 5.64/5.92 ! [X2: real,Y4: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.92 => ( ( ord_max_real @ X2 @ Y4 )
% 5.64/5.92 = Y4 ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_absorb2
% 5.64/5.92 thf(fact_4160_max__add__distrib__left,axiom,
% 5.64/5.92 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.92 ( ( plus_plus_real @ ( ord_max_real @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_real @ ( plus_plus_real @ X2 @ Z ) @ ( plus_plus_real @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_left
% 5.64/5.92 thf(fact_4161_max__add__distrib__left,axiom,
% 5.64/5.92 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.92 ( ( plus_plus_rat @ ( ord_max_rat @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Z ) @ ( plus_plus_rat @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_left
% 5.64/5.92 thf(fact_4162_max__add__distrib__left,axiom,
% 5.64/5.92 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.92 ( ( plus_plus_nat @ ( ord_max_nat @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Z ) @ ( plus_plus_nat @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_left
% 5.64/5.92 thf(fact_4163_max__add__distrib__left,axiom,
% 5.64/5.92 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.92 ( ( plus_plus_int @ ( ord_max_int @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_int @ ( plus_plus_int @ X2 @ Z ) @ ( plus_plus_int @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_left
% 5.64/5.92 thf(fact_4164_max__add__distrib__right,axiom,
% 5.64/5.92 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.92 ( ( plus_plus_real @ X2 @ ( ord_max_real @ Y4 @ Z ) )
% 5.64/5.92 = ( ord_max_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_right
% 5.64/5.92 thf(fact_4165_max__add__distrib__right,axiom,
% 5.64/5.92 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.92 ( ( plus_plus_rat @ X2 @ ( ord_max_rat @ Y4 @ Z ) )
% 5.64/5.92 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Y4 ) @ ( plus_plus_rat @ X2 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_right
% 5.64/5.92 thf(fact_4166_max__add__distrib__right,axiom,
% 5.64/5.92 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.92 ( ( plus_plus_nat @ X2 @ ( ord_max_nat @ Y4 @ Z ) )
% 5.64/5.92 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Y4 ) @ ( plus_plus_nat @ X2 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_right
% 5.64/5.92 thf(fact_4167_max__add__distrib__right,axiom,
% 5.64/5.92 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.92 ( ( plus_plus_int @ X2 @ ( ord_max_int @ Y4 @ Z ) )
% 5.64/5.92 = ( ord_max_int @ ( plus_plus_int @ X2 @ Y4 ) @ ( plus_plus_int @ X2 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_add_distrib_right
% 5.64/5.92 thf(fact_4168_max__diff__distrib__left,axiom,
% 5.64/5.92 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.92 ( ( minus_minus_real @ ( ord_max_real @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_real @ ( minus_minus_real @ X2 @ Z ) @ ( minus_minus_real @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_diff_distrib_left
% 5.64/5.92 thf(fact_4169_max__diff__distrib__left,axiom,
% 5.64/5.92 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.92 ( ( minus_minus_rat @ ( ord_max_rat @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_rat @ ( minus_minus_rat @ X2 @ Z ) @ ( minus_minus_rat @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_diff_distrib_left
% 5.64/5.92 thf(fact_4170_max__diff__distrib__left,axiom,
% 5.64/5.92 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.92 ( ( minus_minus_int @ ( ord_max_int @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ord_max_int @ ( minus_minus_int @ X2 @ Z ) @ ( minus_minus_int @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_diff_distrib_left
% 5.64/5.92 thf(fact_4171_nat__add__max__left,axiom,
% 5.64/5.92 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.92 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 5.64/5.92 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N @ Q3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_add_max_left
% 5.64/5.92 thf(fact_4172_nat__add__max__right,axiom,
% 5.64/5.92 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.92 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 5.64/5.92 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_add_max_right
% 5.64/5.92 thf(fact_4173_nat__mult__max__left,axiom,
% 5.64/5.92 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.92 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q3 )
% 5.64/5.92 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_mult_max_left
% 5.64/5.92 thf(fact_4174_nat__mult__max__right,axiom,
% 5.64/5.92 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.92 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q3 ) )
% 5.64/5.92 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_mult_max_right
% 5.64/5.92 thf(fact_4175_max__def__raw,axiom,
% 5.64/5.92 ( ord_ma741700101516333627d_enat
% 5.64/5.92 = ( ^ [A3: extended_enat,B3: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4176_max__def__raw,axiom,
% 5.64/5.92 ( ord_max_set_nat
% 5.64/5.92 = ( ^ [A3: set_nat,B3: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4177_max__def__raw,axiom,
% 5.64/5.92 ( ord_max_rat
% 5.64/5.92 = ( ^ [A3: rat,B3: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4178_max__def__raw,axiom,
% 5.64/5.92 ( ord_max_num
% 5.64/5.92 = ( ^ [A3: num,B3: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4179_max__def__raw,axiom,
% 5.64/5.92 ( ord_max_nat
% 5.64/5.92 = ( ^ [A3: nat,B3: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4180_max__def__raw,axiom,
% 5.64/5.92 ( ord_max_int
% 5.64/5.92 = ( ^ [A3: int,B3: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4181_max__def__raw,axiom,
% 5.64/5.92 ( ord_max_real
% 5.64/5.92 = ( ^ [A3: real,B3: real] : ( if_real @ ( ord_less_eq_real @ A3 @ B3 ) @ B3 @ A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_def_raw
% 5.64/5.92 thf(fact_4182_nat__minus__add__max,axiom,
% 5.64/5.92 ! [N: nat,M: nat] :
% 5.64/5.92 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.64/5.92 = ( ord_max_nat @ N @ M ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_minus_add_max
% 5.64/5.92 thf(fact_4183_set__update__subsetI,axiom,
% 5.64/5.92 ! [Xs2: list_P6011104703257516679at_nat,A4: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,I: nat] :
% 5.64/5.92 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ A4 )
% 5.64/5.92 => ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 5.64/5.92 => ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I @ X2 ) ) @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_subsetI
% 5.64/5.92 thf(fact_4184_set__update__subsetI,axiom,
% 5.64/5.92 ! [Xs2: list_complex,A4: set_complex,X2: complex,I: nat] :
% 5.64/5.92 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A4 )
% 5.64/5.92 => ( ( member_complex @ X2 @ A4 )
% 5.64/5.92 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs2 @ I @ X2 ) ) @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_subsetI
% 5.64/5.92 thf(fact_4185_set__update__subsetI,axiom,
% 5.64/5.92 ! [Xs2: list_real,A4: set_real,X2: real,I: nat] :
% 5.64/5.92 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs2 ) @ A4 )
% 5.64/5.92 => ( ( member_real @ X2 @ A4 )
% 5.64/5.92 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X2 ) ) @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_subsetI
% 5.64/5.92 thf(fact_4186_set__update__subsetI,axiom,
% 5.64/5.92 ! [Xs2: list_int,A4: set_int,X2: int,I: nat] :
% 5.64/5.92 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A4 )
% 5.64/5.92 => ( ( member_int @ X2 @ A4 )
% 5.64/5.92 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X2 ) ) @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_subsetI
% 5.64/5.92 thf(fact_4187_set__update__subsetI,axiom,
% 5.64/5.92 ! [Xs2: list_VEBT_VEBT,A4: set_VEBT_VEBT,X2: vEBT_VEBT,I: nat] :
% 5.64/5.92 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A4 )
% 5.64/5.92 => ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.92 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) ) @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_subsetI
% 5.64/5.92 thf(fact_4188_set__update__subsetI,axiom,
% 5.64/5.92 ! [Xs2: list_nat,A4: set_nat,X2: nat,I: nat] :
% 5.64/5.92 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A4 )
% 5.64/5.92 => ( ( member_nat @ X2 @ A4 )
% 5.64/5.92 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X2 ) ) @ A4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_subsetI
% 5.64/5.92 thf(fact_4189_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_P6011104703257516679at_nat,X2: product_prod_nat_nat] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 5.64/5.92 => ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4190_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_complex,X2: complex] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 5.64/5.92 => ( member_complex @ X2 @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4191_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_real,X2: real] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 5.64/5.92 => ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4192_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.92 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4193_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_o,X2: $o] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.92 => ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4194_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_nat,X2: nat] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.92 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4195_set__update__memI,axiom,
% 5.64/5.92 ! [N: nat,Xs2: list_int,X2: int] :
% 5.64/5.92 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.92 => ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X2 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % set_update_memI
% 5.64/5.92 thf(fact_4196_list__update__same__conv,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.92 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 )
% 5.64/5.92 = ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 5.64/5.92 = X2 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_same_conv
% 5.64/5.92 thf(fact_4197_list__update__same__conv,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_o,X2: $o] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.92 => ( ( ( list_update_o @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 )
% 5.64/5.92 = ( ( nth_o @ Xs2 @ I )
% 5.64/5.92 = X2 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_same_conv
% 5.64/5.92 thf(fact_4198_list__update__same__conv,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_nat,X2: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.92 => ( ( ( list_update_nat @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 )
% 5.64/5.92 = ( ( nth_nat @ Xs2 @ I )
% 5.64/5.92 = X2 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_same_conv
% 5.64/5.92 thf(fact_4199_list__update__same__conv,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_int,X2: int] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.92 => ( ( ( list_update_int @ Xs2 @ I @ X2 )
% 5.64/5.92 = Xs2 )
% 5.64/5.92 = ( ( nth_int @ Xs2 @ I )
% 5.64/5.92 = X2 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % list_update_same_conv
% 5.64/5.92 thf(fact_4200_nth__list__update,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.64/5.92 => ( ( ( I = J )
% 5.64/5.92 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = X2 ) )
% 5.64/5.92 & ( ( I != J )
% 5.64/5.92 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update
% 5.64/5.92 thf(fact_4201_nth__list__update,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_o,X2: $o,J: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 5.64/5.92 => ( ( nth_o @ ( list_update_o @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( ( ( I = J )
% 5.64/5.92 => X2 )
% 5.64/5.92 & ( ( I != J )
% 5.64/5.92 => ( nth_o @ Xs2 @ J ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update
% 5.64/5.92 thf(fact_4202_nth__list__update,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_nat,J: nat,X2: nat] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 5.64/5.92 => ( ( ( I = J )
% 5.64/5.92 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = X2 ) )
% 5.64/5.92 & ( ( I != J )
% 5.64/5.92 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( nth_nat @ Xs2 @ J ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update
% 5.64/5.92 thf(fact_4203_nth__list__update,axiom,
% 5.64/5.92 ! [I: nat,Xs2: list_int,J: nat,X2: int] :
% 5.64/5.92 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 5.64/5.92 => ( ( ( I = J )
% 5.64/5.92 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = X2 ) )
% 5.64/5.92 & ( ( I != J )
% 5.64/5.92 => ( ( nth_int @ ( list_update_int @ Xs2 @ I @ X2 ) @ J )
% 5.64/5.92 = ( nth_int @ Xs2 @ J ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nth_list_update
% 5.64/5.92 thf(fact_4204_dbl__inc__def,axiom,
% 5.64/5.92 ( neg_nu8557863876264182079omplex
% 5.64/5.92 = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_def
% 5.64/5.92 thf(fact_4205_dbl__inc__def,axiom,
% 5.64/5.92 ( neg_nu8295874005876285629c_real
% 5.64/5.92 = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_def
% 5.64/5.92 thf(fact_4206_dbl__inc__def,axiom,
% 5.64/5.92 ( neg_nu5219082963157363817nc_rat
% 5.64/5.92 = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_def
% 5.64/5.92 thf(fact_4207_dbl__inc__def,axiom,
% 5.64/5.92 ( neg_nu5851722552734809277nc_int
% 5.64/5.92 = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dbl_inc_def
% 5.64/5.92 thf(fact_4208_Euclid__induct,axiom,
% 5.64/5.92 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.64/5.92 ( ! [A5: nat,B5: nat] :
% 5.64/5.92 ( ( P @ A5 @ B5 )
% 5.64/5.92 = ( P @ B5 @ A5 ) )
% 5.64/5.92 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.64/5.92 => ( ! [A5: nat,B5: nat] :
% 5.64/5.92 ( ( P @ A5 @ B5 )
% 5.64/5.92 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 5.64/5.92 => ( P @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % Euclid_induct
% 5.64/5.92 thf(fact_4209_vebt__insert_Osimps_I5_J,axiom,
% 5.64/5.92 ! [Mi: nat,Ma: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.64/5.92 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) @ X2 )
% 5.64/5.92 = ( if_VEBT_VEBT
% 5.64/5.92 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.64/5.92 & ~ ( ( X2 = Mi )
% 5.64/5.92 | ( X2 = Ma ) ) )
% 5.64/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ X2 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.64/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % vebt_insert.simps(5)
% 5.64/5.92 thf(fact_4210_vebt__insert_Oelims,axiom,
% 5.64/5.92 ! [X2: vEBT_VEBT,Xa2: nat,Y4: vEBT_VEBT] :
% 5.64/5.92 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.64/5.92 = Y4 )
% 5.64/5.92 => ( ! [A5: $o,B5: $o] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.92 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.92 => ( Y4
% 5.64/5.92 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.64/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.92 => ( Y4
% 5.64/5.92 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.64/5.92 & ( ( Xa2 != one_one_nat )
% 5.64/5.92 => ( Y4
% 5.64/5.92 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 5.64/5.92 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.64/5.92 => ( Y4
% 5.64/5.92 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) ) )
% 5.64/5.92 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.64/5.92 => ( Y4
% 5.64/5.92 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) )
% 5.64/5.92 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.92 => ( Y4
% 5.64/5.92 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.64/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.92 => ( Y4
% 5.64/5.92 != ( if_VEBT_VEBT
% 5.64/5.92 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.92 & ~ ( ( Xa2 = Mi2 )
% 5.64/5.92 | ( Xa2 = Ma2 ) ) )
% 5.64/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( 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 @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( 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 @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.64/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % vebt_insert.elims
% 5.64/5.92 thf(fact_4211_vebt__insert_Opelims,axiom,
% 5.64/5.92 ! [X2: vEBT_VEBT,Xa2: nat,Y4: vEBT_VEBT] :
% 5.64/5.92 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.64/5.92 = Y4 )
% 5.64/5.92 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/5.92 => ( ! [A5: $o,B5: $o] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/5.92 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.64/5.92 => ( Y4
% 5.64/5.92 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.64/5.92 & ( ( Xa2 != zero_zero_nat )
% 5.64/5.92 => ( ( ( Xa2 = one_one_nat )
% 5.64/5.92 => ( Y4
% 5.64/5.92 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.64/5.92 & ( ( Xa2 != one_one_nat )
% 5.64/5.92 => ( Y4
% 5.64/5.92 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 5.64/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.64/5.92 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.64/5.92 => ( ( Y4
% 5.64/5.92 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) )
% 5.64/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts @ S ) @ Xa2 ) ) ) )
% 5.64/5.92 => ( ! [Info2: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.64/5.92 => ( ( Y4
% 5.64/5.92 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 5.64/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ Xa2 ) ) ) )
% 5.64/5.92 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.92 => ( ( Y4
% 5.64/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.64/5.92 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/5.92 ( ( X2
% 5.64/5.92 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) )
% 5.64/5.92 => ( ( Y4
% 5.64/5.92 = ( if_VEBT_VEBT
% 5.64/5.92 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.64/5.92 & ~ ( ( Xa2 = Mi2 )
% 5.64/5.92 | ( Xa2 = Ma2 ) ) )
% 5.64/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( 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 @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( 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 @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.64/5.92 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) ) )
% 5.64/5.92 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % vebt_insert.pelims
% 5.64/5.92 thf(fact_4212_max__less__iff__conj,axiom,
% 5.64/5.92 ! [X2: extended_enat,Y4: extended_enat,Z: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ( ord_le72135733267957522d_enat @ X2 @ Z )
% 5.64/5.92 & ( ord_le72135733267957522d_enat @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_less_iff_conj
% 5.64/5.92 thf(fact_4213_max__less__iff__conj,axiom,
% 5.64/5.92 ! [X2: real,Y4: real,Z: real] :
% 5.64/5.92 ( ( ord_less_real @ ( ord_max_real @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ( ord_less_real @ X2 @ Z )
% 5.64/5.92 & ( ord_less_real @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_less_iff_conj
% 5.64/5.92 thf(fact_4214_max__less__iff__conj,axiom,
% 5.64/5.92 ! [X2: rat,Y4: rat,Z: rat] :
% 5.64/5.92 ( ( ord_less_rat @ ( ord_max_rat @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ( ord_less_rat @ X2 @ Z )
% 5.64/5.92 & ( ord_less_rat @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_less_iff_conj
% 5.64/5.92 thf(fact_4215_max__less__iff__conj,axiom,
% 5.64/5.92 ! [X2: num,Y4: num,Z: num] :
% 5.64/5.92 ( ( ord_less_num @ ( ord_max_num @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ( ord_less_num @ X2 @ Z )
% 5.64/5.92 & ( ord_less_num @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_less_iff_conj
% 5.64/5.92 thf(fact_4216_max__less__iff__conj,axiom,
% 5.64/5.92 ! [X2: nat,Y4: nat,Z: nat] :
% 5.64/5.92 ( ( ord_less_nat @ ( ord_max_nat @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ( ord_less_nat @ X2 @ Z )
% 5.64/5.92 & ( ord_less_nat @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_less_iff_conj
% 5.64/5.92 thf(fact_4217_max__less__iff__conj,axiom,
% 5.64/5.92 ! [X2: int,Y4: int,Z: int] :
% 5.64/5.92 ( ( ord_less_int @ ( ord_max_int @ X2 @ Y4 ) @ Z )
% 5.64/5.92 = ( ( ord_less_int @ X2 @ Z )
% 5.64/5.92 & ( ord_less_int @ Y4 @ Z ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max_less_iff_conj
% 5.64/5.92 thf(fact_4218_max_Oabsorb4,axiom,
% 5.64/5.92 ! [A: extended_enat,B: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb4
% 5.64/5.92 thf(fact_4219_max_Oabsorb4,axiom,
% 5.64/5.92 ! [A: real,B: real] :
% 5.64/5.92 ( ( ord_less_real @ A @ B )
% 5.64/5.92 => ( ( ord_max_real @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb4
% 5.64/5.92 thf(fact_4220_max_Oabsorb4,axiom,
% 5.64/5.92 ! [A: rat,B: rat] :
% 5.64/5.92 ( ( ord_less_rat @ A @ B )
% 5.64/5.92 => ( ( ord_max_rat @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb4
% 5.64/5.92 thf(fact_4221_max_Oabsorb4,axiom,
% 5.64/5.92 ! [A: num,B: num] :
% 5.64/5.92 ( ( ord_less_num @ A @ B )
% 5.64/5.92 => ( ( ord_max_num @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb4
% 5.64/5.92 thf(fact_4222_max_Oabsorb4,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( ord_less_nat @ A @ B )
% 5.64/5.92 => ( ( ord_max_nat @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb4
% 5.64/5.92 thf(fact_4223_max_Oabsorb4,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( ord_less_int @ A @ B )
% 5.64/5.92 => ( ( ord_max_int @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb4
% 5.64/5.92 thf(fact_4224_max_Oabsorb3,axiom,
% 5.64/5.92 ! [B: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb3
% 5.64/5.92 thf(fact_4225_max_Oabsorb3,axiom,
% 5.64/5.92 ! [B: real,A: real] :
% 5.64/5.92 ( ( ord_less_real @ B @ A )
% 5.64/5.92 => ( ( ord_max_real @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb3
% 5.64/5.92 thf(fact_4226_max_Oabsorb3,axiom,
% 5.64/5.92 ! [B: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_rat @ B @ A )
% 5.64/5.92 => ( ( ord_max_rat @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb3
% 5.64/5.92 thf(fact_4227_max_Oabsorb3,axiom,
% 5.64/5.92 ! [B: num,A: num] :
% 5.64/5.92 ( ( ord_less_num @ B @ A )
% 5.64/5.92 => ( ( ord_max_num @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb3
% 5.64/5.92 thf(fact_4228_max_Oabsorb3,axiom,
% 5.64/5.92 ! [B: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_nat @ B @ A )
% 5.64/5.92 => ( ( ord_max_nat @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb3
% 5.64/5.92 thf(fact_4229_max_Oabsorb3,axiom,
% 5.64/5.92 ! [B: int,A: int] :
% 5.64/5.92 ( ( ord_less_int @ B @ A )
% 5.64/5.92 => ( ( ord_max_int @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb3
% 5.64/5.92 thf(fact_4230_max_Oabsorb1,axiom,
% 5.64/5.92 ! [B: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb1
% 5.64/5.92 thf(fact_4231_max_Oabsorb1,axiom,
% 5.64/5.92 ! [B: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.92 => ( ( ord_max_rat @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb1
% 5.64/5.92 thf(fact_4232_max_Oabsorb1,axiom,
% 5.64/5.92 ! [B: num,A: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ B @ A )
% 5.64/5.92 => ( ( ord_max_num @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb1
% 5.64/5.92 thf(fact_4233_max_Oabsorb1,axiom,
% 5.64/5.92 ! [B: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.92 => ( ( ord_max_nat @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb1
% 5.64/5.92 thf(fact_4234_max_Oabsorb1,axiom,
% 5.64/5.92 ! [B: int,A: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.92 => ( ( ord_max_int @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb1
% 5.64/5.92 thf(fact_4235_max_Oabsorb1,axiom,
% 5.64/5.92 ! [B: real,A: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.92 => ( ( ord_max_real @ A @ B )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb1
% 5.64/5.92 thf(fact_4236_max_Oabsorb2,axiom,
% 5.64/5.92 ! [A: extended_enat,B: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.64/5.92 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb2
% 5.64/5.92 thf(fact_4237_max_Oabsorb2,axiom,
% 5.64/5.92 ! [A: rat,B: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.92 => ( ( ord_max_rat @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb2
% 5.64/5.92 thf(fact_4238_max_Oabsorb2,axiom,
% 5.64/5.92 ! [A: num,B: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ A @ B )
% 5.64/5.92 => ( ( ord_max_num @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb2
% 5.64/5.92 thf(fact_4239_max_Oabsorb2,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.92 => ( ( ord_max_nat @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb2
% 5.64/5.92 thf(fact_4240_max_Oabsorb2,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.92 => ( ( ord_max_int @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb2
% 5.64/5.92 thf(fact_4241_max_Oabsorb2,axiom,
% 5.64/5.92 ! [A: real,B: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.92 => ( ( ord_max_real @ A @ B )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb2
% 5.64/5.92 thf(fact_4242_max_Obounded__iff,axiom,
% 5.64/5.92 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.64/5.92 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.64/5.92 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.bounded_iff
% 5.64/5.92 thf(fact_4243_max_Obounded__iff,axiom,
% 5.64/5.92 ! [B: rat,C: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.64/5.92 = ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.92 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.bounded_iff
% 5.64/5.92 thf(fact_4244_max_Obounded__iff,axiom,
% 5.64/5.92 ! [B: num,C: num,A: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.64/5.92 = ( ( ord_less_eq_num @ B @ A )
% 5.64/5.92 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.bounded_iff
% 5.64/5.92 thf(fact_4245_max_Obounded__iff,axiom,
% 5.64/5.92 ! [B: nat,C: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.64/5.92 = ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.92 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.bounded_iff
% 5.64/5.92 thf(fact_4246_max_Obounded__iff,axiom,
% 5.64/5.92 ! [B: int,C: int,A: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.64/5.92 = ( ( ord_less_eq_int @ B @ A )
% 5.64/5.92 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.bounded_iff
% 5.64/5.92 thf(fact_4247_max_Obounded__iff,axiom,
% 5.64/5.92 ! [B: real,C: real,A: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A )
% 5.64/5.92 = ( ( ord_less_eq_real @ B @ A )
% 5.64/5.92 & ( ord_less_eq_real @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.bounded_iff
% 5.64/5.92 thf(fact_4248_max__enat__simps_I2_J,axiom,
% 5.64/5.92 ! [Q3: extended_enat] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.64/5.92 = Q3 ) ).
% 5.64/5.92
% 5.64/5.92 % max_enat_simps(2)
% 5.64/5.92 thf(fact_4249_max__enat__simps_I3_J,axiom,
% 5.64/5.92 ! [Q3: extended_enat] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.64/5.92 = Q3 ) ).
% 5.64/5.92
% 5.64/5.92 % max_enat_simps(3)
% 5.64/5.92 thf(fact_4250_max_Omono,axiom,
% 5.64/5.92 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.64/5.92 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.64/5.92 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.mono
% 5.64/5.92 thf(fact_4251_max_Omono,axiom,
% 5.64/5.92 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ C @ A )
% 5.64/5.92 => ( ( ord_less_eq_rat @ D @ B )
% 5.64/5.92 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.mono
% 5.64/5.92 thf(fact_4252_max_Omono,axiom,
% 5.64/5.92 ! [C: num,A: num,D: num,B: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ C @ A )
% 5.64/5.92 => ( ( ord_less_eq_num @ D @ B )
% 5.64/5.92 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.mono
% 5.64/5.92 thf(fact_4253_max_Omono,axiom,
% 5.64/5.92 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ C @ A )
% 5.64/5.92 => ( ( ord_less_eq_nat @ D @ B )
% 5.64/5.92 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.mono
% 5.64/5.92 thf(fact_4254_max_Omono,axiom,
% 5.64/5.92 ! [C: int,A: int,D: int,B: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ C @ A )
% 5.64/5.92 => ( ( ord_less_eq_int @ D @ B )
% 5.64/5.92 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.mono
% 5.64/5.92 thf(fact_4255_max_Omono,axiom,
% 5.64/5.92 ! [C: real,A: real,D: real,B: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ C @ A )
% 5.64/5.92 => ( ( ord_less_eq_real @ D @ B )
% 5.64/5.92 => ( ord_less_eq_real @ ( ord_max_real @ C @ D ) @ ( ord_max_real @ A @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.mono
% 5.64/5.92 thf(fact_4256_max_OorderE,axiom,
% 5.64/5.92 ! [B: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.64/5.92 => ( A
% 5.64/5.92 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderE
% 5.64/5.92 thf(fact_4257_max_OorderE,axiom,
% 5.64/5.92 ! [B: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.92 => ( A
% 5.64/5.92 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderE
% 5.64/5.92 thf(fact_4258_max_OorderE,axiom,
% 5.64/5.92 ! [B: num,A: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ B @ A )
% 5.64/5.92 => ( A
% 5.64/5.92 = ( ord_max_num @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderE
% 5.64/5.92 thf(fact_4259_max_OorderE,axiom,
% 5.64/5.92 ! [B: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.92 => ( A
% 5.64/5.92 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderE
% 5.64/5.92 thf(fact_4260_max_OorderE,axiom,
% 5.64/5.92 ! [B: int,A: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.92 => ( A
% 5.64/5.92 = ( ord_max_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderE
% 5.64/5.92 thf(fact_4261_max_OorderE,axiom,
% 5.64/5.92 ! [B: real,A: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.92 => ( A
% 5.64/5.92 = ( ord_max_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderE
% 5.64/5.92 thf(fact_4262_max_OorderI,axiom,
% 5.64/5.92 ! [A: extended_enat,B: extended_enat] :
% 5.64/5.92 ( ( A
% 5.64/5.92 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.64/5.92 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderI
% 5.64/5.92 thf(fact_4263_max_OorderI,axiom,
% 5.64/5.92 ! [A: rat,B: rat] :
% 5.64/5.92 ( ( A
% 5.64/5.92 = ( ord_max_rat @ A @ B ) )
% 5.64/5.92 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderI
% 5.64/5.92 thf(fact_4264_max_OorderI,axiom,
% 5.64/5.92 ! [A: num,B: num] :
% 5.64/5.92 ( ( A
% 5.64/5.92 = ( ord_max_num @ A @ B ) )
% 5.64/5.92 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderI
% 5.64/5.92 thf(fact_4265_max_OorderI,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( A
% 5.64/5.92 = ( ord_max_nat @ A @ B ) )
% 5.64/5.92 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderI
% 5.64/5.92 thf(fact_4266_max_OorderI,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( A
% 5.64/5.92 = ( ord_max_int @ A @ B ) )
% 5.64/5.92 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderI
% 5.64/5.92 thf(fact_4267_max_OorderI,axiom,
% 5.64/5.92 ! [A: real,B: real] :
% 5.64/5.92 ( ( A
% 5.64/5.92 = ( ord_max_real @ A @ B ) )
% 5.64/5.92 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.orderI
% 5.64/5.92 thf(fact_4268_max_OboundedE,axiom,
% 5.64/5.92 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.64/5.92 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedE
% 5.64/5.92 thf(fact_4269_max_OboundedE,axiom,
% 5.64/5.92 ! [B: rat,C: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.92 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedE
% 5.64/5.92 thf(fact_4270_max_OboundedE,axiom,
% 5.64/5.92 ! [B: num,C: num,A: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.64/5.92 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedE
% 5.64/5.92 thf(fact_4271_max_OboundedE,axiom,
% 5.64/5.92 ! [B: nat,C: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.92 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedE
% 5.64/5.92 thf(fact_4272_max_OboundedE,axiom,
% 5.64/5.92 ! [B: int,C: int,A: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.64/5.92 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedE
% 5.64/5.92 thf(fact_4273_max_OboundedE,axiom,
% 5.64/5.92 ! [B: real,C: real,A: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_eq_real @ B @ A )
% 5.64/5.92 => ~ ( ord_less_eq_real @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedE
% 5.64/5.92 thf(fact_4274_max_OboundedI,axiom,
% 5.64/5.92 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.64/5.92 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.64/5.92 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedI
% 5.64/5.92 thf(fact_4275_max_OboundedI,axiom,
% 5.64/5.92 ! [B: rat,A: rat,C: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ B @ A )
% 5.64/5.92 => ( ( ord_less_eq_rat @ C @ A )
% 5.64/5.92 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedI
% 5.64/5.92 thf(fact_4276_max_OboundedI,axiom,
% 5.64/5.92 ! [B: num,A: num,C: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ B @ A )
% 5.64/5.92 => ( ( ord_less_eq_num @ C @ A )
% 5.64/5.92 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedI
% 5.64/5.92 thf(fact_4277_max_OboundedI,axiom,
% 5.64/5.92 ! [B: nat,A: nat,C: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ B @ A )
% 5.64/5.92 => ( ( ord_less_eq_nat @ C @ A )
% 5.64/5.92 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedI
% 5.64/5.92 thf(fact_4278_max_OboundedI,axiom,
% 5.64/5.92 ! [B: int,A: int,C: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ B @ A )
% 5.64/5.92 => ( ( ord_less_eq_int @ C @ A )
% 5.64/5.92 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedI
% 5.64/5.92 thf(fact_4279_max_OboundedI,axiom,
% 5.64/5.92 ! [B: real,A: real,C: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ B @ A )
% 5.64/5.92 => ( ( ord_less_eq_real @ C @ A )
% 5.64/5.92 => ( ord_less_eq_real @ ( ord_max_real @ B @ C ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.boundedI
% 5.64/5.92 thf(fact_4280_max_Oorder__iff,axiom,
% 5.64/5.92 ( ord_le2932123472753598470d_enat
% 5.64/5.92 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 5.64/5.92 ( A3
% 5.64/5.92 = ( ord_ma741700101516333627d_enat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.order_iff
% 5.64/5.92 thf(fact_4281_max_Oorder__iff,axiom,
% 5.64/5.92 ( ord_less_eq_rat
% 5.64/5.92 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.92 ( A3
% 5.64/5.92 = ( ord_max_rat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.order_iff
% 5.64/5.92 thf(fact_4282_max_Oorder__iff,axiom,
% 5.64/5.92 ( ord_less_eq_num
% 5.64/5.92 = ( ^ [B3: num,A3: num] :
% 5.64/5.92 ( A3
% 5.64/5.92 = ( ord_max_num @ A3 @ B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.order_iff
% 5.64/5.92 thf(fact_4283_max_Oorder__iff,axiom,
% 5.64/5.92 ( ord_less_eq_nat
% 5.64/5.92 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.92 ( A3
% 5.64/5.92 = ( ord_max_nat @ A3 @ B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.order_iff
% 5.64/5.92 thf(fact_4284_max_Oorder__iff,axiom,
% 5.64/5.92 ( ord_less_eq_int
% 5.64/5.92 = ( ^ [B3: int,A3: int] :
% 5.64/5.92 ( A3
% 5.64/5.92 = ( ord_max_int @ A3 @ B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.order_iff
% 5.64/5.92 thf(fact_4285_max_Oorder__iff,axiom,
% 5.64/5.92 ( ord_less_eq_real
% 5.64/5.92 = ( ^ [B3: real,A3: real] :
% 5.64/5.92 ( A3
% 5.64/5.92 = ( ord_max_real @ A3 @ B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.order_iff
% 5.64/5.92 thf(fact_4286_max_Ocobounded1,axiom,
% 5.64/5.92 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded1
% 5.64/5.92 thf(fact_4287_max_Ocobounded1,axiom,
% 5.64/5.92 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded1
% 5.64/5.92 thf(fact_4288_max_Ocobounded1,axiom,
% 5.64/5.92 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded1
% 5.64/5.92 thf(fact_4289_max_Ocobounded1,axiom,
% 5.64/5.92 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded1
% 5.64/5.92 thf(fact_4290_max_Ocobounded1,axiom,
% 5.64/5.92 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded1
% 5.64/5.92 thf(fact_4291_max_Ocobounded1,axiom,
% 5.64/5.92 ! [A: real,B: real] : ( ord_less_eq_real @ A @ ( ord_max_real @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded1
% 5.64/5.92 thf(fact_4292_max_Ocobounded2,axiom,
% 5.64/5.92 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded2
% 5.64/5.92 thf(fact_4293_max_Ocobounded2,axiom,
% 5.64/5.92 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded2
% 5.64/5.92 thf(fact_4294_max_Ocobounded2,axiom,
% 5.64/5.92 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded2
% 5.64/5.92 thf(fact_4295_max_Ocobounded2,axiom,
% 5.64/5.92 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded2
% 5.64/5.92 thf(fact_4296_max_Ocobounded2,axiom,
% 5.64/5.92 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded2
% 5.64/5.92 thf(fact_4297_max_Ocobounded2,axiom,
% 5.64/5.92 ! [B: real,A: real] : ( ord_less_eq_real @ B @ ( ord_max_real @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.cobounded2
% 5.64/5.92 thf(fact_4298_le__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: extended_enat,X2: extended_enat,Y4: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_le2932123472753598470d_enat @ Z @ X2 )
% 5.64/5.92 | ( ord_le2932123472753598470d_enat @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % le_max_iff_disj
% 5.64/5.92 thf(fact_4299_le__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_eq_rat @ Z @ X2 )
% 5.64/5.92 | ( ord_less_eq_rat @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % le_max_iff_disj
% 5.64/5.92 thf(fact_4300_le__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: num,X2: num,Y4: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_eq_num @ Z @ X2 )
% 5.64/5.92 | ( ord_less_eq_num @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % le_max_iff_disj
% 5.64/5.92 thf(fact_4301_le__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: nat,X2: nat,Y4: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_eq_nat @ Z @ X2 )
% 5.64/5.92 | ( ord_less_eq_nat @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % le_max_iff_disj
% 5.64/5.92 thf(fact_4302_le__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: int,X2: int,Y4: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_eq_int @ Z @ X2 )
% 5.64/5.92 | ( ord_less_eq_int @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % le_max_iff_disj
% 5.64/5.92 thf(fact_4303_le__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ Z @ ( ord_max_real @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_eq_real @ Z @ X2 )
% 5.64/5.92 | ( ord_less_eq_real @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % le_max_iff_disj
% 5.64/5.92 thf(fact_4304_max_Oabsorb__iff1,axiom,
% 5.64/5.92 ( ord_le2932123472753598470d_enat
% 5.64/5.92 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ A3 @ B3 )
% 5.64/5.92 = A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff1
% 5.64/5.92 thf(fact_4305_max_Oabsorb__iff1,axiom,
% 5.64/5.92 ( ord_less_eq_rat
% 5.64/5.92 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.92 ( ( ord_max_rat @ A3 @ B3 )
% 5.64/5.92 = A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff1
% 5.64/5.92 thf(fact_4306_max_Oabsorb__iff1,axiom,
% 5.64/5.92 ( ord_less_eq_num
% 5.64/5.92 = ( ^ [B3: num,A3: num] :
% 5.64/5.92 ( ( ord_max_num @ A3 @ B3 )
% 5.64/5.92 = A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff1
% 5.64/5.92 thf(fact_4307_max_Oabsorb__iff1,axiom,
% 5.64/5.92 ( ord_less_eq_nat
% 5.64/5.92 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.92 ( ( ord_max_nat @ A3 @ B3 )
% 5.64/5.92 = A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff1
% 5.64/5.92 thf(fact_4308_max_Oabsorb__iff1,axiom,
% 5.64/5.92 ( ord_less_eq_int
% 5.64/5.92 = ( ^ [B3: int,A3: int] :
% 5.64/5.92 ( ( ord_max_int @ A3 @ B3 )
% 5.64/5.92 = A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff1
% 5.64/5.92 thf(fact_4309_max_Oabsorb__iff1,axiom,
% 5.64/5.92 ( ord_less_eq_real
% 5.64/5.92 = ( ^ [B3: real,A3: real] :
% 5.64/5.92 ( ( ord_max_real @ A3 @ B3 )
% 5.64/5.92 = A3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff1
% 5.64/5.92 thf(fact_4310_max_Oabsorb__iff2,axiom,
% 5.64/5.92 ( ord_le2932123472753598470d_enat
% 5.64/5.92 = ( ^ [A3: extended_enat,B3: extended_enat] :
% 5.64/5.92 ( ( ord_ma741700101516333627d_enat @ A3 @ B3 )
% 5.64/5.92 = B3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff2
% 5.64/5.92 thf(fact_4311_max_Oabsorb__iff2,axiom,
% 5.64/5.92 ( ord_less_eq_rat
% 5.64/5.92 = ( ^ [A3: rat,B3: rat] :
% 5.64/5.92 ( ( ord_max_rat @ A3 @ B3 )
% 5.64/5.92 = B3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff2
% 5.64/5.92 thf(fact_4312_max_Oabsorb__iff2,axiom,
% 5.64/5.92 ( ord_less_eq_num
% 5.64/5.92 = ( ^ [A3: num,B3: num] :
% 5.64/5.92 ( ( ord_max_num @ A3 @ B3 )
% 5.64/5.92 = B3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff2
% 5.64/5.92 thf(fact_4313_max_Oabsorb__iff2,axiom,
% 5.64/5.92 ( ord_less_eq_nat
% 5.64/5.92 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.92 ( ( ord_max_nat @ A3 @ B3 )
% 5.64/5.92 = B3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff2
% 5.64/5.92 thf(fact_4314_max_Oabsorb__iff2,axiom,
% 5.64/5.92 ( ord_less_eq_int
% 5.64/5.92 = ( ^ [A3: int,B3: int] :
% 5.64/5.92 ( ( ord_max_int @ A3 @ B3 )
% 5.64/5.92 = B3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff2
% 5.64/5.92 thf(fact_4315_max_Oabsorb__iff2,axiom,
% 5.64/5.92 ( ord_less_eq_real
% 5.64/5.92 = ( ^ [A3: real,B3: real] :
% 5.64/5.92 ( ( ord_max_real @ A3 @ B3 )
% 5.64/5.92 = B3 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.absorb_iff2
% 5.64/5.92 thf(fact_4316_max_OcoboundedI1,axiom,
% 5.64/5.92 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.64/5.92 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI1
% 5.64/5.92 thf(fact_4317_max_OcoboundedI1,axiom,
% 5.64/5.92 ! [C: rat,A: rat,B: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ C @ A )
% 5.64/5.92 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI1
% 5.64/5.92 thf(fact_4318_max_OcoboundedI1,axiom,
% 5.64/5.92 ! [C: num,A: num,B: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ C @ A )
% 5.64/5.92 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI1
% 5.64/5.92 thf(fact_4319_max_OcoboundedI1,axiom,
% 5.64/5.92 ! [C: nat,A: nat,B: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ C @ A )
% 5.64/5.92 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI1
% 5.64/5.92 thf(fact_4320_max_OcoboundedI1,axiom,
% 5.64/5.92 ! [C: int,A: int,B: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ C @ A )
% 5.64/5.92 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI1
% 5.64/5.92 thf(fact_4321_max_OcoboundedI1,axiom,
% 5.64/5.92 ! [C: real,A: real,B: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ C @ A )
% 5.64/5.92 => ( ord_less_eq_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI1
% 5.64/5.92 thf(fact_4322_max_OcoboundedI2,axiom,
% 5.64/5.92 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.64/5.92 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI2
% 5.64/5.92 thf(fact_4323_max_OcoboundedI2,axiom,
% 5.64/5.92 ! [C: rat,B: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_eq_rat @ C @ B )
% 5.64/5.92 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI2
% 5.64/5.92 thf(fact_4324_max_OcoboundedI2,axiom,
% 5.64/5.92 ! [C: num,B: num,A: num] :
% 5.64/5.92 ( ( ord_less_eq_num @ C @ B )
% 5.64/5.92 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI2
% 5.64/5.92 thf(fact_4325_max_OcoboundedI2,axiom,
% 5.64/5.92 ! [C: nat,B: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_eq_nat @ C @ B )
% 5.64/5.92 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI2
% 5.64/5.92 thf(fact_4326_max_OcoboundedI2,axiom,
% 5.64/5.92 ! [C: int,B: int,A: int] :
% 5.64/5.92 ( ( ord_less_eq_int @ C @ B )
% 5.64/5.92 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI2
% 5.64/5.92 thf(fact_4327_max_OcoboundedI2,axiom,
% 5.64/5.92 ! [C: real,B: real,A: real] :
% 5.64/5.92 ( ( ord_less_eq_real @ C @ B )
% 5.64/5.92 => ( ord_less_eq_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.coboundedI2
% 5.64/5.92 thf(fact_4328_max_Ostrict__coboundedI2,axiom,
% 5.64/5.92 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.64/5.92 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI2
% 5.64/5.92 thf(fact_4329_max_Ostrict__coboundedI2,axiom,
% 5.64/5.92 ! [C: real,B: real,A: real] :
% 5.64/5.92 ( ( ord_less_real @ C @ B )
% 5.64/5.92 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI2
% 5.64/5.92 thf(fact_4330_max_Ostrict__coboundedI2,axiom,
% 5.64/5.92 ! [C: rat,B: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_rat @ C @ B )
% 5.64/5.92 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI2
% 5.64/5.92 thf(fact_4331_max_Ostrict__coboundedI2,axiom,
% 5.64/5.92 ! [C: num,B: num,A: num] :
% 5.64/5.92 ( ( ord_less_num @ C @ B )
% 5.64/5.92 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI2
% 5.64/5.92 thf(fact_4332_max_Ostrict__coboundedI2,axiom,
% 5.64/5.92 ! [C: nat,B: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_nat @ C @ B )
% 5.64/5.92 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI2
% 5.64/5.92 thf(fact_4333_max_Ostrict__coboundedI2,axiom,
% 5.64/5.92 ! [C: int,B: int,A: int] :
% 5.64/5.92 ( ( ord_less_int @ C @ B )
% 5.64/5.92 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI2
% 5.64/5.92 thf(fact_4334_max_Ostrict__coboundedI1,axiom,
% 5.64/5.92 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.64/5.92 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI1
% 5.64/5.92 thf(fact_4335_max_Ostrict__coboundedI1,axiom,
% 5.64/5.92 ! [C: real,A: real,B: real] :
% 5.64/5.92 ( ( ord_less_real @ C @ A )
% 5.64/5.92 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI1
% 5.64/5.92 thf(fact_4336_max_Ostrict__coboundedI1,axiom,
% 5.64/5.92 ! [C: rat,A: rat,B: rat] :
% 5.64/5.92 ( ( ord_less_rat @ C @ A )
% 5.64/5.92 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI1
% 5.64/5.92 thf(fact_4337_max_Ostrict__coboundedI1,axiom,
% 5.64/5.92 ! [C: num,A: num,B: num] :
% 5.64/5.92 ( ( ord_less_num @ C @ A )
% 5.64/5.92 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI1
% 5.64/5.92 thf(fact_4338_max_Ostrict__coboundedI1,axiom,
% 5.64/5.92 ! [C: nat,A: nat,B: nat] :
% 5.64/5.92 ( ( ord_less_nat @ C @ A )
% 5.64/5.92 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI1
% 5.64/5.92 thf(fact_4339_max_Ostrict__coboundedI1,axiom,
% 5.64/5.92 ! [C: int,A: int,B: int] :
% 5.64/5.92 ( ( ord_less_int @ C @ A )
% 5.64/5.92 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_coboundedI1
% 5.64/5.92 thf(fact_4340_max_Ostrict__order__iff,axiom,
% 5.64/5.92 ( ord_le72135733267957522d_enat
% 5.64/5.92 = ( ^ [B3: extended_enat,A3: extended_enat] :
% 5.64/5.92 ( ( A3
% 5.64/5.92 = ( ord_ma741700101516333627d_enat @ A3 @ B3 ) )
% 5.64/5.92 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_order_iff
% 5.64/5.92 thf(fact_4341_max_Ostrict__order__iff,axiom,
% 5.64/5.92 ( ord_less_real
% 5.64/5.92 = ( ^ [B3: real,A3: real] :
% 5.64/5.92 ( ( A3
% 5.64/5.92 = ( ord_max_real @ A3 @ B3 ) )
% 5.64/5.92 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_order_iff
% 5.64/5.92 thf(fact_4342_max_Ostrict__order__iff,axiom,
% 5.64/5.92 ( ord_less_rat
% 5.64/5.92 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.92 ( ( A3
% 5.64/5.92 = ( ord_max_rat @ A3 @ B3 ) )
% 5.64/5.92 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_order_iff
% 5.64/5.92 thf(fact_4343_max_Ostrict__order__iff,axiom,
% 5.64/5.92 ( ord_less_num
% 5.64/5.92 = ( ^ [B3: num,A3: num] :
% 5.64/5.92 ( ( A3
% 5.64/5.92 = ( ord_max_num @ A3 @ B3 ) )
% 5.64/5.92 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_order_iff
% 5.64/5.92 thf(fact_4344_max_Ostrict__order__iff,axiom,
% 5.64/5.92 ( ord_less_nat
% 5.64/5.92 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.92 ( ( A3
% 5.64/5.92 = ( ord_max_nat @ A3 @ B3 ) )
% 5.64/5.92 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_order_iff
% 5.64/5.92 thf(fact_4345_max_Ostrict__order__iff,axiom,
% 5.64/5.92 ( ord_less_int
% 5.64/5.92 = ( ^ [B3: int,A3: int] :
% 5.64/5.92 ( ( A3
% 5.64/5.92 = ( ord_max_int @ A3 @ B3 ) )
% 5.64/5.92 & ( A3 != B3 ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_order_iff
% 5.64/5.92 thf(fact_4346_max_Ostrict__boundedE,axiom,
% 5.64/5.92 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.64/5.92 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_boundedE
% 5.64/5.92 thf(fact_4347_max_Ostrict__boundedE,axiom,
% 5.64/5.92 ! [B: real,C: real,A: real] :
% 5.64/5.92 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_real @ B @ A )
% 5.64/5.92 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_boundedE
% 5.64/5.92 thf(fact_4348_max_Ostrict__boundedE,axiom,
% 5.64/5.92 ! [B: rat,C: rat,A: rat] :
% 5.64/5.92 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_rat @ B @ A )
% 5.64/5.92 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_boundedE
% 5.64/5.92 thf(fact_4349_max_Ostrict__boundedE,axiom,
% 5.64/5.92 ! [B: num,C: num,A: num] :
% 5.64/5.92 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_num @ B @ A )
% 5.64/5.92 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_boundedE
% 5.64/5.92 thf(fact_4350_max_Ostrict__boundedE,axiom,
% 5.64/5.92 ! [B: nat,C: nat,A: nat] :
% 5.64/5.92 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_nat @ B @ A )
% 5.64/5.92 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_boundedE
% 5.64/5.92 thf(fact_4351_max_Ostrict__boundedE,axiom,
% 5.64/5.92 ! [B: int,C: int,A: int] :
% 5.64/5.92 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.64/5.92 => ~ ( ( ord_less_int @ B @ A )
% 5.64/5.92 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % max.strict_boundedE
% 5.64/5.92 thf(fact_4352_less__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: extended_enat,X2: extended_enat,Y4: extended_enat] :
% 5.64/5.92 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_le72135733267957522d_enat @ Z @ X2 )
% 5.64/5.92 | ( ord_le72135733267957522d_enat @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % less_max_iff_disj
% 5.64/5.92 thf(fact_4353_less__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.92 ( ( ord_less_real @ Z @ ( ord_max_real @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_real @ Z @ X2 )
% 5.64/5.92 | ( ord_less_real @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % less_max_iff_disj
% 5.64/5.92 thf(fact_4354_less__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.92 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_rat @ Z @ X2 )
% 5.64/5.92 | ( ord_less_rat @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % less_max_iff_disj
% 5.64/5.92 thf(fact_4355_less__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: num,X2: num,Y4: num] :
% 5.64/5.92 ( ( ord_less_num @ Z @ ( ord_max_num @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_num @ Z @ X2 )
% 5.64/5.92 | ( ord_less_num @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % less_max_iff_disj
% 5.64/5.92 thf(fact_4356_less__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: nat,X2: nat,Y4: nat] :
% 5.64/5.92 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_nat @ Z @ X2 )
% 5.64/5.92 | ( ord_less_nat @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % less_max_iff_disj
% 5.64/5.92 thf(fact_4357_less__max__iff__disj,axiom,
% 5.64/5.92 ! [Z: int,X2: int,Y4: int] :
% 5.64/5.92 ( ( ord_less_int @ Z @ ( ord_max_int @ X2 @ Y4 ) )
% 5.64/5.92 = ( ( ord_less_int @ Z @ X2 )
% 5.64/5.92 | ( ord_less_int @ Z @ Y4 ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % less_max_iff_disj
% 5.64/5.92 thf(fact_4358_divmod__BitM__2__eq,axiom,
% 5.64/5.92 ! [M: num] :
% 5.64/5.92 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.64/5.92 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_BitM_2_eq
% 5.64/5.92 thf(fact_4359_concat__bit__Suc,axiom,
% 5.64/5.92 ! [N: nat,K: int,L: int] :
% 5.64/5.92 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L )
% 5.64/5.92 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % concat_bit_Suc
% 5.64/5.92 thf(fact_4360_even__succ__mod__exp,axiom,
% 5.64/5.92 ! [A: nat,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.92 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_succ_mod_exp
% 5.64/5.92 thf(fact_4361_even__succ__mod__exp,axiom,
% 5.64/5.92 ! [A: int,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.92 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_succ_mod_exp
% 5.64/5.92 thf(fact_4362_even__succ__mod__exp,axiom,
% 5.64/5.92 ! [A: code_integer,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.92 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_succ_mod_exp
% 5.64/5.92 thf(fact_4363_divmod__algorithm__code_I6_J,axiom,
% 5.64/5.92 ! [M: num,N: num] :
% 5.64/5.92 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.92 = ( produc4245557441103728435nt_int
% 5.64/5.92 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.64/5.92 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_algorithm_code(6)
% 5.64/5.92 thf(fact_4364_divmod__algorithm__code_I6_J,axiom,
% 5.64/5.92 ! [M: num,N: num] :
% 5.64/5.92 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.92 = ( produc2626176000494625587at_nat
% 5.64/5.92 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.64/5.92 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_algorithm_code(6)
% 5.64/5.92 thf(fact_4365_divmod__algorithm__code_I6_J,axiom,
% 5.64/5.92 ! [M: num,N: num] :
% 5.64/5.92 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/5.92 = ( produc6916734918728496179nteger
% 5.64/5.92 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.64/5.92 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % divmod_algorithm_code(6)
% 5.64/5.92 thf(fact_4366_even__succ__div__exp,axiom,
% 5.64/5.92 ! [A: code_integer,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.92 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_succ_div_exp
% 5.64/5.92 thf(fact_4367_even__succ__div__exp,axiom,
% 5.64/5.92 ! [A: nat,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.92 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_succ_div_exp
% 5.64/5.92 thf(fact_4368_even__succ__div__exp,axiom,
% 5.64/5.92 ! [A: int,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.92 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_succ_div_exp
% 5.64/5.92 thf(fact_4369_nat__dvd__1__iff__1,axiom,
% 5.64/5.92 ! [M: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.64/5.92 = ( M = one_one_nat ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_dvd_1_iff_1
% 5.64/5.92 thf(fact_4370_dvd__add__triv__left__iff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_left_iff
% 5.64/5.92 thf(fact_4371_dvd__add__triv__left__iff,axiom,
% 5.64/5.92 ! [A: real,B: real] :
% 5.64/5.92 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_left_iff
% 5.64/5.92 thf(fact_4372_dvd__add__triv__left__iff,axiom,
% 5.64/5.92 ! [A: rat,B: rat] :
% 5.64/5.92 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_left_iff
% 5.64/5.92 thf(fact_4373_dvd__add__triv__left__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_left_iff
% 5.64/5.92 thf(fact_4374_dvd__add__triv__left__iff,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_left_iff
% 5.64/5.92 thf(fact_4375_dvd__add__triv__right__iff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_right_iff
% 5.64/5.92 thf(fact_4376_dvd__add__triv__right__iff,axiom,
% 5.64/5.92 ! [A: real,B: real] :
% 5.64/5.92 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.64/5.92 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_right_iff
% 5.64/5.92 thf(fact_4377_dvd__add__triv__right__iff,axiom,
% 5.64/5.92 ! [A: rat,B: rat] :
% 5.64/5.92 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.64/5.92 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_right_iff
% 5.64/5.92 thf(fact_4378_dvd__add__triv__right__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.64/5.92 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_right_iff
% 5.64/5.92 thf(fact_4379_dvd__add__triv__right__iff,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.64/5.92 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_triv_right_iff
% 5.64/5.92 thf(fact_4380_dvd__1__left,axiom,
% 5.64/5.92 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_1_left
% 5.64/5.92 thf(fact_4381_dvd__1__iff__1,axiom,
% 5.64/5.92 ! [M: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.64/5.92 = ( M
% 5.64/5.92 = ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_1_iff_1
% 5.64/5.92 thf(fact_4382_div__dvd__div,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_dvd_div
% 5.64/5.92 thf(fact_4383_div__dvd__div,axiom,
% 5.64/5.92 ! [A: nat,B: nat,C: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.92 => ( ( dvd_dvd_nat @ A @ C )
% 5.64/5.92 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.64/5.92 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_dvd_div
% 5.64/5.92 thf(fact_4384_div__dvd__div,axiom,
% 5.64/5.92 ! [A: int,B: int,C: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.92 => ( ( dvd_dvd_int @ A @ C )
% 5.64/5.92 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.64/5.92 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_dvd_div
% 5.64/5.92 thf(fact_4385_nat__mult__dvd__cancel__disj,axiom,
% 5.64/5.92 ! [K: nat,M: nat,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.92 = ( ( K = zero_zero_nat )
% 5.64/5.92 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % nat_mult_dvd_cancel_disj
% 5.64/5.92 thf(fact_4386_case__prod__conv,axiom,
% 5.64/5.92 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.64/5.92 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.64/5.92 = ( F @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % case_prod_conv
% 5.64/5.92 thf(fact_4387_case__prod__conv,axiom,
% 5.64/5.92 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.64/5.92 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.64/5.92 = ( F @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % case_prod_conv
% 5.64/5.92 thf(fact_4388_case__prod__conv,axiom,
% 5.64/5.92 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.64/5.92 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.64/5.92 = ( F @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % case_prod_conv
% 5.64/5.92 thf(fact_4389_case__prod__conv,axiom,
% 5.64/5.92 ! [F: int > int > $o,A: int,B: int] :
% 5.64/5.92 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.64/5.92 = ( F @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % case_prod_conv
% 5.64/5.92 thf(fact_4390_case__prod__conv,axiom,
% 5.64/5.92 ! [F: int > int > int,A: int,B: int] :
% 5.64/5.92 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.64/5.92 = ( F @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % case_prod_conv
% 5.64/5.92 thf(fact_4391_dvd__times__right__cancel__iff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.92 ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_times_right_cancel_iff
% 5.64/5.92 thf(fact_4392_dvd__times__right__cancel__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat,C: nat] :
% 5.64/5.92 ( ( A != zero_zero_nat )
% 5.64/5.92 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.64/5.92 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_times_right_cancel_iff
% 5.64/5.92 thf(fact_4393_dvd__times__right__cancel__iff,axiom,
% 5.64/5.92 ! [A: int,B: int,C: int] :
% 5.64/5.92 ( ( A != zero_zero_int )
% 5.64/5.92 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.64/5.92 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_times_right_cancel_iff
% 5.64/5.92 thf(fact_4394_dvd__times__left__cancel__iff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.92 ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_times_left_cancel_iff
% 5.64/5.92 thf(fact_4395_dvd__times__left__cancel__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat,C: nat] :
% 5.64/5.92 ( ( A != zero_zero_nat )
% 5.64/5.92 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.64/5.92 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_times_left_cancel_iff
% 5.64/5.92 thf(fact_4396_dvd__times__left__cancel__iff,axiom,
% 5.64/5.92 ! [A: int,B: int,C: int] :
% 5.64/5.92 ( ( A != zero_zero_int )
% 5.64/5.92 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.64/5.92 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_times_left_cancel_iff
% 5.64/5.92 thf(fact_4397_dvd__mult__cancel__right,axiom,
% 5.64/5.92 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.92 = ( ( C = zero_z3403309356797280102nteger )
% 5.64/5.92 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_right
% 5.64/5.92 thf(fact_4398_dvd__mult__cancel__right,axiom,
% 5.64/5.92 ! [A: complex,C: complex,B: complex] :
% 5.64/5.92 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.64/5.92 = ( ( C = zero_zero_complex )
% 5.64/5.92 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_right
% 5.64/5.92 thf(fact_4399_dvd__mult__cancel__right,axiom,
% 5.64/5.92 ! [A: real,C: real,B: real] :
% 5.64/5.92 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.64/5.92 = ( ( C = zero_zero_real )
% 5.64/5.92 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_right
% 5.64/5.92 thf(fact_4400_dvd__mult__cancel__right,axiom,
% 5.64/5.92 ! [A: rat,C: rat,B: rat] :
% 5.64/5.92 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.64/5.92 = ( ( C = zero_zero_rat )
% 5.64/5.92 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_right
% 5.64/5.92 thf(fact_4401_dvd__mult__cancel__right,axiom,
% 5.64/5.92 ! [A: int,C: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.64/5.92 = ( ( C = zero_zero_int )
% 5.64/5.92 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_right
% 5.64/5.92 thf(fact_4402_dvd__mult__cancel__left,axiom,
% 5.64/5.92 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.64/5.92 = ( ( C = zero_z3403309356797280102nteger )
% 5.64/5.92 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_left
% 5.64/5.92 thf(fact_4403_dvd__mult__cancel__left,axiom,
% 5.64/5.92 ! [C: complex,A: complex,B: complex] :
% 5.64/5.92 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.64/5.92 = ( ( C = zero_zero_complex )
% 5.64/5.92 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_left
% 5.64/5.92 thf(fact_4404_dvd__mult__cancel__left,axiom,
% 5.64/5.92 ! [C: real,A: real,B: real] :
% 5.64/5.92 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.64/5.92 = ( ( C = zero_zero_real )
% 5.64/5.92 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_left
% 5.64/5.92 thf(fact_4405_dvd__mult__cancel__left,axiom,
% 5.64/5.92 ! [C: rat,A: rat,B: rat] :
% 5.64/5.92 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.64/5.92 = ( ( C = zero_zero_rat )
% 5.64/5.92 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_left
% 5.64/5.92 thf(fact_4406_dvd__mult__cancel__left,axiom,
% 5.64/5.92 ! [C: int,A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/5.92 = ( ( C = zero_zero_int )
% 5.64/5.92 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_cancel_left
% 5.64/5.92 thf(fact_4407_unit__prod,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.92 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_prod
% 5.64/5.92 thf(fact_4408_unit__prod,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.92 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.92 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_prod
% 5.64/5.92 thf(fact_4409_unit__prod,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.92 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.92 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_prod
% 5.64/5.92 thf(fact_4410_dvd__add__times__triv__right__iff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_right_iff
% 5.64/5.92 thf(fact_4411_dvd__add__times__triv__right__iff,axiom,
% 5.64/5.92 ! [A: real,B: real,C: real] :
% 5.64/5.92 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.64/5.92 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_right_iff
% 5.64/5.92 thf(fact_4412_dvd__add__times__triv__right__iff,axiom,
% 5.64/5.92 ! [A: rat,B: rat,C: rat] :
% 5.64/5.92 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.64/5.92 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_right_iff
% 5.64/5.92 thf(fact_4413_dvd__add__times__triv__right__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat,C: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.64/5.92 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_right_iff
% 5.64/5.92 thf(fact_4414_dvd__add__times__triv__right__iff,axiom,
% 5.64/5.92 ! [A: int,B: int,C: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.64/5.92 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_right_iff
% 5.64/5.92 thf(fact_4415_dvd__add__times__triv__left__iff,axiom,
% 5.64/5.92 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_left_iff
% 5.64/5.92 thf(fact_4416_dvd__add__times__triv__left__iff,axiom,
% 5.64/5.92 ! [A: real,C: real,B: real] :
% 5.64/5.92 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.64/5.92 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_left_iff
% 5.64/5.92 thf(fact_4417_dvd__add__times__triv__left__iff,axiom,
% 5.64/5.92 ! [A: rat,C: rat,B: rat] :
% 5.64/5.92 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.64/5.92 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_left_iff
% 5.64/5.92 thf(fact_4418_dvd__add__times__triv__left__iff,axiom,
% 5.64/5.92 ! [A: nat,C: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.64/5.92 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_left_iff
% 5.64/5.92 thf(fact_4419_dvd__add__times__triv__left__iff,axiom,
% 5.64/5.92 ! [A: int,C: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.64/5.92 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_add_times_triv_left_iff
% 5.64/5.92 thf(fact_4420_dvd__mult__div__cancel,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.92 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_div_cancel
% 5.64/5.92 thf(fact_4421_dvd__mult__div__cancel,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.92 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_div_cancel
% 5.64/5.92 thf(fact_4422_dvd__mult__div__cancel,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.92 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_mult_div_cancel
% 5.64/5.92 thf(fact_4423_dvd__div__mult__self,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.92 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_div_mult_self
% 5.64/5.92 thf(fact_4424_dvd__div__mult__self,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.92 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_div_mult_self
% 5.64/5.92 thf(fact_4425_dvd__div__mult__self,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.92 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_div_mult_self
% 5.64/5.92 thf(fact_4426_unit__div,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.92 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div
% 5.64/5.92 thf(fact_4427_unit__div,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.92 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.92 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div
% 5.64/5.92 thf(fact_4428_unit__div,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.92 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.92 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div
% 5.64/5.92 thf(fact_4429_unit__div__1__unit,axiom,
% 5.64/5.92 ! [A: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.92 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_1_unit
% 5.64/5.92 thf(fact_4430_unit__div__1__unit,axiom,
% 5.64/5.92 ! [A: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.92 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_1_unit
% 5.64/5.92 thf(fact_4431_unit__div__1__unit,axiom,
% 5.64/5.92 ! [A: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.92 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_1_unit
% 5.64/5.92 thf(fact_4432_unit__div__1__div__1,axiom,
% 5.64/5.92 ! [A: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.92 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_1_div_1
% 5.64/5.92 thf(fact_4433_unit__div__1__div__1,axiom,
% 5.64/5.92 ! [A: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.92 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_1_div_1
% 5.64/5.92 thf(fact_4434_unit__div__1__div__1,axiom,
% 5.64/5.92 ! [A: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.92 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.64/5.92 = A ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_1_div_1
% 5.64/5.92 thf(fact_4435_div__add,axiom,
% 5.64/5.92 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.92 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.64/5.92 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_add
% 5.64/5.92 thf(fact_4436_div__add,axiom,
% 5.64/5.92 ! [C: nat,A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ C @ A )
% 5.64/5.92 => ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.92 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.92 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_add
% 5.64/5.92 thf(fact_4437_div__add,axiom,
% 5.64/5.92 ! [C: int,A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ C @ A )
% 5.64/5.92 => ( ( dvd_dvd_int @ C @ B )
% 5.64/5.92 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.92 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_add
% 5.64/5.92 thf(fact_4438_div__diff,axiom,
% 5.64/5.92 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.64/5.92 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.92 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.64/5.92 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_diff
% 5.64/5.92 thf(fact_4439_div__diff,axiom,
% 5.64/5.92 ! [C: int,A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ C @ A )
% 5.64/5.92 => ( ( dvd_dvd_int @ C @ B )
% 5.64/5.92 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.64/5.92 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % div_diff
% 5.64/5.92 thf(fact_4440_concat__bit__negative__iff,axiom,
% 5.64/5.92 ! [N: nat,K: int,L: int] :
% 5.64/5.92 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L ) @ zero_zero_int )
% 5.64/5.92 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.64/5.92
% 5.64/5.92 % concat_bit_negative_iff
% 5.64/5.92 thf(fact_4441_even__Suc__Suc__iff,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.64/5.92 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_Suc_Suc_iff
% 5.64/5.92 thf(fact_4442_even__Suc,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_Suc
% 5.64/5.92 thf(fact_4443_unit__mult__div__div,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.92 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.64/5.92 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_mult_div_div
% 5.64/5.92 thf(fact_4444_unit__mult__div__div,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.92 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.64/5.92 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_mult_div_div
% 5.64/5.92 thf(fact_4445_unit__mult__div__div,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.92 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.64/5.92 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_mult_div_div
% 5.64/5.92 thf(fact_4446_unit__div__mult__self,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.92 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_mult_self
% 5.64/5.92 thf(fact_4447_unit__div__mult__self,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.92 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_mult_self
% 5.64/5.92 thf(fact_4448_unit__div__mult__self,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.92 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.64/5.92 = B ) ) ).
% 5.64/5.92
% 5.64/5.92 % unit_div_mult_self
% 5.64/5.92 thf(fact_4449_pow__divides__pow__iff,axiom,
% 5.64/5.92 ! [N: nat,A: nat,B: nat] :
% 5.64/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.64/5.92 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % pow_divides_pow_iff
% 5.64/5.92 thf(fact_4450_pow__divides__pow__iff,axiom,
% 5.64/5.92 ! [N: nat,A: int,B: int] :
% 5.64/5.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.92 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.64/5.92 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % pow_divides_pow_iff
% 5.64/5.92 thf(fact_4451_even__mult__iff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.64/5.92 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_mult_iff
% 5.64/5.92 thf(fact_4452_even__mult__iff,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.64/5.92 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_mult_iff
% 5.64/5.92 thf(fact_4453_even__mult__iff,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.64/5.92 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_mult_iff
% 5.64/5.92 thf(fact_4454_even__add,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.64/5.92 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_add
% 5.64/5.92 thf(fact_4455_even__add,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.92 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_add
% 5.64/5.92 thf(fact_4456_even__add,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.64/5.92 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.92 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_add
% 5.64/5.92 thf(fact_4457_odd__add,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.64/5.92 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.92 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % odd_add
% 5.64/5.92 thf(fact_4458_odd__add,axiom,
% 5.64/5.92 ! [A: nat,B: nat] :
% 5.64/5.92 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.64/5.92 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.92 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % odd_add
% 5.64/5.92 thf(fact_4459_odd__add,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.64/5.92 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.92 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % odd_add
% 5.64/5.92 thf(fact_4460_even__mod__2__iff,axiom,
% 5.64/5.92 ! [A: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.92 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_mod_2_iff
% 5.64/5.92 thf(fact_4461_even__mod__2__iff,axiom,
% 5.64/5.92 ! [A: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.64/5.92 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_mod_2_iff
% 5.64/5.92 thf(fact_4462_even__mod__2__iff,axiom,
% 5.64/5.92 ! [A: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_mod_2_iff
% 5.64/5.92 thf(fact_4463_even__Suc__div__two,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.92 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.92 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_Suc_div_two
% 5.64/5.92 thf(fact_4464_odd__Suc__div__two,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.92 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.92 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % odd_Suc_div_two
% 5.64/5.92 thf(fact_4465_dvd__numeral__simp,axiom,
% 5.64/5.92 ! [M: num,N: num] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.92 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_numeral_simp
% 5.64/5.92 thf(fact_4466_dvd__numeral__simp,axiom,
% 5.64/5.92 ! [M: num,N: num] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.92 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_numeral_simp
% 5.64/5.92 thf(fact_4467_dvd__numeral__simp,axiom,
% 5.64/5.92 ! [M: num,N: num] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.64/5.92 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % dvd_numeral_simp
% 5.64/5.92 thf(fact_4468_zero__le__power__eq__numeral,axiom,
% 5.64/5.92 ! [A: rat,W: num] :
% 5.64/5.92 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.64/5.92 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % zero_le_power_eq_numeral
% 5.64/5.92 thf(fact_4469_zero__le__power__eq__numeral,axiom,
% 5.64/5.92 ! [A: int,W: num] :
% 5.64/5.92 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.64/5.92 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % zero_le_power_eq_numeral
% 5.64/5.92 thf(fact_4470_zero__le__power__eq__numeral,axiom,
% 5.64/5.92 ! [A: real,W: num] :
% 5.64/5.92 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.64/5.92 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % zero_le_power_eq_numeral
% 5.64/5.92 thf(fact_4471_power__less__zero__eq__numeral,axiom,
% 5.64/5.92 ! [A: real,W: num] :
% 5.64/5.92 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % power_less_zero_eq_numeral
% 5.64/5.92 thf(fact_4472_power__less__zero__eq__numeral,axiom,
% 5.64/5.92 ! [A: rat,W: num] :
% 5.64/5.92 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % power_less_zero_eq_numeral
% 5.64/5.92 thf(fact_4473_power__less__zero__eq__numeral,axiom,
% 5.64/5.92 ! [A: int,W: num] :
% 5.64/5.92 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % power_less_zero_eq_numeral
% 5.64/5.92 thf(fact_4474_power__less__zero__eq,axiom,
% 5.64/5.92 ! [A: real,N: nat] :
% 5.64/5.92 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.92 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % power_less_zero_eq
% 5.64/5.92 thf(fact_4475_power__less__zero__eq,axiom,
% 5.64/5.92 ! [A: rat,N: nat] :
% 5.64/5.92 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.92 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % power_less_zero_eq
% 5.64/5.92 thf(fact_4476_power__less__zero__eq,axiom,
% 5.64/5.92 ! [A: int,N: nat] :
% 5.64/5.92 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.92 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % power_less_zero_eq
% 5.64/5.92 thf(fact_4477_even__plus__one__iff,axiom,
% 5.64/5.92 ! [A: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.64/5.92 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_plus_one_iff
% 5.64/5.92 thf(fact_4478_even__plus__one__iff,axiom,
% 5.64/5.92 ! [A: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.64/5.92 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_plus_one_iff
% 5.64/5.92 thf(fact_4479_even__plus__one__iff,axiom,
% 5.64/5.92 ! [A: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.64/5.92 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_plus_one_iff
% 5.64/5.92 thf(fact_4480_even__diff,axiom,
% 5.64/5.92 ! [A: code_integer,B: code_integer] :
% 5.64/5.92 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_diff
% 5.64/5.92 thf(fact_4481_even__diff,axiom,
% 5.64/5.92 ! [A: int,B: int] :
% 5.64/5.92 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.64/5.92 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_diff
% 5.64/5.92 thf(fact_4482_odd__Suc__minus__one,axiom,
% 5.64/5.92 ! [N: nat] :
% 5.64/5.92 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.92 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.64/5.92 = N ) ) ).
% 5.64/5.92
% 5.64/5.92 % odd_Suc_minus_one
% 5.64/5.92 thf(fact_4483_even__diff__nat,axiom,
% 5.64/5.92 ! [M: nat,N: nat] :
% 5.64/5.92 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.92 = ( ( ord_less_nat @ M @ N )
% 5.64/5.92 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % even_diff_nat
% 5.64/5.92 thf(fact_4484_zero__less__power__eq__numeral,axiom,
% 5.64/5.92 ! [A: real,W: num] :
% 5.64/5.92 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.64/5.92 = ( ( ( numeral_numeral_nat @ W )
% 5.64/5.92 = zero_zero_nat )
% 5.64/5.92 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( A != zero_zero_real ) )
% 5.64/5.92 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.92 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.64/5.92
% 5.64/5.92 % zero_less_power_eq_numeral
% 5.64/5.92 thf(fact_4485_zero__less__power__eq__numeral,axiom,
% 5.64/5.92 ! [A: rat,W: num] :
% 5.64/5.92 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.64/5.92 = ( ( ( numeral_numeral_nat @ W )
% 5.64/5.92 = zero_zero_nat )
% 5.64/5.92 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( A != zero_zero_rat ) )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_power_eq_numeral
% 5.64/5.93 thf(fact_4486_zero__less__power__eq__numeral,axiom,
% 5.64/5.93 ! [A: int,W: num] :
% 5.64/5.93 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.64/5.93 = ( ( ( numeral_numeral_nat @ W )
% 5.64/5.93 = zero_zero_nat )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( A != zero_zero_int ) )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_power_eq_numeral
% 5.64/5.93 thf(fact_4487_even__succ__div__2,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_succ_div_2
% 5.64/5.93 thf(fact_4488_even__succ__div__2,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_succ_div_2
% 5.64/5.93 thf(fact_4489_even__succ__div__2,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_succ_div_2
% 5.64/5.93 thf(fact_4490_odd__succ__div__two,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_succ_div_two
% 5.64/5.93 thf(fact_4491_odd__succ__div__two,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_succ_div_two
% 5.64/5.93 thf(fact_4492_odd__succ__div__two,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_succ_div_two
% 5.64/5.93 thf(fact_4493_even__succ__div__two,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_succ_div_two
% 5.64/5.93 thf(fact_4494_even__succ__div__two,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_succ_div_two
% 5.64/5.93 thf(fact_4495_even__succ__div__two,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_succ_div_two
% 5.64/5.93 thf(fact_4496_even__power,axiom,
% 5.64/5.93 ! [A: code_integer,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_power
% 5.64/5.93 thf(fact_4497_even__power,axiom,
% 5.64/5.93 ! [A: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_power
% 5.64/5.93 thf(fact_4498_even__power,axiom,
% 5.64/5.93 ! [A: int,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_power
% 5.64/5.93 thf(fact_4499_odd__two__times__div__two__nat,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.93 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_two_times_div_two_nat
% 5.64/5.93 thf(fact_4500_divmod__algorithm__code_I5_J,axiom,
% 5.64/5.93 ! [M: num,N: num] :
% 5.64/5.93 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.93 = ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.64/5.93 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_algorithm_code(5)
% 5.64/5.93 thf(fact_4501_divmod__algorithm__code_I5_J,axiom,
% 5.64/5.93 ! [M: num,N: num] :
% 5.64/5.93 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.93 = ( produc2626176000494625587at_nat
% 5.64/5.93 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.64/5.93 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_algorithm_code(5)
% 5.64/5.93 thf(fact_4502_divmod__algorithm__code_I5_J,axiom,
% 5.64/5.93 ! [M: num,N: num] :
% 5.64/5.93 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/5.93 = ( produc6916734918728496179nteger
% 5.64/5.93 @ ^ [Q4: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.64/5.93 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_algorithm_code(5)
% 5.64/5.93 thf(fact_4503_odd__two__times__div__two__succ,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.64/5.93 = A ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_two_times_div_two_succ
% 5.64/5.93 thf(fact_4504_odd__two__times__div__two__succ,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.64/5.93 = A ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_two_times_div_two_succ
% 5.64/5.93 thf(fact_4505_odd__two__times__div__two__succ,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.64/5.93 = A ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_two_times_div_two_succ
% 5.64/5.93 thf(fact_4506_power__le__zero__eq__numeral,axiom,
% 5.64/5.93 ! [A: rat,W: num] :
% 5.64/5.93 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.64/5.93 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_zero_eq_numeral
% 5.64/5.93 thf(fact_4507_power__le__zero__eq__numeral,axiom,
% 5.64/5.93 ! [A: int,W: num] :
% 5.64/5.93 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.64/5.93 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_zero_eq_numeral
% 5.64/5.93 thf(fact_4508_power__le__zero__eq__numeral,axiom,
% 5.64/5.93 ! [A: real,W: num] :
% 5.64/5.93 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.64/5.93 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.93 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_zero_eq_numeral
% 5.64/5.93 thf(fact_4509_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.64/5.93 = ( N = zero_zero_nat ) ) ).
% 5.64/5.93
% 5.64/5.93 % semiring_parity_class.even_mask_iff
% 5.64/5.93 thf(fact_4510_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.64/5.93 = ( N = zero_zero_nat ) ) ).
% 5.64/5.93
% 5.64/5.93 % semiring_parity_class.even_mask_iff
% 5.64/5.93 thf(fact_4511_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.64/5.93 = ( N = zero_zero_nat ) ) ).
% 5.64/5.93
% 5.64/5.93 % semiring_parity_class.even_mask_iff
% 5.64/5.93 thf(fact_4512_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.64/5.93 = ( produc4947309494688390418_int_o
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4513_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.64/5.93 = ( produc8211389475949308722nt_int
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4514_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.64/5.93 = ( produc4947309494688390418_int_o
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4515_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.64/5.93 = ( produc8211389475949308722nt_int
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4516_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.64/5.93 = ( produc4947309494688390418_int_o
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4517_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.64/5.93 = ( produc8211389475949308722nt_int
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4518_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.64/5.93 = ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4519_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.64/5.93 = ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4520_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.64/5.93 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.64/5.93 = ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4521_prod_Ocase__distrib,axiom,
% 5.64/5.93 ! [H2: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 5.64/5.93 ( ( H2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 5.64/5.93 = ( produc8739625826339149834_nat_o
% 5.64/5.93 @ ^ [X15: nat,X24: nat] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.64/5.93 @ Prod ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod.case_distrib
% 5.64/5.93 thf(fact_4522_division__decomp,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.93 => ? [B8: nat,C5: nat] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_times_nat @ B8 @ C5 ) )
% 5.64/5.93 & ( dvd_dvd_nat @ B8 @ B )
% 5.64/5.93 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % division_decomp
% 5.64/5.93 thf(fact_4523_division__decomp,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.93 => ? [B8: int,C5: int] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_times_int @ B8 @ C5 ) )
% 5.64/5.93 & ( dvd_dvd_int @ B8 @ B )
% 5.64/5.93 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % division_decomp
% 5.64/5.93 thf(fact_4524_dvd__productE,axiom,
% 5.64/5.93 ! [P2: nat,A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ P2 @ ( times_times_nat @ A @ B ) )
% 5.64/5.93 => ~ ! [X4: nat,Y3: nat] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( times_times_nat @ X4 @ Y3 ) )
% 5.64/5.93 => ( ( dvd_dvd_nat @ X4 @ A )
% 5.64/5.93 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_productE
% 5.64/5.93 thf(fact_4525_dvd__productE,axiom,
% 5.64/5.93 ! [P2: int,A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ P2 @ ( times_times_int @ A @ B ) )
% 5.64/5.93 => ~ ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( times_times_int @ X4 @ Y3 ) )
% 5.64/5.93 => ( ( dvd_dvd_int @ X4 @ A )
% 5.64/5.93 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_productE
% 5.64/5.93 thf(fact_4526_dvd__triv__right,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_right
% 5.64/5.93 thf(fact_4527_dvd__triv__right,axiom,
% 5.64/5.93 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_right
% 5.64/5.93 thf(fact_4528_dvd__triv__right,axiom,
% 5.64/5.93 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_right
% 5.64/5.93 thf(fact_4529_dvd__triv__right,axiom,
% 5.64/5.93 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_right
% 5.64/5.93 thf(fact_4530_dvd__triv__right,axiom,
% 5.64/5.93 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_right
% 5.64/5.93 thf(fact_4531_dvd__mult__right,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_right
% 5.64/5.93 thf(fact_4532_dvd__mult__right,axiom,
% 5.64/5.93 ! [A: real,B: real,C: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_right
% 5.64/5.93 thf(fact_4533_dvd__mult__right,axiom,
% 5.64/5.93 ! [A: rat,B: rat,C: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_right
% 5.64/5.93 thf(fact_4534_dvd__mult__right,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_right
% 5.64/5.93 thf(fact_4535_dvd__mult__right,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_right
% 5.64/5.93 thf(fact_4536_mult__dvd__mono,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_dvd_mono
% 5.64/5.93 thf(fact_4537_mult__dvd__mono,axiom,
% 5.64/5.93 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_real @ C @ D )
% 5.64/5.93 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_dvd_mono
% 5.64/5.93 thf(fact_4538_mult__dvd__mono,axiom,
% 5.64/5.93 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_rat @ C @ D )
% 5.64/5.93 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_dvd_mono
% 5.64/5.93 thf(fact_4539_mult__dvd__mono,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ D )
% 5.64/5.93 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_dvd_mono
% 5.64/5.93 thf(fact_4540_mult__dvd__mono,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ D )
% 5.64/5.93 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_dvd_mono
% 5.64/5.93 thf(fact_4541_dvd__triv__left,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_left
% 5.64/5.93 thf(fact_4542_dvd__triv__left,axiom,
% 5.64/5.93 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_left
% 5.64/5.93 thf(fact_4543_dvd__triv__left,axiom,
% 5.64/5.93 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_left
% 5.64/5.93 thf(fact_4544_dvd__triv__left,axiom,
% 5.64/5.93 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_left
% 5.64/5.93 thf(fact_4545_dvd__triv__left,axiom,
% 5.64/5.93 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_triv_left
% 5.64/5.93 thf(fact_4546_dvd__mult__left,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_left
% 5.64/5.93 thf(fact_4547_dvd__mult__left,axiom,
% 5.64/5.93 ! [A: real,B: real,C: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_left
% 5.64/5.93 thf(fact_4548_dvd__mult__left,axiom,
% 5.64/5.93 ! [A: rat,B: rat,C: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_left
% 5.64/5.93 thf(fact_4549_dvd__mult__left,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_left
% 5.64/5.93 thf(fact_4550_dvd__mult__left,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.93 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_left
% 5.64/5.93 thf(fact_4551_dvd__mult2,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult2
% 5.64/5.93 thf(fact_4552_dvd__mult2,axiom,
% 5.64/5.93 ! [A: real,B: real,C: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ A @ B )
% 5.64/5.93 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult2
% 5.64/5.93 thf(fact_4553_dvd__mult2,axiom,
% 5.64/5.93 ! [A: rat,B: rat,C: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ A @ B )
% 5.64/5.93 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult2
% 5.64/5.93 thf(fact_4554_dvd__mult2,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult2
% 5.64/5.93 thf(fact_4555_dvd__mult2,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult2
% 5.64/5.93 thf(fact_4556_dvd__mult,axiom,
% 5.64/5.93 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult
% 5.64/5.93 thf(fact_4557_dvd__mult,axiom,
% 5.64/5.93 ! [A: real,C: real,B: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ A @ C )
% 5.64/5.93 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult
% 5.64/5.93 thf(fact_4558_dvd__mult,axiom,
% 5.64/5.93 ! [A: rat,C: rat,B: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ A @ C )
% 5.64/5.93 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult
% 5.64/5.93 thf(fact_4559_dvd__mult,axiom,
% 5.64/5.93 ! [A: nat,C: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ C )
% 5.64/5.93 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult
% 5.64/5.93 thf(fact_4560_dvd__mult,axiom,
% 5.64/5.93 ! [A: int,C: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ C )
% 5.64/5.93 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult
% 5.64/5.93 thf(fact_4561_dvd__def,axiom,
% 5.64/5.93 ( dvd_dvd_Code_integer
% 5.64/5.93 = ( ^ [B3: code_integer,A3: code_integer] :
% 5.64/5.93 ? [K2: code_integer] :
% 5.64/5.93 ( A3
% 5.64/5.93 = ( times_3573771949741848930nteger @ B3 @ K2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_def
% 5.64/5.93 thf(fact_4562_dvd__def,axiom,
% 5.64/5.93 ( dvd_dvd_real
% 5.64/5.93 = ( ^ [B3: real,A3: real] :
% 5.64/5.93 ? [K2: real] :
% 5.64/5.93 ( A3
% 5.64/5.93 = ( times_times_real @ B3 @ K2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_def
% 5.64/5.93 thf(fact_4563_dvd__def,axiom,
% 5.64/5.93 ( dvd_dvd_rat
% 5.64/5.93 = ( ^ [B3: rat,A3: rat] :
% 5.64/5.93 ? [K2: rat] :
% 5.64/5.93 ( A3
% 5.64/5.93 = ( times_times_rat @ B3 @ K2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_def
% 5.64/5.93 thf(fact_4564_dvd__def,axiom,
% 5.64/5.93 ( dvd_dvd_nat
% 5.64/5.93 = ( ^ [B3: nat,A3: nat] :
% 5.64/5.93 ? [K2: nat] :
% 5.64/5.93 ( A3
% 5.64/5.93 = ( times_times_nat @ B3 @ K2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_def
% 5.64/5.93 thf(fact_4565_dvd__def,axiom,
% 5.64/5.93 ( dvd_dvd_int
% 5.64/5.93 = ( ^ [B3: int,A3: int] :
% 5.64/5.93 ? [K2: int] :
% 5.64/5.93 ( A3
% 5.64/5.93 = ( times_times_int @ B3 @ K2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_def
% 5.64/5.93 thf(fact_4566_dvdI,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdI
% 5.64/5.93 thf(fact_4567_dvdI,axiom,
% 5.64/5.93 ! [A: real,B: real,K: real] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_times_real @ B @ K ) )
% 5.64/5.93 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdI
% 5.64/5.93 thf(fact_4568_dvdI,axiom,
% 5.64/5.93 ! [A: rat,B: rat,K: rat] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_times_rat @ B @ K ) )
% 5.64/5.93 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdI
% 5.64/5.93 thf(fact_4569_dvdI,axiom,
% 5.64/5.93 ! [A: nat,B: nat,K: nat] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_times_nat @ B @ K ) )
% 5.64/5.93 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdI
% 5.64/5.93 thf(fact_4570_dvdI,axiom,
% 5.64/5.93 ! [A: int,B: int,K: int] :
% 5.64/5.93 ( ( A
% 5.64/5.93 = ( times_times_int @ B @ K ) )
% 5.64/5.93 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdI
% 5.64/5.93 thf(fact_4571_dvdE,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ~ ! [K3: code_integer] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdE
% 5.64/5.93 thf(fact_4572_dvdE,axiom,
% 5.64/5.93 ! [B: real,A: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ B @ A )
% 5.64/5.93 => ~ ! [K3: real] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_times_real @ B @ K3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdE
% 5.64/5.93 thf(fact_4573_dvdE,axiom,
% 5.64/5.93 ! [B: rat,A: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ B @ A )
% 5.64/5.93 => ~ ! [K3: rat] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_times_rat @ B @ K3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdE
% 5.64/5.93 thf(fact_4574_dvdE,axiom,
% 5.64/5.93 ! [B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ~ ! [K3: nat] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_times_nat @ B @ K3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdE
% 5.64/5.93 thf(fact_4575_dvdE,axiom,
% 5.64/5.93 ! [B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ~ ! [K3: int] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_times_int @ B @ K3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvdE
% 5.64/5.93 thf(fact_4576_one__dvd,axiom,
% 5.64/5.93 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.64/5.93
% 5.64/5.93 % one_dvd
% 5.64/5.93 thf(fact_4577_one__dvd,axiom,
% 5.64/5.93 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.64/5.93
% 5.64/5.93 % one_dvd
% 5.64/5.93 thf(fact_4578_one__dvd,axiom,
% 5.64/5.93 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.64/5.93
% 5.64/5.93 % one_dvd
% 5.64/5.93 thf(fact_4579_one__dvd,axiom,
% 5.64/5.93 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.64/5.93
% 5.64/5.93 % one_dvd
% 5.64/5.93 thf(fact_4580_one__dvd,axiom,
% 5.64/5.93 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.64/5.93
% 5.64/5.93 % one_dvd
% 5.64/5.93 thf(fact_4581_one__dvd,axiom,
% 5.64/5.93 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.64/5.93
% 5.64/5.93 % one_dvd
% 5.64/5.93 thf(fact_4582_unit__imp__dvd,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_imp_dvd
% 5.64/5.93 thf(fact_4583_unit__imp__dvd,axiom,
% 5.64/5.93 ! [B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_imp_dvd
% 5.64/5.93 thf(fact_4584_unit__imp__dvd,axiom,
% 5.64/5.93 ! [B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_imp_dvd
% 5.64/5.93 thf(fact_4585_dvd__unit__imp__unit,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_unit_imp_unit
% 5.64/5.93 thf(fact_4586_dvd__unit__imp__unit,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_unit_imp_unit
% 5.64/5.93 thf(fact_4587_dvd__unit__imp__unit,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_unit_imp_unit
% 5.64/5.93 thf(fact_4588_dvd__add,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add
% 5.64/5.93 thf(fact_4589_dvd__add,axiom,
% 5.64/5.93 ! [A: real,B: real,C: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_real @ A @ C )
% 5.64/5.93 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add
% 5.64/5.93 thf(fact_4590_dvd__add,axiom,
% 5.64/5.93 ! [A: rat,B: rat,C: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_rat @ A @ C )
% 5.64/5.93 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add
% 5.64/5.93 thf(fact_4591_dvd__add,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ C )
% 5.64/5.93 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add
% 5.64/5.93 thf(fact_4592_dvd__add,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ C )
% 5.64/5.93 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add
% 5.64/5.93 thf(fact_4593_dvd__add__left__iff,axiom,
% 5.64/5.93 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_left_iff
% 5.64/5.93 thf(fact_4594_dvd__add__left__iff,axiom,
% 5.64/5.93 ! [A: real,C: real,B: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ A @ C )
% 5.64/5.93 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_left_iff
% 5.64/5.93 thf(fact_4595_dvd__add__left__iff,axiom,
% 5.64/5.93 ! [A: rat,C: rat,B: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ A @ C )
% 5.64/5.93 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_left_iff
% 5.64/5.93 thf(fact_4596_dvd__add__left__iff,axiom,
% 5.64/5.93 ! [A: nat,C: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ C )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_left_iff
% 5.64/5.93 thf(fact_4597_dvd__add__left__iff,axiom,
% 5.64/5.93 ! [A: int,C: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ C )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_left_iff
% 5.64/5.93 thf(fact_4598_dvd__add__right__iff,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_right_iff
% 5.64/5.93 thf(fact_4599_dvd__add__right__iff,axiom,
% 5.64/5.93 ! [A: real,B: real,C: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_right_iff
% 5.64/5.93 thf(fact_4600_dvd__add__right__iff,axiom,
% 5.64/5.93 ! [A: rat,B: rat,C: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_right_iff
% 5.64/5.93 thf(fact_4601_dvd__add__right__iff,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_right_iff
% 5.64/5.93 thf(fact_4602_dvd__add__right__iff,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_add_right_iff
% 5.64/5.93 thf(fact_4603_div__div__div__same,axiom,
% 5.64/5.93 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_div_div_same
% 5.64/5.93 thf(fact_4604_div__div__div__same,axiom,
% 5.64/5.93 ! [D: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ D @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.64/5.93 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_div_div_same
% 5.64/5.93 thf(fact_4605_div__div__div__same,axiom,
% 5.64/5.93 ! [D: int,B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ D @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.64/5.93 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_div_div_same
% 5.64/5.93 thf(fact_4606_dvd__div__eq__cancel,axiom,
% 5.64/5.93 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.93 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.64/5.93 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_cancel
% 5.64/5.93 thf(fact_4607_dvd__div__eq__cancel,axiom,
% 5.64/5.93 ! [A: complex,C: complex,B: complex] :
% 5.64/5.93 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.64/5.93 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.93 => ( ( dvd_dvd_complex @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_complex @ C @ B )
% 5.64/5.93 => ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_cancel
% 5.64/5.93 thf(fact_4608_dvd__div__eq__cancel,axiom,
% 5.64/5.93 ! [A: real,C: real,B: real] :
% 5.64/5.93 ( ( ( divide_divide_real @ A @ C )
% 5.64/5.93 = ( divide_divide_real @ B @ C ) )
% 5.64/5.93 => ( ( dvd_dvd_real @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_real @ C @ B )
% 5.64/5.93 => ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_cancel
% 5.64/5.93 thf(fact_4609_dvd__div__eq__cancel,axiom,
% 5.64/5.93 ! [A: rat,C: rat,B: rat] :
% 5.64/5.93 ( ( ( divide_divide_rat @ A @ C )
% 5.64/5.93 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.93 => ( ( dvd_dvd_rat @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_rat @ C @ B )
% 5.64/5.93 => ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_cancel
% 5.64/5.93 thf(fact_4610_dvd__div__eq__cancel,axiom,
% 5.64/5.93 ! [A: nat,C: nat,B: nat] :
% 5.64/5.93 ( ( ( divide_divide_nat @ A @ C )
% 5.64/5.93 = ( divide_divide_nat @ B @ C ) )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_cancel
% 5.64/5.93 thf(fact_4611_dvd__div__eq__cancel,axiom,
% 5.64/5.93 ! [A: int,C: int,B: int] :
% 5.64/5.93 ( ( ( divide_divide_int @ A @ C )
% 5.64/5.93 = ( divide_divide_int @ B @ C ) )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_cancel
% 5.64/5.93 thf(fact_4612_dvd__div__eq__iff,axiom,
% 5.64/5.93 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.64/5.93 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.64/5.93 = ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_iff
% 5.64/5.93 thf(fact_4613_dvd__div__eq__iff,axiom,
% 5.64/5.93 ! [C: complex,A: complex,B: complex] :
% 5.64/5.93 ( ( dvd_dvd_complex @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_complex @ C @ B )
% 5.64/5.93 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.64/5.93 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.93 = ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_iff
% 5.64/5.93 thf(fact_4614_dvd__div__eq__iff,axiom,
% 5.64/5.93 ! [C: real,A: real,B: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_real @ C @ B )
% 5.64/5.93 => ( ( ( divide_divide_real @ A @ C )
% 5.64/5.93 = ( divide_divide_real @ B @ C ) )
% 5.64/5.93 = ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_iff
% 5.64/5.93 thf(fact_4615_dvd__div__eq__iff,axiom,
% 5.64/5.93 ! [C: rat,A: rat,B: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_rat @ C @ B )
% 5.64/5.93 => ( ( ( divide_divide_rat @ A @ C )
% 5.64/5.93 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.93 = ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_iff
% 5.64/5.93 thf(fact_4616_dvd__div__eq__iff,axiom,
% 5.64/5.93 ! [C: nat,A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( ( ( divide_divide_nat @ A @ C )
% 5.64/5.93 = ( divide_divide_nat @ B @ C ) )
% 5.64/5.93 = ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_iff
% 5.64/5.93 thf(fact_4617_dvd__div__eq__iff,axiom,
% 5.64/5.93 ! [C: int,A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ A )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( ( ( divide_divide_int @ A @ C )
% 5.64/5.93 = ( divide_divide_int @ B @ C ) )
% 5.64/5.93 = ( A = B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_iff
% 5.64/5.93 thf(fact_4618_dvd__power__same,axiom,
% 5.64/5.93 ! [X2: code_integer,Y4: code_integer,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ X2 @ Y4 )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y4 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_same
% 5.64/5.93 thf(fact_4619_dvd__power__same,axiom,
% 5.64/5.93 ! [X2: nat,Y4: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ X2 @ Y4 )
% 5.64/5.93 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y4 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_same
% 5.64/5.93 thf(fact_4620_dvd__power__same,axiom,
% 5.64/5.93 ! [X2: real,Y4: real,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_real @ X2 @ Y4 )
% 5.64/5.93 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y4 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_same
% 5.64/5.93 thf(fact_4621_dvd__power__same,axiom,
% 5.64/5.93 ! [X2: int,Y4: int,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ X2 @ Y4 )
% 5.64/5.93 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y4 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_same
% 5.64/5.93 thf(fact_4622_dvd__power__same,axiom,
% 5.64/5.93 ! [X2: complex,Y4: complex,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_complex @ X2 @ Y4 )
% 5.64/5.93 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y4 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_same
% 5.64/5.93 thf(fact_4623_old_Oprod_Ocase,axiom,
% 5.64/5.93 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.64/5.93 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.64/5.93 = ( F @ X1 @ X22 ) ) ).
% 5.64/5.93
% 5.64/5.93 % old.prod.case
% 5.64/5.93 thf(fact_4624_old_Oprod_Ocase,axiom,
% 5.64/5.93 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.64/5.93 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.64/5.93 = ( F @ X1 @ X22 ) ) ).
% 5.64/5.93
% 5.64/5.93 % old.prod.case
% 5.64/5.93 thf(fact_4625_old_Oprod_Ocase,axiom,
% 5.64/5.93 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.64/5.93 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.64/5.93 = ( F @ X1 @ X22 ) ) ).
% 5.64/5.93
% 5.64/5.93 % old.prod.case
% 5.64/5.93 thf(fact_4626_old_Oprod_Ocase,axiom,
% 5.64/5.93 ! [F: int > int > $o,X1: int,X22: int] :
% 5.64/5.93 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.64/5.93 = ( F @ X1 @ X22 ) ) ).
% 5.64/5.93
% 5.64/5.93 % old.prod.case
% 5.64/5.93 thf(fact_4627_old_Oprod_Ocase,axiom,
% 5.64/5.93 ! [F: int > int > int,X1: int,X22: int] :
% 5.64/5.93 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.64/5.93 = ( F @ X1 @ X22 ) ) ).
% 5.64/5.93
% 5.64/5.93 % old.prod.case
% 5.64/5.93 thf(fact_4628_dvd__diff__nat,axiom,
% 5.64/5.93 ! [K: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ K @ M )
% 5.64/5.93 => ( ( dvd_dvd_nat @ K @ N )
% 5.64/5.93 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_diff_nat
% 5.64/5.93 thf(fact_4629_semiring__norm_I26_J,axiom,
% 5.64/5.93 ( ( bitM @ one )
% 5.64/5.93 = one ) ).
% 5.64/5.93
% 5.64/5.93 % semiring_norm(26)
% 5.64/5.93 thf(fact_4630_odd__numeral__BitM,axiom,
% 5.64/5.93 ! [W: num] :
% 5.64/5.93 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_numeral_BitM
% 5.64/5.93 thf(fact_4631_odd__numeral__BitM,axiom,
% 5.64/5.93 ! [W: num] :
% 5.64/5.93 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_numeral_BitM
% 5.64/5.93 thf(fact_4632_odd__numeral__BitM,axiom,
% 5.64/5.93 ! [W: num] :
% 5.64/5.93 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_numeral_BitM
% 5.64/5.93 thf(fact_4633_case__prodE2,axiom,
% 5.64/5.93 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.64/5.93 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.64/5.93 => ~ ! [X4: nat,Y3: nat] :
% 5.64/5.93 ( ( Z
% 5.64/5.93 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.64/5.93 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodE2
% 5.64/5.93 thf(fact_4634_case__prodE2,axiom,
% 5.64/5.93 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.64/5.93 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.64/5.93 => ~ ! [X4: nat,Y3: nat] :
% 5.64/5.93 ( ( Z
% 5.64/5.93 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.64/5.93 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodE2
% 5.64/5.93 thf(fact_4635_case__prodE2,axiom,
% 5.64/5.93 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.64/5.93 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.64/5.93 => ~ ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( Z
% 5.64/5.93 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.64/5.93 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodE2
% 5.64/5.93 thf(fact_4636_case__prodE2,axiom,
% 5.64/5.93 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.64/5.93 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.64/5.93 => ~ ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( Z
% 5.64/5.93 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.64/5.93 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodE2
% 5.64/5.93 thf(fact_4637_case__prodE2,axiom,
% 5.64/5.93 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.64/5.93 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.64/5.93 => ~ ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( Z
% 5.64/5.93 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.64/5.93 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodE2
% 5.64/5.93 thf(fact_4638_case__prod__eta,axiom,
% 5.64/5.93 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.64/5.93 ( ( produc27273713700761075at_nat
% 5.64/5.93 @ ^ [X: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 5.64/5.93 = F ) ).
% 5.64/5.93
% 5.64/5.93 % case_prod_eta
% 5.64/5.93 thf(fact_4639_case__prod__eta,axiom,
% 5.64/5.93 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.64/5.93 ( ( produc8739625826339149834_nat_o
% 5.64/5.93 @ ^ [X: nat,Y: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y ) ) )
% 5.64/5.93 = F ) ).
% 5.64/5.93
% 5.64/5.93 % case_prod_eta
% 5.64/5.93 thf(fact_4640_case__prod__eta,axiom,
% 5.64/5.93 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.64/5.93 ( ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.64/5.93 = F ) ).
% 5.64/5.93
% 5.64/5.93 % case_prod_eta
% 5.64/5.93 thf(fact_4641_case__prod__eta,axiom,
% 5.64/5.93 ! [F: product_prod_int_int > $o] :
% 5.64/5.93 ( ( produc4947309494688390418_int_o
% 5.64/5.93 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.64/5.93 = F ) ).
% 5.64/5.93
% 5.64/5.93 % case_prod_eta
% 5.64/5.93 thf(fact_4642_case__prod__eta,axiom,
% 5.64/5.93 ! [F: product_prod_int_int > int] :
% 5.64/5.93 ( ( produc8211389475949308722nt_int
% 5.64/5.93 @ ^ [X: int,Y: int] : ( F @ ( product_Pair_int_int @ X @ Y ) ) )
% 5.64/5.93 = F ) ).
% 5.64/5.93
% 5.64/5.93 % case_prod_eta
% 5.64/5.93 thf(fact_4643_cond__case__prod__eta,axiom,
% 5.64/5.93 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.64/5.93 ( ! [X4: nat,Y3: nat] :
% 5.64/5.93 ( ( F @ X4 @ Y3 )
% 5.64/5.93 = ( G @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) )
% 5.64/5.93 => ( ( produc27273713700761075at_nat @ F )
% 5.64/5.93 = G ) ) ).
% 5.64/5.93
% 5.64/5.93 % cond_case_prod_eta
% 5.64/5.93 thf(fact_4644_cond__case__prod__eta,axiom,
% 5.64/5.93 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.64/5.93 ( ! [X4: nat,Y3: nat] :
% 5.64/5.93 ( ( F @ X4 @ Y3 )
% 5.64/5.93 = ( G @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) )
% 5.64/5.93 => ( ( produc8739625826339149834_nat_o @ F )
% 5.64/5.93 = G ) ) ).
% 5.64/5.93
% 5.64/5.93 % cond_case_prod_eta
% 5.64/5.93 thf(fact_4645_cond__case__prod__eta,axiom,
% 5.64/5.93 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.64/5.93 ( ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( F @ X4 @ Y3 )
% 5.64/5.93 = ( G @ ( product_Pair_int_int @ X4 @ Y3 ) ) )
% 5.64/5.93 => ( ( produc4245557441103728435nt_int @ F )
% 5.64/5.93 = G ) ) ).
% 5.64/5.93
% 5.64/5.93 % cond_case_prod_eta
% 5.64/5.93 thf(fact_4646_cond__case__prod__eta,axiom,
% 5.64/5.93 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.64/5.93 ( ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( F @ X4 @ Y3 )
% 5.64/5.93 = ( G @ ( product_Pair_int_int @ X4 @ Y3 ) ) )
% 5.64/5.93 => ( ( produc4947309494688390418_int_o @ F )
% 5.64/5.93 = G ) ) ).
% 5.64/5.93
% 5.64/5.93 % cond_case_prod_eta
% 5.64/5.93 thf(fact_4647_cond__case__prod__eta,axiom,
% 5.64/5.93 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.64/5.93 ( ! [X4: int,Y3: int] :
% 5.64/5.93 ( ( F @ X4 @ Y3 )
% 5.64/5.93 = ( G @ ( product_Pair_int_int @ X4 @ Y3 ) ) )
% 5.64/5.93 => ( ( produc8211389475949308722nt_int @ F )
% 5.64/5.93 = G ) ) ).
% 5.64/5.93
% 5.64/5.93 % cond_case_prod_eta
% 5.64/5.93 thf(fact_4648_concat__bit__assoc,axiom,
% 5.64/5.93 ! [N: nat,K: int,M: nat,L: int,R2: int] :
% 5.64/5.93 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 5.64/5.93 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L ) @ R2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % concat_bit_assoc
% 5.64/5.93 thf(fact_4649_strict__subset__divisors__dvd,axiom,
% 5.64/5.93 ! [A: complex,B: complex] :
% 5.64/5.93 ( ( ord_less_set_complex
% 5.64/5.93 @ ( collect_complex
% 5.64/5.93 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.64/5.93 @ ( collect_complex
% 5.64/5.93 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.64/5.93 = ( ( dvd_dvd_complex @ A @ B )
% 5.64/5.93 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % strict_subset_divisors_dvd
% 5.64/5.93 thf(fact_4650_strict__subset__divisors__dvd,axiom,
% 5.64/5.93 ! [A: real,B: real] :
% 5.64/5.93 ( ( ord_less_set_real
% 5.64/5.93 @ ( collect_real
% 5.64/5.93 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.64/5.93 @ ( collect_real
% 5.64/5.93 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 5.64/5.93 = ( ( dvd_dvd_real @ A @ B )
% 5.64/5.93 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % strict_subset_divisors_dvd
% 5.64/5.93 thf(fact_4651_strict__subset__divisors__dvd,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( ord_less_set_nat
% 5.64/5.93 @ ( collect_nat
% 5.64/5.93 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.64/5.93 @ ( collect_nat
% 5.64/5.93 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % strict_subset_divisors_dvd
% 5.64/5.93 thf(fact_4652_strict__subset__divisors__dvd,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ( ord_less_set_int
% 5.64/5.93 @ ( collect_int
% 5.64/5.93 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.64/5.93 @ ( collect_int
% 5.64/5.93 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % strict_subset_divisors_dvd
% 5.64/5.93 thf(fact_4653_strict__subset__divisors__dvd,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( ord_le1307284697595431911nteger
% 5.64/5.93 @ ( collect_Code_integer
% 5.64/5.93 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.64/5.93 @ ( collect_Code_integer
% 5.64/5.93 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % strict_subset_divisors_dvd
% 5.64/5.93 thf(fact_4654_not__is__unit__0,axiom,
% 5.64/5.93 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.64/5.93
% 5.64/5.93 % not_is_unit_0
% 5.64/5.93 thf(fact_4655_not__is__unit__0,axiom,
% 5.64/5.93 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.64/5.93
% 5.64/5.93 % not_is_unit_0
% 5.64/5.93 thf(fact_4656_not__is__unit__0,axiom,
% 5.64/5.93 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.64/5.93
% 5.64/5.93 % not_is_unit_0
% 5.64/5.93 thf(fact_4657_pinf_I9_J,axiom,
% 5.64/5.93 ! [D: code_integer,S2: code_integer] :
% 5.64/5.93 ? [Z2: code_integer] :
% 5.64/5.93 ! [X3: code_integer] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ Z2 @ X3 )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(9)
% 5.64/5.93 thf(fact_4658_pinf_I9_J,axiom,
% 5.64/5.93 ! [D: real,S2: real] :
% 5.64/5.93 ? [Z2: real] :
% 5.64/5.93 ! [X3: real] :
% 5.64/5.93 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.93 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(9)
% 5.64/5.93 thf(fact_4659_pinf_I9_J,axiom,
% 5.64/5.93 ! [D: rat,S2: rat] :
% 5.64/5.93 ? [Z2: rat] :
% 5.64/5.93 ! [X3: rat] :
% 5.64/5.93 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.93 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(9)
% 5.64/5.93 thf(fact_4660_pinf_I9_J,axiom,
% 5.64/5.93 ! [D: nat,S2: nat] :
% 5.64/5.93 ? [Z2: nat] :
% 5.64/5.93 ! [X3: nat] :
% 5.64/5.93 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.93 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(9)
% 5.64/5.93 thf(fact_4661_pinf_I9_J,axiom,
% 5.64/5.93 ! [D: int,S2: int] :
% 5.64/5.93 ? [Z2: int] :
% 5.64/5.93 ! [X3: int] :
% 5.64/5.93 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.93 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(9)
% 5.64/5.93 thf(fact_4662_pinf_I10_J,axiom,
% 5.64/5.93 ! [D: code_integer,S2: code_integer] :
% 5.64/5.93 ? [Z2: code_integer] :
% 5.64/5.93 ! [X3: code_integer] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ Z2 @ X3 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(10)
% 5.64/5.93 thf(fact_4663_pinf_I10_J,axiom,
% 5.64/5.93 ! [D: real,S2: real] :
% 5.64/5.93 ? [Z2: real] :
% 5.64/5.93 ! [X3: real] :
% 5.64/5.93 ( ( ord_less_real @ Z2 @ X3 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(10)
% 5.64/5.93 thf(fact_4664_pinf_I10_J,axiom,
% 5.64/5.93 ! [D: rat,S2: rat] :
% 5.64/5.93 ? [Z2: rat] :
% 5.64/5.93 ! [X3: rat] :
% 5.64/5.93 ( ( ord_less_rat @ Z2 @ X3 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(10)
% 5.64/5.93 thf(fact_4665_pinf_I10_J,axiom,
% 5.64/5.93 ! [D: nat,S2: nat] :
% 5.64/5.93 ? [Z2: nat] :
% 5.64/5.93 ! [X3: nat] :
% 5.64/5.93 ( ( ord_less_nat @ Z2 @ X3 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(10)
% 5.64/5.93 thf(fact_4666_pinf_I10_J,axiom,
% 5.64/5.93 ! [D: int,S2: int] :
% 5.64/5.93 ? [Z2: int] :
% 5.64/5.93 ! [X3: int] :
% 5.64/5.93 ( ( ord_less_int @ Z2 @ X3 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % pinf(10)
% 5.64/5.93 thf(fact_4667_minf_I9_J,axiom,
% 5.64/5.93 ! [D: code_integer,S2: code_integer] :
% 5.64/5.93 ? [Z2: code_integer] :
% 5.64/5.93 ! [X3: code_integer] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ X3 @ Z2 )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(9)
% 5.64/5.93 thf(fact_4668_minf_I9_J,axiom,
% 5.64/5.93 ! [D: real,S2: real] :
% 5.64/5.93 ? [Z2: real] :
% 5.64/5.93 ! [X3: real] :
% 5.64/5.93 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.93 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(9)
% 5.64/5.93 thf(fact_4669_minf_I9_J,axiom,
% 5.64/5.93 ! [D: rat,S2: rat] :
% 5.64/5.93 ? [Z2: rat] :
% 5.64/5.93 ! [X3: rat] :
% 5.64/5.93 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.93 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(9)
% 5.64/5.93 thf(fact_4670_minf_I9_J,axiom,
% 5.64/5.93 ! [D: nat,S2: nat] :
% 5.64/5.93 ? [Z2: nat] :
% 5.64/5.93 ! [X3: nat] :
% 5.64/5.93 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.93 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(9)
% 5.64/5.93 thf(fact_4671_minf_I9_J,axiom,
% 5.64/5.93 ! [D: int,S2: int] :
% 5.64/5.93 ? [Z2: int] :
% 5.64/5.93 ! [X3: int] :
% 5.64/5.93 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.93 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) )
% 5.64/5.93 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(9)
% 5.64/5.93 thf(fact_4672_minf_I10_J,axiom,
% 5.64/5.93 ! [D: code_integer,S2: code_integer] :
% 5.64/5.93 ? [Z2: code_integer] :
% 5.64/5.93 ! [X3: code_integer] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ X3 @ Z2 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(10)
% 5.64/5.93 thf(fact_4673_minf_I10_J,axiom,
% 5.64/5.93 ! [D: real,S2: real] :
% 5.64/5.93 ? [Z2: real] :
% 5.64/5.93 ! [X3: real] :
% 5.64/5.93 ( ( ord_less_real @ X3 @ Z2 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(10)
% 5.64/5.93 thf(fact_4674_minf_I10_J,axiom,
% 5.64/5.93 ! [D: rat,S2: rat] :
% 5.64/5.93 ? [Z2: rat] :
% 5.64/5.93 ! [X3: rat] :
% 5.64/5.93 ( ( ord_less_rat @ X3 @ Z2 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(10)
% 5.64/5.93 thf(fact_4675_minf_I10_J,axiom,
% 5.64/5.93 ! [D: nat,S2: nat] :
% 5.64/5.93 ? [Z2: nat] :
% 5.64/5.93 ! [X3: nat] :
% 5.64/5.93 ( ( ord_less_nat @ X3 @ Z2 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(10)
% 5.64/5.93 thf(fact_4676_minf_I10_J,axiom,
% 5.64/5.93 ! [D: int,S2: int] :
% 5.64/5.93 ? [Z2: int] :
% 5.64/5.93 ! [X3: int] :
% 5.64/5.93 ( ( ord_less_int @ X3 @ Z2 )
% 5.64/5.93 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % minf(10)
% 5.64/5.93 thf(fact_4677_dvd__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.64/5.93 = zero_z3403309356797280102nteger )
% 5.64/5.93 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_0_iff
% 5.64/5.93 thf(fact_4678_dvd__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: complex,A: complex] :
% 5.64/5.93 ( ( dvd_dvd_complex @ B @ A )
% 5.64/5.93 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.64/5.93 = zero_zero_complex )
% 5.64/5.93 = ( A = zero_zero_complex ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_0_iff
% 5.64/5.93 thf(fact_4679_dvd__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: real,A: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ B @ A )
% 5.64/5.93 => ( ( ( divide_divide_real @ A @ B )
% 5.64/5.93 = zero_zero_real )
% 5.64/5.93 = ( A = zero_zero_real ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_0_iff
% 5.64/5.93 thf(fact_4680_dvd__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: rat,A: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ B @ A )
% 5.64/5.93 => ( ( ( divide_divide_rat @ A @ B )
% 5.64/5.93 = zero_zero_rat )
% 5.64/5.93 = ( A = zero_zero_rat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_0_iff
% 5.64/5.93 thf(fact_4681_dvd__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( ( divide_divide_nat @ A @ B )
% 5.64/5.93 = zero_zero_nat )
% 5.64/5.93 = ( A = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_0_iff
% 5.64/5.93 thf(fact_4682_dvd__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( ( divide_divide_int @ A @ B )
% 5.64/5.93 = zero_zero_int )
% 5.64/5.93 = ( A = zero_zero_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_0_iff
% 5.64/5.93 thf(fact_4683_is__unit__mult__iff,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_mult_iff
% 5.64/5.93 thf(fact_4684_is__unit__mult__iff,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.64/5.93 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_mult_iff
% 5.64/5.93 thf(fact_4685_is__unit__mult__iff,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.64/5.93 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_mult_iff
% 5.64/5.93 thf(fact_4686_dvd__mult__unit__iff,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_unit_iff
% 5.64/5.93 thf(fact_4687_dvd__mult__unit__iff,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_unit_iff
% 5.64/5.93 thf(fact_4688_dvd__mult__unit__iff,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.64/5.93 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_unit_iff
% 5.64/5.93 thf(fact_4689_mult__unit__dvd__iff,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_unit_dvd_iff
% 5.64/5.93 thf(fact_4690_mult__unit__dvd__iff,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_unit_dvd_iff
% 5.64/5.93 thf(fact_4691_mult__unit__dvd__iff,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_unit_dvd_iff
% 5.64/5.93 thf(fact_4692_dvd__mult__unit__iff_H,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_unit_iff'
% 5.64/5.93 thf(fact_4693_dvd__mult__unit__iff_H,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_unit_iff'
% 5.64/5.93 thf(fact_4694_dvd__mult__unit__iff_H,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_unit_iff'
% 5.64/5.93 thf(fact_4695_mult__unit__dvd__iff_H,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_unit_dvd_iff'
% 5.64/5.93 thf(fact_4696_mult__unit__dvd__iff_H,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_unit_dvd_iff'
% 5.64/5.93 thf(fact_4697_mult__unit__dvd__iff_H,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mult_unit_dvd_iff'
% 5.64/5.93 thf(fact_4698_unit__mult__left__cancel,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.64/5.93 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_mult_left_cancel
% 5.64/5.93 thf(fact_4699_unit__mult__left__cancel,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 => ( ( ( times_times_nat @ A @ B )
% 5.64/5.93 = ( times_times_nat @ A @ C ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_mult_left_cancel
% 5.64/5.93 thf(fact_4700_unit__mult__left__cancel,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 => ( ( ( times_times_int @ A @ B )
% 5.64/5.93 = ( times_times_int @ A @ C ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_mult_left_cancel
% 5.64/5.93 thf(fact_4701_unit__mult__right__cancel,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.64/5.93 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_mult_right_cancel
% 5.64/5.93 thf(fact_4702_unit__mult__right__cancel,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 => ( ( ( times_times_nat @ B @ A )
% 5.64/5.93 = ( times_times_nat @ C @ A ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_mult_right_cancel
% 5.64/5.93 thf(fact_4703_unit__mult__right__cancel,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 => ( ( ( times_times_int @ B @ A )
% 5.64/5.93 = ( times_times_int @ C @ A ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_mult_right_cancel
% 5.64/5.93 thf(fact_4704_div__mult__div__if__dvd,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.64/5.93 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_div_if_dvd
% 5.64/5.93 thf(fact_4705_div__mult__div__if__dvd,axiom,
% 5.64/5.93 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( dvd_dvd_nat @ D @ C )
% 5.64/5.93 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.64/5.93 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_div_if_dvd
% 5.64/5.93 thf(fact_4706_div__mult__div__if__dvd,axiom,
% 5.64/5.93 ! [B: int,A: int,D: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( dvd_dvd_int @ D @ C )
% 5.64/5.93 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.64/5.93 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_div_if_dvd
% 5.64/5.93 thf(fact_4707_dvd__mult__imp__div,axiom,
% 5.64/5.93 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_imp_div
% 5.64/5.93 thf(fact_4708_dvd__mult__imp__div,axiom,
% 5.64/5.93 ! [A: nat,C: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.64/5.93 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_imp_div
% 5.64/5.93 thf(fact_4709_dvd__mult__imp__div,axiom,
% 5.64/5.93 ! [A: int,C: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.64/5.93 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_imp_div
% 5.64/5.93 thf(fact_4710_dvd__div__mult2__eq,axiom,
% 5.64/5.93 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_mult2_eq
% 5.64/5.93 thf(fact_4711_dvd__div__mult2__eq,axiom,
% 5.64/5.93 ! [B: nat,C: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.93 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_mult2_eq
% 5.64/5.93 thf(fact_4712_dvd__div__mult2__eq,axiom,
% 5.64/5.93 ! [B: int,C: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.64/5.93 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.93 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_mult2_eq
% 5.64/5.93 thf(fact_4713_div__div__eq__right,axiom,
% 5.64/5.93 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.64/5.93 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_div_eq_right
% 5.64/5.93 thf(fact_4714_div__div__eq__right,axiom,
% 5.64/5.93 ! [C: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.64/5.93 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_div_eq_right
% 5.64/5.93 thf(fact_4715_div__div__eq__right,axiom,
% 5.64/5.93 ! [C: int,B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.64/5.93 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_div_eq_right
% 5.64/5.93 thf(fact_4716_div__mult__swap,axiom,
% 5.64/5.93 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_swap
% 5.64/5.93 thf(fact_4717_div__mult__swap,axiom,
% 5.64/5.93 ! [C: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.64/5.93 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_swap
% 5.64/5.93 thf(fact_4718_div__mult__swap,axiom,
% 5.64/5.93 ! [C: int,B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.64/5.93 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_swap
% 5.64/5.93 thf(fact_4719_dvd__div__mult,axiom,
% 5.64/5.93 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_mult
% 5.64/5.93 thf(fact_4720_dvd__div__mult,axiom,
% 5.64/5.93 ! [C: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.64/5.93 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_mult
% 5.64/5.93 thf(fact_4721_dvd__div__mult,axiom,
% 5.64/5.93 ! [C: int,B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.64/5.93 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_mult
% 5.64/5.93 thf(fact_4722_unit__div__cancel,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.64/5.93 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_cancel
% 5.64/5.93 thf(fact_4723_unit__div__cancel,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 => ( ( ( divide_divide_nat @ B @ A )
% 5.64/5.93 = ( divide_divide_nat @ C @ A ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_cancel
% 5.64/5.93 thf(fact_4724_unit__div__cancel,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 => ( ( ( divide_divide_int @ B @ A )
% 5.64/5.93 = ( divide_divide_int @ C @ A ) )
% 5.64/5.93 = ( B = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_cancel
% 5.64/5.93 thf(fact_4725_div__unit__dvd__iff,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_unit_dvd_iff
% 5.64/5.93 thf(fact_4726_div__unit__dvd__iff,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_unit_dvd_iff
% 5.64/5.93 thf(fact_4727_div__unit__dvd__iff,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_unit_dvd_iff
% 5.64/5.93 thf(fact_4728_dvd__div__unit__iff,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_unit_iff
% 5.64/5.93 thf(fact_4729_dvd__div__unit__iff,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_unit_iff
% 5.64/5.93 thf(fact_4730_dvd__div__unit__iff,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.64/5.93 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_unit_iff
% 5.64/5.93 thf(fact_4731_div__plus__div__distrib__dvd__right,axiom,
% 5.64/5.93 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.64/5.93 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_plus_div_distrib_dvd_right
% 5.64/5.93 thf(fact_4732_div__plus__div__distrib__dvd__right,axiom,
% 5.64/5.93 ! [C: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.93 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_plus_div_distrib_dvd_right
% 5.64/5.93 thf(fact_4733_div__plus__div__distrib__dvd__right,axiom,
% 5.64/5.93 ! [C: int,B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.93 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_plus_div_distrib_dvd_right
% 5.64/5.93 thf(fact_4734_div__plus__div__distrib__dvd__left,axiom,
% 5.64/5.93 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.64/5.93 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_plus_div_distrib_dvd_left
% 5.64/5.93 thf(fact_4735_div__plus__div__distrib__dvd__left,axiom,
% 5.64/5.93 ! [C: nat,A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.64/5.93 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_plus_div_distrib_dvd_left
% 5.64/5.93 thf(fact_4736_div__plus__div__distrib__dvd__left,axiom,
% 5.64/5.93 ! [C: int,A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ A )
% 5.64/5.93 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.64/5.93 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_plus_div_distrib_dvd_left
% 5.64/5.93 thf(fact_4737_div__power,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_power
% 5.64/5.93 thf(fact_4738_div__power,axiom,
% 5.64/5.93 ! [B: nat,A: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.64/5.93 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_power
% 5.64/5.93 thf(fact_4739_div__power,axiom,
% 5.64/5.93 ! [B: int,A: int,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.64/5.93 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_power
% 5.64/5.93 thf(fact_4740_le__imp__power__dvd,axiom,
% 5.64/5.93 ! [M: nat,N: nat,A: code_integer] :
% 5.64/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % le_imp_power_dvd
% 5.64/5.93 thf(fact_4741_le__imp__power__dvd,axiom,
% 5.64/5.93 ! [M: nat,N: nat,A: nat] :
% 5.64/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % le_imp_power_dvd
% 5.64/5.93 thf(fact_4742_le__imp__power__dvd,axiom,
% 5.64/5.93 ! [M: nat,N: nat,A: real] :
% 5.64/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % le_imp_power_dvd
% 5.64/5.93 thf(fact_4743_le__imp__power__dvd,axiom,
% 5.64/5.93 ! [M: nat,N: nat,A: int] :
% 5.64/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % le_imp_power_dvd
% 5.64/5.93 thf(fact_4744_le__imp__power__dvd,axiom,
% 5.64/5.93 ! [M: nat,N: nat,A: complex] :
% 5.64/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % le_imp_power_dvd
% 5.64/5.93 thf(fact_4745_power__le__dvd,axiom,
% 5.64/5.93 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.64/5.93 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_dvd
% 5.64/5.93 thf(fact_4746_power__le__dvd,axiom,
% 5.64/5.93 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.64/5.93 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_dvd
% 5.64/5.93 thf(fact_4747_power__le__dvd,axiom,
% 5.64/5.93 ! [A: real,N: nat,B: real,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.64/5.93 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_dvd
% 5.64/5.93 thf(fact_4748_power__le__dvd,axiom,
% 5.64/5.93 ! [A: int,N: nat,B: int,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.64/5.93 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_dvd
% 5.64/5.93 thf(fact_4749_power__le__dvd,axiom,
% 5.64/5.93 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.64/5.93 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_dvd
% 5.64/5.93 thf(fact_4750_dvd__power__le,axiom,
% 5.64/5.93 ! [X2: code_integer,Y4: code_integer,N: nat,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ X2 @ Y4 )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N ) @ ( power_8256067586552552935nteger @ Y4 @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_le
% 5.64/5.93 thf(fact_4751_dvd__power__le,axiom,
% 5.64/5.93 ! [X2: nat,Y4: nat,N: nat,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ X2 @ Y4 )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N ) @ ( power_power_nat @ Y4 @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_le
% 5.64/5.93 thf(fact_4752_dvd__power__le,axiom,
% 5.64/5.93 ! [X2: real,Y4: real,N: nat,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_real @ X2 @ Y4 )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y4 @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_le
% 5.64/5.93 thf(fact_4753_dvd__power__le,axiom,
% 5.64/5.93 ! [X2: int,Y4: int,N: nat,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ X2 @ Y4 )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y4 @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_le
% 5.64/5.93 thf(fact_4754_dvd__power__le,axiom,
% 5.64/5.93 ! [X2: complex,Y4: complex,N: nat,M: nat] :
% 5.64/5.93 ( ( dvd_dvd_complex @ X2 @ Y4 )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y4 @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_le
% 5.64/5.93 thf(fact_4755_dvd__pos__nat,axiom,
% 5.64/5.93 ! [N: nat,M: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 => ( ( dvd_dvd_nat @ M @ N )
% 5.64/5.93 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_pos_nat
% 5.64/5.93 thf(fact_4756_nat__dvd__not__less,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.93 => ( ( ord_less_nat @ M @ N )
% 5.64/5.93 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % nat_dvd_not_less
% 5.64/5.93 thf(fact_4757_dvd__minus__self,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.64/5.93 = ( ( ord_less_nat @ N @ M )
% 5.64/5.93 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_minus_self
% 5.64/5.93 thf(fact_4758_less__eq__dvd__minus,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 => ( ( dvd_dvd_nat @ M @ N )
% 5.64/5.93 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % less_eq_dvd_minus
% 5.64/5.93 thf(fact_4759_dvd__diffD1,axiom,
% 5.64/5.93 ! [K: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.93 => ( ( dvd_dvd_nat @ K @ M )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_diffD1
% 5.64/5.93 thf(fact_4760_dvd__diffD,axiom,
% 5.64/5.93 ! [K: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.93 => ( ( dvd_dvd_nat @ K @ N )
% 5.64/5.93 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_diffD
% 5.64/5.93 thf(fact_4761_zdvd__not__zless,axiom,
% 5.64/5.93 ! [M: int,N: int] :
% 5.64/5.93 ( ( ord_less_int @ zero_zero_int @ M )
% 5.64/5.93 => ( ( ord_less_int @ M @ N )
% 5.64/5.93 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zdvd_not_zless
% 5.64/5.93 thf(fact_4762_bezout__lemma__nat,axiom,
% 5.64/5.93 ! [D: nat,A: nat,B: nat,X2: nat,Y4: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ D @ A )
% 5.64/5.93 => ( ( dvd_dvd_nat @ D @ B )
% 5.64/5.93 => ( ( ( ( times_times_nat @ A @ X2 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D ) )
% 5.64/5.93 | ( ( times_times_nat @ B @ X2 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) )
% 5.64/5.93 => ? [X4: nat,Y3: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ D @ A )
% 5.64/5.93 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.93 & ( ( ( times_times_nat @ A @ X4 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.64/5.93 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bezout_lemma_nat
% 5.64/5.93 thf(fact_4763_bezout__add__nat,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ? [D3: nat,X4: nat,Y3: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ D3 @ A )
% 5.64/5.93 & ( dvd_dvd_nat @ D3 @ B )
% 5.64/5.93 & ( ( ( times_times_nat @ A @ X4 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.64/5.93 | ( ( times_times_nat @ B @ X4 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bezout_add_nat
% 5.64/5.93 thf(fact_4764_zdvd__mono,axiom,
% 5.64/5.93 ! [K: int,M: int,T: int] :
% 5.64/5.93 ( ( K != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ M @ T )
% 5.64/5.93 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zdvd_mono
% 5.64/5.93 thf(fact_4765_zdvd__mult__cancel,axiom,
% 5.64/5.93 ! [K: int,M: int,N: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.64/5.93 => ( ( K != zero_zero_int )
% 5.64/5.93 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zdvd_mult_cancel
% 5.64/5.93 thf(fact_4766_bezout1__nat,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ? [D3: nat,X4: nat,Y3: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ D3 @ A )
% 5.64/5.93 & ( dvd_dvd_nat @ D3 @ B )
% 5.64/5.93 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.64/5.93 = D3 )
% 5.64/5.93 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.64/5.93 = D3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bezout1_nat
% 5.64/5.93 thf(fact_4767_zdvd__period,axiom,
% 5.64/5.93 ! [A: int,D: int,X2: int,T: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ D )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X2 @ T ) )
% 5.64/5.93 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X2 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zdvd_period
% 5.64/5.93 thf(fact_4768_zdvd__reduce,axiom,
% 5.64/5.93 ! [K: int,N: int,M: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.64/5.93 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % zdvd_reduce
% 5.64/5.93 thf(fact_4769_semiring__norm_I27_J,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( bitM @ ( bit0 @ N ) )
% 5.64/5.93 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % semiring_norm(27)
% 5.64/5.93 thf(fact_4770_semiring__norm_I28_J,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( bitM @ ( bit1 @ N ) )
% 5.64/5.93 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % semiring_norm(28)
% 5.64/5.93 thf(fact_4771_div2__even__ext__nat,axiom,
% 5.64/5.93 ! [X2: nat,Y4: nat] :
% 5.64/5.93 ( ( ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_nat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.93 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
% 5.64/5.93 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y4 ) )
% 5.64/5.93 => ( X2 = Y4 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div2_even_ext_nat
% 5.64/5.93 thf(fact_4772_unit__dvdE,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.93 => ! [C3: code_integer] :
% 5.64/5.93 ( B
% 5.64/5.93 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_dvdE
% 5.64/5.93 thf(fact_4773_unit__dvdE,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 => ~ ( ( A != zero_zero_nat )
% 5.64/5.93 => ! [C3: nat] :
% 5.64/5.93 ( B
% 5.64/5.93 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_dvdE
% 5.64/5.93 thf(fact_4774_unit__dvdE,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 => ~ ( ( A != zero_zero_int )
% 5.64/5.93 => ! [C3: int] :
% 5.64/5.93 ( B
% 5.64/5.93 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_dvdE
% 5.64/5.93 thf(fact_4775_unity__coeff__ex,axiom,
% 5.64/5.93 ! [P: code_integer > $o,L: code_integer] :
% 5.64/5.93 ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 5.64/5.93 = ( ? [X: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 5.64/5.93 & ( P @ X ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unity_coeff_ex
% 5.64/5.93 thf(fact_4776_unity__coeff__ex,axiom,
% 5.64/5.93 ! [P: complex > $o,L: complex] :
% 5.64/5.93 ( ( ? [X: complex] : ( P @ ( times_times_complex @ L @ X ) ) )
% 5.64/5.93 = ( ? [X: complex] :
% 5.64/5.93 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 5.64/5.93 & ( P @ X ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unity_coeff_ex
% 5.64/5.93 thf(fact_4777_unity__coeff__ex,axiom,
% 5.64/5.93 ! [P: real > $o,L: real] :
% 5.64/5.93 ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 5.64/5.93 = ( ? [X: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 5.64/5.93 & ( P @ X ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unity_coeff_ex
% 5.64/5.93 thf(fact_4778_unity__coeff__ex,axiom,
% 5.64/5.93 ! [P: rat > $o,L: rat] :
% 5.64/5.93 ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 5.64/5.93 = ( ? [X: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 5.64/5.93 & ( P @ X ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unity_coeff_ex
% 5.64/5.93 thf(fact_4779_unity__coeff__ex,axiom,
% 5.64/5.93 ! [P: nat > $o,L: nat] :
% 5.64/5.93 ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 5.64/5.93 = ( ? [X: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 5.64/5.93 & ( P @ X ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unity_coeff_ex
% 5.64/5.93 thf(fact_4780_unity__coeff__ex,axiom,
% 5.64/5.93 ! [P: int > $o,L: int] :
% 5.64/5.93 ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 5.64/5.93 = ( ? [X: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 5.64/5.93 & ( P @ X ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unity_coeff_ex
% 5.64/5.93 thf(fact_4781_dvd__div__div__eq__mult,axiom,
% 5.64/5.93 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.64/5.93 ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( C != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.64/5.93 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.64/5.93 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.64/5.93 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_div_eq_mult
% 5.64/5.93 thf(fact_4782_dvd__div__div__eq__mult,axiom,
% 5.64/5.93 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.64/5.93 ( ( A != zero_zero_nat )
% 5.64/5.93 => ( ( C != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ D )
% 5.64/5.93 => ( ( ( divide_divide_nat @ B @ A )
% 5.64/5.93 = ( divide_divide_nat @ D @ C ) )
% 5.64/5.93 = ( ( times_times_nat @ B @ C )
% 5.64/5.93 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_div_eq_mult
% 5.64/5.93 thf(fact_4783_dvd__div__div__eq__mult,axiom,
% 5.64/5.93 ! [A: int,C: int,B: int,D: int] :
% 5.64/5.93 ( ( A != zero_zero_int )
% 5.64/5.93 => ( ( C != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ D )
% 5.64/5.93 => ( ( ( divide_divide_int @ B @ A )
% 5.64/5.93 = ( divide_divide_int @ D @ C ) )
% 5.64/5.93 = ( ( times_times_int @ B @ C )
% 5.64/5.93 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_div_eq_mult
% 5.64/5.93 thf(fact_4784_dvd__div__iff__mult,axiom,
% 5.64/5.93 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( C != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_iff_mult
% 5.64/5.93 thf(fact_4785_dvd__div__iff__mult,axiom,
% 5.64/5.93 ! [C: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( C != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ B )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_iff_mult
% 5.64/5.93 thf(fact_4786_dvd__div__iff__mult,axiom,
% 5.64/5.93 ! [C: int,B: int,A: int] :
% 5.64/5.93 ( ( C != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ B )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.64/5.93 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_iff_mult
% 5.64/5.93 thf(fact_4787_div__dvd__iff__mult,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( B != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_dvd_iff_mult
% 5.64/5.93 thf(fact_4788_div__dvd__iff__mult,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( B != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_dvd_iff_mult
% 5.64/5.93 thf(fact_4789_div__dvd__iff__mult,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( B != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.64/5.93 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_dvd_iff_mult
% 5.64/5.93 thf(fact_4790_dvd__div__eq__mult,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.64/5.93 ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.64/5.93 = C )
% 5.64/5.93 = ( B
% 5.64/5.93 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_mult
% 5.64/5.93 thf(fact_4791_dvd__div__eq__mult,axiom,
% 5.64/5.93 ! [A: nat,B: nat,C: nat] :
% 5.64/5.93 ( ( A != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ A @ B )
% 5.64/5.93 => ( ( ( divide_divide_nat @ B @ A )
% 5.64/5.93 = C )
% 5.64/5.93 = ( B
% 5.64/5.93 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_mult
% 5.64/5.93 thf(fact_4792_dvd__div__eq__mult,axiom,
% 5.64/5.93 ! [A: int,B: int,C: int] :
% 5.64/5.93 ( ( A != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ A @ B )
% 5.64/5.93 => ( ( ( divide_divide_int @ B @ A )
% 5.64/5.93 = C )
% 5.64/5.93 = ( B
% 5.64/5.93 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_div_eq_mult
% 5.64/5.93 thf(fact_4793_unit__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.64/5.93 = zero_z3403309356797280102nteger )
% 5.64/5.93 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_eq_0_iff
% 5.64/5.93 thf(fact_4794_unit__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( ( divide_divide_nat @ A @ B )
% 5.64/5.93 = zero_zero_nat )
% 5.64/5.93 = ( A = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_eq_0_iff
% 5.64/5.93 thf(fact_4795_unit__div__eq__0__iff,axiom,
% 5.64/5.93 ! [B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( ( divide_divide_int @ A @ B )
% 5.64/5.93 = zero_zero_int )
% 5.64/5.93 = ( A = zero_zero_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_eq_0_iff
% 5.64/5.93 thf(fact_4796_even__numeral,axiom,
% 5.64/5.93 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_numeral
% 5.64/5.93 thf(fact_4797_even__numeral,axiom,
% 5.64/5.93 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_numeral
% 5.64/5.93 thf(fact_4798_even__numeral,axiom,
% 5.64/5.93 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_numeral
% 5.64/5.93 thf(fact_4799_inf__period_I3_J,axiom,
% 5.64/5.93 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.64/5.93 => ! [X3: code_integer,K4: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ T ) )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(3)
% 5.64/5.93 thf(fact_4800_inf__period_I3_J,axiom,
% 5.64/5.93 ! [D: real,D4: real,T: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ D @ D4 )
% 5.64/5.93 => ! [X3: real,K4: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ T ) )
% 5.64/5.93 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(3)
% 5.64/5.93 thf(fact_4801_inf__period_I3_J,axiom,
% 5.64/5.93 ! [D: rat,D4: rat,T: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ D @ D4 )
% 5.64/5.93 => ! [X3: rat,K4: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ T ) )
% 5.64/5.93 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(3)
% 5.64/5.93 thf(fact_4802_inf__period_I3_J,axiom,
% 5.64/5.93 ! [D: int,D4: int,T: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ D @ D4 )
% 5.64/5.93 => ! [X3: int,K4: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) )
% 5.64/5.93 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(3)
% 5.64/5.93 thf(fact_4803_inf__period_I4_J,axiom,
% 5.64/5.93 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.64/5.93 => ! [X3: code_integer,K4: code_integer] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ T ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(4)
% 5.64/5.93 thf(fact_4804_inf__period_I4_J,axiom,
% 5.64/5.93 ! [D: real,D4: real,T: real] :
% 5.64/5.93 ( ( dvd_dvd_real @ D @ D4 )
% 5.64/5.93 => ! [X3: real,K4: real] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ T ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(4)
% 5.64/5.93 thf(fact_4805_inf__period_I4_J,axiom,
% 5.64/5.93 ! [D: rat,D4: rat,T: rat] :
% 5.64/5.93 ( ( dvd_dvd_rat @ D @ D4 )
% 5.64/5.93 => ! [X3: rat,K4: rat] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ T ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(4)
% 5.64/5.93 thf(fact_4806_inf__period_I4_J,axiom,
% 5.64/5.93 ! [D: int,D4: int,T: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ D @ D4 )
% 5.64/5.93 => ! [X3: int,K4: int] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T ) ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % inf_period(4)
% 5.64/5.93 thf(fact_4807_unit__eq__div1,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.64/5.93 = C )
% 5.64/5.93 = ( A
% 5.64/5.93 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_eq_div1
% 5.64/5.93 thf(fact_4808_unit__eq__div1,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( ( divide_divide_nat @ A @ B )
% 5.64/5.93 = C )
% 5.64/5.93 = ( A
% 5.64/5.93 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_eq_div1
% 5.64/5.93 thf(fact_4809_unit__eq__div1,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( ( divide_divide_int @ A @ B )
% 5.64/5.93 = C )
% 5.64/5.93 = ( A
% 5.64/5.93 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_eq_div1
% 5.64/5.93 thf(fact_4810_unit__eq__div2,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( A
% 5.64/5.93 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.64/5.93 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.64/5.93 = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_eq_div2
% 5.64/5.93 thf(fact_4811_unit__eq__div2,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( A
% 5.64/5.93 = ( divide_divide_nat @ C @ B ) )
% 5.64/5.93 = ( ( times_times_nat @ A @ B )
% 5.64/5.93 = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_eq_div2
% 5.64/5.93 thf(fact_4812_unit__eq__div2,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( A
% 5.64/5.93 = ( divide_divide_int @ C @ B ) )
% 5.64/5.93 = ( ( times_times_int @ A @ B )
% 5.64/5.93 = C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_eq_div2
% 5.64/5.93 thf(fact_4813_div__mult__unit2,axiom,
% 5.64/5.93 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_unit2
% 5.64/5.93 thf(fact_4814_div__mult__unit2,axiom,
% 5.64/5.93 ! [C: nat,B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ A )
% 5.64/5.93 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.93 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_unit2
% 5.64/5.93 thf(fact_4815_div__mult__unit2,axiom,
% 5.64/5.93 ! [C: int,B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ A )
% 5.64/5.93 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.93 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % div_mult_unit2
% 5.64/5.93 thf(fact_4816_unit__div__commute,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_commute
% 5.64/5.93 thf(fact_4817_unit__div__commute,axiom,
% 5.64/5.93 ! [B: nat,A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.64/5.93 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_commute
% 5.64/5.93 thf(fact_4818_unit__div__commute,axiom,
% 5.64/5.93 ! [B: int,A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.64/5.93 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_commute
% 5.64/5.93 thf(fact_4819_unit__div__mult__swap,axiom,
% 5.64/5.93 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.64/5.93 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_mult_swap
% 5.64/5.93 thf(fact_4820_unit__div__mult__swap,axiom,
% 5.64/5.93 ! [C: nat,A: nat,B: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.64/5.93 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.64/5.93 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_mult_swap
% 5.64/5.93 thf(fact_4821_unit__div__mult__swap,axiom,
% 5.64/5.93 ! [C: int,A: int,B: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.64/5.93 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.64/5.93 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_div_mult_swap
% 5.64/5.93 thf(fact_4822_is__unit__div__mult2__eq,axiom,
% 5.64/5.93 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult2_eq
% 5.64/5.93 thf(fact_4823_is__unit__div__mult2__eq,axiom,
% 5.64/5.93 ! [B: nat,C: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.64/5.93 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.64/5.93 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult2_eq
% 5.64/5.93 thf(fact_4824_is__unit__div__mult2__eq,axiom,
% 5.64/5.93 ! [B: int,C: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.64/5.93 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.64/5.93 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult2_eq
% 5.64/5.93 thf(fact_4825_is__unit__power__iff,axiom,
% 5.64/5.93 ! [A: code_integer,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_power_iff
% 5.64/5.93 thf(fact_4826_is__unit__power__iff,axiom,
% 5.64/5.93 ! [A: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.64/5.93 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_power_iff
% 5.64/5.93 thf(fact_4827_is__unit__power__iff,axiom,
% 5.64/5.93 ! [A: int,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.64/5.93 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_power_iff
% 5.64/5.93 thf(fact_4828_unit__imp__mod__eq__0,axiom,
% 5.64/5.93 ! [B: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( modulo_modulo_nat @ A @ B )
% 5.64/5.93 = zero_zero_nat ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_imp_mod_eq_0
% 5.64/5.93 thf(fact_4829_unit__imp__mod__eq__0,axiom,
% 5.64/5.93 ! [B: int,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( modulo_modulo_int @ A @ B )
% 5.64/5.93 = zero_zero_int ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_imp_mod_eq_0
% 5.64/5.93 thf(fact_4830_unit__imp__mod__eq__0,axiom,
% 5.64/5.93 ! [B: code_integer,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.64/5.93 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.93
% 5.64/5.93 % unit_imp_mod_eq_0
% 5.64/5.93 thf(fact_4831_dvd__imp__le,axiom,
% 5.64/5.93 ! [K: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ K @ N )
% 5.64/5.93 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_imp_le
% 5.64/5.93 thf(fact_4832_dvd__mult__cancel,axiom,
% 5.64/5.93 ! [K: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.93 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.93 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_cancel
% 5.64/5.93 thf(fact_4833_nat__mult__dvd__cancel1,axiom,
% 5.64/5.93 ! [K: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.64/5.93 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % nat_mult_dvd_cancel1
% 5.64/5.93 thf(fact_4834_bezout__add__strong__nat,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( A != zero_zero_nat )
% 5.64/5.93 => ? [D3: nat,X4: nat,Y3: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ D3 @ A )
% 5.64/5.93 & ( dvd_dvd_nat @ D3 @ B )
% 5.64/5.93 & ( ( times_times_nat @ A @ X4 )
% 5.64/5.93 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bezout_add_strong_nat
% 5.64/5.93 thf(fact_4835_zdvd__imp__le,axiom,
% 5.64/5.93 ! [Z: int,N: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ Z @ N )
% 5.64/5.93 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.64/5.93 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zdvd_imp_le
% 5.64/5.93 thf(fact_4836_mod__greater__zero__iff__not__dvd,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod_greater_zero_iff_not_dvd
% 5.64/5.93 thf(fact_4837_mod__eq__dvd__iff__nat,axiom,
% 5.64/5.93 ! [N: nat,M: nat,Q3: nat] :
% 5.64/5.93 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.93 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.64/5.93 = ( modulo_modulo_nat @ N @ Q3 ) )
% 5.64/5.93 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod_eq_dvd_iff_nat
% 5.64/5.93 thf(fact_4838_eval__nat__numeral_I2_J,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.64/5.93 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % eval_nat_numeral(2)
% 5.64/5.93 thf(fact_4839_prod__decode__aux_Ocases,axiom,
% 5.64/5.93 ! [X2: product_prod_nat_nat] :
% 5.64/5.93 ~ ! [K3: nat,M4: nat] :
% 5.64/5.93 ( X2
% 5.64/5.93 != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 5.64/5.93
% 5.64/5.93 % prod_decode_aux.cases
% 5.64/5.93 thf(fact_4840_finite__divisors__nat,axiom,
% 5.64/5.93 ! [M: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.93 => ( finite_finite_nat
% 5.64/5.93 @ ( collect_nat
% 5.64/5.93 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % finite_divisors_nat
% 5.64/5.93 thf(fact_4841_one__plus__BitM,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.64/5.93 = ( bit0 @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % one_plus_BitM
% 5.64/5.93 thf(fact_4842_BitM__plus__one,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.64/5.93 = ( bit0 @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % BitM_plus_one
% 5.64/5.93 thf(fact_4843_even__zero,axiom,
% 5.64/5.93 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.64/5.93
% 5.64/5.93 % even_zero
% 5.64/5.93 thf(fact_4844_even__zero,axiom,
% 5.64/5.93 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.64/5.93
% 5.64/5.93 % even_zero
% 5.64/5.93 thf(fact_4845_even__zero,axiom,
% 5.64/5.93 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.64/5.93
% 5.64/5.93 % even_zero
% 5.64/5.93 thf(fact_4846_is__unitE,axiom,
% 5.64/5.93 ! [A: code_integer,C: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.64/5.93 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.93 => ! [B5: code_integer] :
% 5.64/5.93 ( ( B5 != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.64/5.93 = B5 )
% 5.64/5.93 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 5.64/5.93 = A )
% 5.64/5.93 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 5.64/5.93 = one_one_Code_integer )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.64/5.93 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unitE
% 5.64/5.93 thf(fact_4847_is__unitE,axiom,
% 5.64/5.93 ! [A: nat,C: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.64/5.93 => ~ ( ( A != zero_zero_nat )
% 5.64/5.93 => ! [B5: nat] :
% 5.64/5.93 ( ( B5 != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 5.64/5.93 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.64/5.93 = B5 )
% 5.64/5.93 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 5.64/5.93 = A )
% 5.64/5.93 => ( ( ( times_times_nat @ A @ B5 )
% 5.64/5.93 = one_one_nat )
% 5.64/5.93 => ( ( divide_divide_nat @ C @ A )
% 5.64/5.93 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unitE
% 5.64/5.93 thf(fact_4848_is__unitE,axiom,
% 5.64/5.93 ! [A: int,C: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.64/5.93 => ~ ( ( A != zero_zero_int )
% 5.64/5.93 => ! [B5: int] :
% 5.64/5.93 ( ( B5 != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 5.64/5.93 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.64/5.93 = B5 )
% 5.64/5.93 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 5.64/5.93 = A )
% 5.64/5.93 => ( ( ( times_times_int @ A @ B5 )
% 5.64/5.93 = one_one_int )
% 5.64/5.93 => ( ( divide_divide_int @ C @ A )
% 5.64/5.93 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unitE
% 5.64/5.93 thf(fact_4849_is__unit__div__mult__cancel__left,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult_cancel_left
% 5.64/5.93 thf(fact_4850_is__unit__div__mult__cancel__left,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( A != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.64/5.93 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult_cancel_left
% 5.64/5.93 thf(fact_4851_is__unit__div__mult__cancel__left,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ( A != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.64/5.93 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult_cancel_left
% 5.64/5.93 thf(fact_4852_is__unit__div__mult__cancel__right,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.64/5.93 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult_cancel_right
% 5.64/5.93 thf(fact_4853_is__unit__div__mult__cancel__right,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ( A != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.64/5.93 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.64/5.93 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult_cancel_right
% 5.64/5.93 thf(fact_4854_is__unit__div__mult__cancel__right,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ( A != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.64/5.93 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.64/5.93 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % is_unit_div_mult_cancel_right
% 5.64/5.93 thf(fact_4855_evenE,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ~ ! [B5: code_integer] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % evenE
% 5.64/5.93 thf(fact_4856_evenE,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ~ ! [B5: nat] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % evenE
% 5.64/5.93 thf(fact_4857_evenE,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ~ ! [B5: int] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % evenE
% 5.64/5.93 thf(fact_4858_odd__one,axiom,
% 5.64/5.93 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.64/5.93
% 5.64/5.93 % odd_one
% 5.64/5.93 thf(fact_4859_odd__one,axiom,
% 5.64/5.93 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.64/5.93
% 5.64/5.93 % odd_one
% 5.64/5.93 thf(fact_4860_odd__one,axiom,
% 5.64/5.93 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.64/5.93
% 5.64/5.93 % odd_one
% 5.64/5.93 thf(fact_4861_odd__even__add,axiom,
% 5.64/5.93 ! [A: code_integer,B: code_integer] :
% 5.64/5.93 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_even_add
% 5.64/5.93 thf(fact_4862_odd__even__add,axiom,
% 5.64/5.93 ! [A: nat,B: nat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.93 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_even_add
% 5.64/5.93 thf(fact_4863_odd__even__add,axiom,
% 5.64/5.93 ! [A: int,B: int] :
% 5.64/5.93 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.64/5.93 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_even_add
% 5.64/5.93 thf(fact_4864_bit__eq__rec,axiom,
% 5.64/5.93 ( ( ^ [Y6: code_integer,Z3: code_integer] : ( Y6 = Z3 ) )
% 5.64/5.93 = ( ^ [A3: code_integer,B3: code_integer] :
% 5.64/5.93 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.64/5.93 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) )
% 5.64/5.93 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide6298287555418463151nteger @ B3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bit_eq_rec
% 5.64/5.93 thf(fact_4865_bit__eq__rec,axiom,
% 5.64/5.93 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/5.93 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.93 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.64/5.93 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) )
% 5.64/5.93 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_nat @ B3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bit_eq_rec
% 5.64/5.93 thf(fact_4866_bit__eq__rec,axiom,
% 5.64/5.93 ( ( ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/5.93 = ( ^ [A3: int,B3: int] :
% 5.64/5.93 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.64/5.93 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) )
% 5.64/5.93 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = ( divide_divide_int @ B3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bit_eq_rec
% 5.64/5.93 thf(fact_4867_dvd__power__iff,axiom,
% 5.64/5.93 ! [X2: code_integer,M: nat,N: nat] :
% 5.64/5.93 ( ( X2 != zero_z3403309356797280102nteger )
% 5.64/5.93 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ X2 @ one_one_Code_integer )
% 5.64/5.93 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_iff
% 5.64/5.93 thf(fact_4868_dvd__power__iff,axiom,
% 5.64/5.93 ! [X2: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( X2 != zero_zero_nat )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( power_power_nat @ X2 @ M ) @ ( power_power_nat @ X2 @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ X2 @ one_one_nat )
% 5.64/5.93 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_iff
% 5.64/5.93 thf(fact_4869_dvd__power__iff,axiom,
% 5.64/5.93 ! [X2: int,M: nat,N: nat] :
% 5.64/5.93 ( ( X2 != zero_zero_int )
% 5.64/5.93 => ( ( dvd_dvd_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.64/5.93 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_iff
% 5.64/5.93 thf(fact_4870_odd__numeral,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_numeral
% 5.64/5.93 thf(fact_4871_odd__numeral,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_numeral
% 5.64/5.93 thf(fact_4872_odd__numeral,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_numeral
% 5.64/5.93 thf(fact_4873_dvd__power,axiom,
% 5.64/5.93 ! [N: nat,X2: code_integer] :
% 5.64/5.93 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 | ( X2 = one_one_Code_integer ) )
% 5.64/5.93 => ( dvd_dvd_Code_integer @ X2 @ ( power_8256067586552552935nteger @ X2 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power
% 5.64/5.93 thf(fact_4874_dvd__power,axiom,
% 5.64/5.93 ! [N: nat,X2: rat] :
% 5.64/5.93 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 | ( X2 = one_one_rat ) )
% 5.64/5.93 => ( dvd_dvd_rat @ X2 @ ( power_power_rat @ X2 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power
% 5.64/5.93 thf(fact_4875_dvd__power,axiom,
% 5.64/5.93 ! [N: nat,X2: nat] :
% 5.64/5.93 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 | ( X2 = one_one_nat ) )
% 5.64/5.93 => ( dvd_dvd_nat @ X2 @ ( power_power_nat @ X2 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power
% 5.64/5.93 thf(fact_4876_dvd__power,axiom,
% 5.64/5.93 ! [N: nat,X2: real] :
% 5.64/5.93 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 | ( X2 = one_one_real ) )
% 5.64/5.93 => ( dvd_dvd_real @ X2 @ ( power_power_real @ X2 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power
% 5.64/5.93 thf(fact_4877_dvd__power,axiom,
% 5.64/5.93 ! [N: nat,X2: int] :
% 5.64/5.93 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 | ( X2 = one_one_int ) )
% 5.64/5.93 => ( dvd_dvd_int @ X2 @ ( power_power_int @ X2 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power
% 5.64/5.93 thf(fact_4878_dvd__power,axiom,
% 5.64/5.93 ! [N: nat,X2: complex] :
% 5.64/5.93 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 | ( X2 = one_one_complex ) )
% 5.64/5.93 => ( dvd_dvd_complex @ X2 @ ( power_power_complex @ X2 @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power
% 5.64/5.93 thf(fact_4879_even__even__mod__4__iff,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_even_mod_4_iff
% 5.64/5.93 thf(fact_4880_dvd__mult__cancel1,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.64/5.93 = ( N = one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_cancel1
% 5.64/5.93 thf(fact_4881_dvd__mult__cancel2,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.64/5.93 = ( N = one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_mult_cancel2
% 5.64/5.93 thf(fact_4882_dvd__minus__add,axiom,
% 5.64/5.93 ! [Q3: nat,N: nat,R2: nat,M: nat] :
% 5.64/5.93 ( ( ord_less_eq_nat @ Q3 @ N )
% 5.64/5.93 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R2 @ M ) )
% 5.64/5.93 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q3 ) )
% 5.64/5.93 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q3 ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_minus_add
% 5.64/5.93 thf(fact_4883_power__dvd__imp__le,axiom,
% 5.64/5.93 ! [I: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.64/5.93 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.64/5.93 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_dvd_imp_le
% 5.64/5.93 thf(fact_4884_mod__nat__eqI,axiom,
% 5.64/5.93 ! [R2: nat,N: nat,M: nat] :
% 5.64/5.93 ( ( ord_less_nat @ R2 @ N )
% 5.64/5.93 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.64/5.93 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R2 ) )
% 5.64/5.93 => ( ( modulo_modulo_nat @ M @ N )
% 5.64/5.93 = R2 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod_nat_eqI
% 5.64/5.93 thf(fact_4885_mod__int__pos__iff,axiom,
% 5.64/5.93 ! [K: int,L: int] :
% 5.64/5.93 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ L @ K )
% 5.64/5.93 | ( ( L = zero_zero_int )
% 5.64/5.93 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.64/5.93 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod_int_pos_iff
% 5.64/5.93 thf(fact_4886_numeral__BitM,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.64/5.93 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.64/5.93
% 5.64/5.93 % numeral_BitM
% 5.64/5.93 thf(fact_4887_numeral__BitM,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.64/5.93 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.64/5.93
% 5.64/5.93 % numeral_BitM
% 5.64/5.93 thf(fact_4888_numeral__BitM,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.64/5.93 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.64/5.93
% 5.64/5.93 % numeral_BitM
% 5.64/5.93 thf(fact_4889_numeral__BitM,axiom,
% 5.64/5.93 ! [N: num] :
% 5.64/5.93 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.64/5.93 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.64/5.93
% 5.64/5.93 % numeral_BitM
% 5.64/5.93 thf(fact_4890_even__two__times__div__two,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.64/5.93 = A ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_two_times_div_two
% 5.64/5.93 thf(fact_4891_even__two__times__div__two,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.93 = A ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_two_times_div_two
% 5.64/5.93 thf(fact_4892_even__two__times__div__two,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.64/5.93 = A ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_two_times_div_two
% 5.64/5.93 thf(fact_4893_even__iff__mod__2__eq__zero,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_zero_nat ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_iff_mod_2_eq_zero
% 5.64/5.93 thf(fact_4894_even__iff__mod__2__eq__zero,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_zero_int ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_iff_mod_2_eq_zero
% 5.64/5.93 thf(fact_4895_even__iff__mod__2__eq__zero,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_iff_mod_2_eq_zero
% 5.64/5.93 thf(fact_4896_odd__iff__mod__2__eq__one,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.93 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = one_one_nat ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_iff_mod_2_eq_one
% 5.64/5.93 thf(fact_4897_odd__iff__mod__2__eq__one,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.93 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = one_one_int ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_iff_mod_2_eq_one
% 5.64/5.93 thf(fact_4898_odd__iff__mod__2__eq__one,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.93 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = one_one_Code_integer ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_iff_mod_2_eq_one
% 5.64/5.93 thf(fact_4899_power__mono__odd,axiom,
% 5.64/5.93 ! [N: nat,A: rat,B: rat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.93 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_mono_odd
% 5.64/5.93 thf(fact_4900_power__mono__odd,axiom,
% 5.64/5.93 ! [N: nat,A: int,B: int] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( ord_less_eq_int @ A @ B )
% 5.64/5.93 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_mono_odd
% 5.64/5.93 thf(fact_4901_power__mono__odd,axiom,
% 5.64/5.93 ! [N: nat,A: real,B: real] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( ord_less_eq_real @ A @ B )
% 5.64/5.93 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_mono_odd
% 5.64/5.93 thf(fact_4902_odd__pos,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_pos
% 5.64/5.93 thf(fact_4903_dvd__power__iff__le,axiom,
% 5.64/5.93 ! [K: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.64/5.93 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.64/5.93 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % dvd_power_iff_le
% 5.64/5.93 thf(fact_4904_even__unset__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 | ( M = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_unset_bit_iff
% 5.64/5.93 thf(fact_4905_even__unset__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 | ( M = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_unset_bit_iff
% 5.64/5.93 thf(fact_4906_even__unset__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 | ( M = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_unset_bit_iff
% 5.64/5.93 thf(fact_4907_even__set__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 & ( M != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_set_bit_iff
% 5.64/5.93 thf(fact_4908_even__set__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 & ( M != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_set_bit_iff
% 5.64/5.93 thf(fact_4909_even__set__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 & ( M != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_set_bit_iff
% 5.64/5.93 thf(fact_4910_even__flip__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: code_integer] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 != ( M = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_flip_bit_iff
% 5.64/5.93 thf(fact_4911_even__flip__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 != ( M = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_flip_bit_iff
% 5.64/5.93 thf(fact_4912_even__flip__bit__iff,axiom,
% 5.64/5.93 ! [M: nat,A: nat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 != ( M = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_flip_bit_iff
% 5.64/5.93 thf(fact_4913_even__diff__iff,axiom,
% 5.64/5.93 ! [K: int,L: int] :
% 5.64/5.93 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.64/5.93 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_diff_iff
% 5.64/5.93 thf(fact_4914_oddE,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ~ ! [B5: code_integer] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % oddE
% 5.64/5.93 thf(fact_4915_oddE,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ~ ! [B5: nat] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % oddE
% 5.64/5.93 thf(fact_4916_oddE,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ~ ! [B5: int] :
% 5.64/5.93 ( A
% 5.64/5.93 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % oddE
% 5.64/5.93 thf(fact_4917_parity__cases,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 != zero_zero_nat ) )
% 5.64/5.93 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 != one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % parity_cases
% 5.64/5.93 thf(fact_4918_parity__cases,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 != zero_zero_int ) )
% 5.64/5.93 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 != one_one_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % parity_cases
% 5.64/5.93 thf(fact_4919_parity__cases,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 != zero_z3403309356797280102nteger ) )
% 5.64/5.93 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 != one_one_Code_integer ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % parity_cases
% 5.64/5.93 thf(fact_4920_mod2__eq__if,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_zero_nat ) )
% 5.64/5.93 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = one_one_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod2_eq_if
% 5.64/5.93 thf(fact_4921_mod2__eq__if,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_zero_int ) )
% 5.64/5.93 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = one_one_int ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod2_eq_if
% 5.64/5.93 thf(fact_4922_mod2__eq__if,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_z3403309356797280102nteger ) )
% 5.64/5.93 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.93 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = one_one_Code_integer ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mod2_eq_if
% 5.64/5.93 thf(fact_4923_zero__le__even__power,axiom,
% 5.64/5.93 ! [N: nat,A: rat] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_even_power
% 5.64/5.93 thf(fact_4924_zero__le__even__power,axiom,
% 5.64/5.93 ! [N: nat,A: int] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_even_power
% 5.64/5.93 thf(fact_4925_zero__le__even__power,axiom,
% 5.64/5.93 ! [N: nat,A: real] :
% 5.64/5.93 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_even_power
% 5.64/5.93 thf(fact_4926_zero__le__odd__power,axiom,
% 5.64/5.93 ! [N: nat,A: rat] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.64/5.93 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_odd_power
% 5.64/5.93 thf(fact_4927_zero__le__odd__power,axiom,
% 5.64/5.93 ! [N: nat,A: int] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.64/5.93 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_odd_power
% 5.64/5.93 thf(fact_4928_zero__le__odd__power,axiom,
% 5.64/5.93 ! [N: nat,A: real] :
% 5.64/5.93 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.64/5.93 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_odd_power
% 5.64/5.93 thf(fact_4929_zero__le__power__eq,axiom,
% 5.64/5.93 ! [A: rat,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_power_eq
% 5.64/5.93 thf(fact_4930_zero__le__power__eq,axiom,
% 5.64/5.93 ! [A: int,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_power_eq
% 5.64/5.93 thf(fact_4931_zero__le__power__eq,axiom,
% 5.64/5.93 ! [A: real,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.64/5.93 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_le_power_eq
% 5.64/5.93 thf(fact_4932_list__decode_Ocases,axiom,
% 5.64/5.93 ! [X2: nat] :
% 5.64/5.93 ( ( X2 != zero_zero_nat )
% 5.64/5.93 => ~ ! [N3: nat] :
% 5.64/5.93 ( X2
% 5.64/5.93 != ( suc @ N3 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % list_decode.cases
% 5.64/5.93 thf(fact_4933_zero__less__power__eq,axiom,
% 5.64/5.93 ! [A: real,N: nat] :
% 5.64/5.93 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.64/5.93 = ( ( N = zero_zero_nat )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( A != zero_zero_real ) )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_power_eq
% 5.64/5.93 thf(fact_4934_zero__less__power__eq,axiom,
% 5.64/5.93 ! [A: rat,N: nat] :
% 5.64/5.93 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.64/5.93 = ( ( N = zero_zero_nat )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( A != zero_zero_rat ) )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_power_eq
% 5.64/5.93 thf(fact_4935_zero__less__power__eq,axiom,
% 5.64/5.93 ! [A: int,N: nat] :
% 5.64/5.93 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.64/5.93 = ( ( N = zero_zero_nat )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( A != zero_zero_int ) )
% 5.64/5.93 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_power_eq
% 5.64/5.93 thf(fact_4936_even__mask__div__iff_H,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mask_div_iff'
% 5.64/5.93 thf(fact_4937_even__mask__div__iff_H,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mask_div_iff'
% 5.64/5.93 thf(fact_4938_even__mask__div__iff_H,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mask_div_iff'
% 5.64/5.93 thf(fact_4939_power__le__zero__eq,axiom,
% 5.64/5.93 ! [A: rat,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.64/5.93 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_zero_eq
% 5.64/5.93 thf(fact_4940_power__le__zero__eq,axiom,
% 5.64/5.93 ! [A: int,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.64/5.93 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_zero_eq
% 5.64/5.93 thf(fact_4941_power__le__zero__eq,axiom,
% 5.64/5.93 ! [A: real,N: nat] :
% 5.64/5.93 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.64/5.93 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.93 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.64/5.93 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % power_le_zero_eq
% 5.64/5.93 thf(fact_4942_even__mod__4__div__2,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.93 = ( suc @ zero_zero_nat ) )
% 5.64/5.93 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mod_4_div_2
% 5.64/5.93 thf(fact_4943_divmod__step__nat__def,axiom,
% 5.64/5.93 ( unique5026877609467782581ep_nat
% 5.64/5.93 = ( ^ [L2: num] :
% 5.64/5.93 ( produc2626176000494625587at_nat
% 5.64/5.93 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_step_nat_def
% 5.64/5.93 thf(fact_4944_even__mask__div__iff,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = zero_z3403309356797280102nteger )
% 5.64/5.93 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mask_div_iff
% 5.64/5.93 thf(fact_4945_even__mask__div__iff,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = zero_zero_nat )
% 5.64/5.93 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mask_div_iff
% 5.64/5.93 thf(fact_4946_even__mask__div__iff,axiom,
% 5.64/5.93 ! [M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = zero_zero_int )
% 5.64/5.93 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mask_div_iff
% 5.64/5.93 thf(fact_4947_divmod__step__int__def,axiom,
% 5.64/5.93 ( unique5024387138958732305ep_int
% 5.64/5.93 = ( ^ [L2: num] :
% 5.64/5.93 ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_step_int_def
% 5.64/5.93 thf(fact_4948_odd__mod__4__div__2,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.93 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.64/5.93 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % odd_mod_4_div_2
% 5.64/5.93 thf(fact_4949_even__mult__exp__div__exp__iff,axiom,
% 5.64/5.93 ! [A: code_integer,M: nat,N: nat] :
% 5.64/5.93 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.93 = ( ( ord_less_nat @ N @ M )
% 5.64/5.93 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = zero_z3403309356797280102nteger )
% 5.64/5.93 | ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mult_exp_div_exp_iff
% 5.64/5.93 thf(fact_4950_even__mult__exp__div__exp__iff,axiom,
% 5.64/5.93 ! [A: nat,M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ( ord_less_nat @ N @ M )
% 5.64/5.93 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = zero_zero_nat )
% 5.64/5.93 | ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 & ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mult_exp_div_exp_iff
% 5.64/5.93 thf(fact_4951_even__mult__exp__div__exp__iff,axiom,
% 5.64/5.93 ! [A: int,M: nat,N: nat] :
% 5.64/5.93 ( ( 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 ) ) )
% 5.64/5.93 = ( ( ord_less_nat @ N @ M )
% 5.64/5.93 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.64/5.93 = zero_zero_int )
% 5.64/5.93 | ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.93 & ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % even_mult_exp_div_exp_iff
% 5.64/5.93 thf(fact_4952_divmod__step__def,axiom,
% 5.64/5.93 ( unique5026877609467782581ep_nat
% 5.64/5.93 = ( ^ [L2: num] :
% 5.64/5.93 ( produc2626176000494625587at_nat
% 5.64/5.93 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_step_def
% 5.64/5.93 thf(fact_4953_divmod__step__def,axiom,
% 5.64/5.93 ( unique5024387138958732305ep_int
% 5.64/5.93 = ( ^ [L2: num] :
% 5.64/5.93 ( produc4245557441103728435nt_int
% 5.64/5.93 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_step_def
% 5.64/5.93 thf(fact_4954_divmod__step__def,axiom,
% 5.64/5.93 ( unique4921790084139445826nteger
% 5.64/5.93 = ( ^ [L2: num] :
% 5.64/5.93 ( produc6916734918728496179nteger
% 5.64/5.93 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_step_def
% 5.64/5.93 thf(fact_4955_infinite__growing,axiom,
% 5.64/5.93 ! [X8: set_real] :
% 5.64/5.93 ( ( X8 != bot_bot_set_real )
% 5.64/5.93 => ( ! [X4: real] :
% 5.64/5.93 ( ( member_real @ X4 @ X8 )
% 5.64/5.93 => ? [Xa: real] :
% 5.64/5.93 ( ( member_real @ Xa @ X8 )
% 5.64/5.93 & ( ord_less_real @ X4 @ Xa ) ) )
% 5.64/5.93 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % infinite_growing
% 5.64/5.93 thf(fact_4956_infinite__growing,axiom,
% 5.64/5.93 ! [X8: set_rat] :
% 5.64/5.93 ( ( X8 != bot_bot_set_rat )
% 5.64/5.93 => ( ! [X4: rat] :
% 5.64/5.93 ( ( member_rat @ X4 @ X8 )
% 5.64/5.93 => ? [Xa: rat] :
% 5.64/5.93 ( ( member_rat @ Xa @ X8 )
% 5.64/5.93 & ( ord_less_rat @ X4 @ Xa ) ) )
% 5.64/5.93 => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % infinite_growing
% 5.64/5.93 thf(fact_4957_infinite__growing,axiom,
% 5.64/5.93 ! [X8: set_num] :
% 5.64/5.93 ( ( X8 != bot_bot_set_num )
% 5.64/5.93 => ( ! [X4: num] :
% 5.64/5.93 ( ( member_num @ X4 @ X8 )
% 5.64/5.93 => ? [Xa: num] :
% 5.64/5.93 ( ( member_num @ Xa @ X8 )
% 5.64/5.93 & ( ord_less_num @ X4 @ Xa ) ) )
% 5.64/5.93 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % infinite_growing
% 5.64/5.93 thf(fact_4958_infinite__growing,axiom,
% 5.64/5.93 ! [X8: set_nat] :
% 5.64/5.93 ( ( X8 != bot_bot_set_nat )
% 5.64/5.93 => ( ! [X4: nat] :
% 5.64/5.93 ( ( member_nat @ X4 @ X8 )
% 5.64/5.93 => ? [Xa: nat] :
% 5.64/5.93 ( ( member_nat @ Xa @ X8 )
% 5.64/5.93 & ( ord_less_nat @ X4 @ Xa ) ) )
% 5.64/5.93 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % infinite_growing
% 5.64/5.93 thf(fact_4959_infinite__growing,axiom,
% 5.64/5.93 ! [X8: set_int] :
% 5.64/5.93 ( ( X8 != bot_bot_set_int )
% 5.64/5.93 => ( ! [X4: int] :
% 5.64/5.93 ( ( member_int @ X4 @ X8 )
% 5.64/5.93 => ? [Xa: int] :
% 5.64/5.93 ( ( member_int @ Xa @ X8 )
% 5.64/5.93 & ( ord_less_int @ X4 @ Xa ) ) )
% 5.64/5.93 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % infinite_growing
% 5.64/5.93 thf(fact_4960_ex__min__if__finite,axiom,
% 5.64/5.93 ! [S3: set_real] :
% 5.64/5.93 ( ( finite_finite_real @ S3 )
% 5.64/5.93 => ( ( S3 != bot_bot_set_real )
% 5.64/5.93 => ? [X4: real] :
% 5.64/5.93 ( ( member_real @ X4 @ S3 )
% 5.64/5.93 & ~ ? [Xa: real] :
% 5.64/5.93 ( ( member_real @ Xa @ S3 )
% 5.64/5.93 & ( ord_less_real @ Xa @ X4 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % ex_min_if_finite
% 5.64/5.93 thf(fact_4961_ex__min__if__finite,axiom,
% 5.64/5.93 ! [S3: set_rat] :
% 5.64/5.93 ( ( finite_finite_rat @ S3 )
% 5.64/5.93 => ( ( S3 != bot_bot_set_rat )
% 5.64/5.93 => ? [X4: rat] :
% 5.64/5.93 ( ( member_rat @ X4 @ S3 )
% 5.64/5.93 & ~ ? [Xa: rat] :
% 5.64/5.93 ( ( member_rat @ Xa @ S3 )
% 5.64/5.93 & ( ord_less_rat @ Xa @ X4 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % ex_min_if_finite
% 5.64/5.93 thf(fact_4962_ex__min__if__finite,axiom,
% 5.64/5.93 ! [S3: set_num] :
% 5.64/5.93 ( ( finite_finite_num @ S3 )
% 5.64/5.93 => ( ( S3 != bot_bot_set_num )
% 5.64/5.93 => ? [X4: num] :
% 5.64/5.93 ( ( member_num @ X4 @ S3 )
% 5.64/5.93 & ~ ? [Xa: num] :
% 5.64/5.93 ( ( member_num @ Xa @ S3 )
% 5.64/5.93 & ( ord_less_num @ Xa @ X4 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % ex_min_if_finite
% 5.64/5.93 thf(fact_4963_ex__min__if__finite,axiom,
% 5.64/5.93 ! [S3: set_nat] :
% 5.64/5.93 ( ( finite_finite_nat @ S3 )
% 5.64/5.93 => ( ( S3 != bot_bot_set_nat )
% 5.64/5.93 => ? [X4: nat] :
% 5.64/5.93 ( ( member_nat @ X4 @ S3 )
% 5.64/5.93 & ~ ? [Xa: nat] :
% 5.64/5.93 ( ( member_nat @ Xa @ S3 )
% 5.64/5.93 & ( ord_less_nat @ Xa @ X4 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % ex_min_if_finite
% 5.64/5.93 thf(fact_4964_ex__min__if__finite,axiom,
% 5.64/5.93 ! [S3: set_int] :
% 5.64/5.93 ( ( finite_finite_int @ S3 )
% 5.64/5.93 => ( ( S3 != bot_bot_set_int )
% 5.64/5.93 => ? [X4: int] :
% 5.64/5.93 ( ( member_int @ X4 @ S3 )
% 5.64/5.93 & ~ ? [Xa: int] :
% 5.64/5.93 ( ( member_int @ Xa @ S3 )
% 5.64/5.93 & ( ord_less_int @ Xa @ X4 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % ex_min_if_finite
% 5.64/5.93 thf(fact_4965_triangle__def,axiom,
% 5.64/5.93 ( nat_triangle
% 5.64/5.93 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % triangle_def
% 5.64/5.93 thf(fact_4966_vebt__buildup_Oelims,axiom,
% 5.64/5.93 ! [X2: nat,Y4: vEBT_VEBT] :
% 5.64/5.93 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.64/5.93 = Y4 )
% 5.64/5.93 => ( ( ( X2 = zero_zero_nat )
% 5.64/5.93 => ( Y4
% 5.64/5.93 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.64/5.93 => ( ( ( X2
% 5.64/5.93 = ( suc @ zero_zero_nat ) )
% 5.64/5.93 => ( Y4
% 5.64/5.93 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.64/5.93 => ~ ! [Va2: nat] :
% 5.64/5.93 ( ( X2
% 5.64/5.93 = ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.93 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.93 => ( Y4
% 5.64/5.93 = ( 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 ) ) ) ) ) ) )
% 5.64/5.93 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.93 => ( Y4
% 5.64/5.93 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % vebt_buildup.elims
% 5.64/5.93 thf(fact_4967_divmod__nat__if,axiom,
% 5.64/5.93 ( divmod_nat
% 5.64/5.93 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.93 ( if_Pro6206227464963214023at_nat
% 5.64/5.93 @ ( ( N2 = zero_zero_nat )
% 5.64/5.93 | ( ord_less_nat @ M2 @ N2 ) )
% 5.64/5.93 @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 5.64/5.93 @ ( produc2626176000494625587at_nat
% 5.64/5.93 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.64/5.93 @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % divmod_nat_if
% 5.64/5.93 thf(fact_4968_flip__bit__0,axiom,
% 5.64/5.93 ! [A: code_integer] :
% 5.64/5.93 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.64/5.93 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % flip_bit_0
% 5.64/5.93 thf(fact_4969_flip__bit__0,axiom,
% 5.64/5.93 ! [A: int] :
% 5.64/5.93 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.64/5.93 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % flip_bit_0
% 5.64/5.93 thf(fact_4970_flip__bit__0,axiom,
% 5.64/5.93 ! [A: nat] :
% 5.64/5.93 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.64/5.93 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % flip_bit_0
% 5.64/5.93 thf(fact_4971_option_Osize__gen_I2_J,axiom,
% 5.64/5.93 ! [X2: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.64/5.93 ( ( size_o8335143837870341156at_nat @ X2 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.64/5.93 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % option.size_gen(2)
% 5.64/5.93 thf(fact_4972_option_Osize__gen_I2_J,axiom,
% 5.64/5.93 ! [X2: nat > nat,X22: nat] :
% 5.64/5.93 ( ( size_option_nat @ X2 @ ( some_nat @ X22 ) )
% 5.64/5.93 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % option.size_gen(2)
% 5.64/5.93 thf(fact_4973_option_Osize__gen_I2_J,axiom,
% 5.64/5.93 ! [X2: num > nat,X22: num] :
% 5.64/5.93 ( ( size_option_num @ X2 @ ( some_num @ X22 ) )
% 5.64/5.93 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % option.size_gen(2)
% 5.64/5.93 thf(fact_4974_signed__take__bit__Suc,axiom,
% 5.64/5.93 ! [N: nat,A: code_integer] :
% 5.64/5.93 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.64/5.93 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % signed_take_bit_Suc
% 5.64/5.93 thf(fact_4975_signed__take__bit__Suc,axiom,
% 5.64/5.93 ! [N: nat,A: int] :
% 5.64/5.93 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.64/5.93 = ( 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 ) ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % signed_take_bit_Suc
% 5.64/5.93 thf(fact_4976_set__decode__Suc,axiom,
% 5.64/5.93 ! [N: nat,X2: nat] :
% 5.64/5.93 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X2 ) )
% 5.64/5.93 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % set_decode_Suc
% 5.64/5.93 thf(fact_4977_intind,axiom,
% 5.64/5.93 ! [I: nat,N: nat,P: int > $o,X2: int] :
% 5.64/5.93 ( ( ord_less_nat @ I @ N )
% 5.64/5.93 => ( ( P @ X2 )
% 5.64/5.93 => ( P @ ( nth_int @ ( replicate_int @ N @ X2 ) @ I ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % intind
% 5.64/5.93 thf(fact_4978_intind,axiom,
% 5.64/5.93 ! [I: nat,N: nat,P: nat > $o,X2: nat] :
% 5.64/5.93 ( ( ord_less_nat @ I @ N )
% 5.64/5.93 => ( ( P @ X2 )
% 5.64/5.93 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % intind
% 5.64/5.93 thf(fact_4979_intind,axiom,
% 5.64/5.93 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.64/5.93 ( ( ord_less_nat @ I @ N )
% 5.64/5.93 => ( ( P @ X2 )
% 5.64/5.93 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % intind
% 5.64/5.93 thf(fact_4980_case__prodI2,axiom,
% 5.64/5.93 ! [P2: produc6271795597528267376eger_o,C: code_integer > $o > $o] :
% 5.64/5.93 ( ! [A5: code_integer,B5: $o] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.64/5.93 => ( C @ A5 @ B5 ) )
% 5.64/5.93 => ( produc7828578312038201481er_o_o @ C @ P2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI2
% 5.64/5.93 thf(fact_4981_case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_num_num,C: num > num > $o] :
% 5.64/5.93 ( ! [A5: num,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.64/5.93 => ( C @ A5 @ B5 ) )
% 5.64/5.93 => ( produc5703948589228662326_num_o @ C @ P2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI2
% 5.64/5.93 thf(fact_4982_case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_nat_num,C: nat > num > $o] :
% 5.64/5.93 ( ! [A5: nat,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.64/5.93 => ( C @ A5 @ B5 ) )
% 5.64/5.93 => ( produc4927758841916487424_num_o @ C @ P2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI2
% 5.64/5.93 thf(fact_4983_case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_nat_nat,C: nat > nat > $o] :
% 5.64/5.93 ( ! [A5: nat,B5: nat] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_nat_nat @ A5 @ B5 ) )
% 5.64/5.93 => ( C @ A5 @ B5 ) )
% 5.64/5.93 => ( produc6081775807080527818_nat_o @ C @ P2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI2
% 5.64/5.93 thf(fact_4984_case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_int_int,C: int > int > $o] :
% 5.64/5.93 ( ! [A5: int,B5: int] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.64/5.93 => ( C @ A5 @ B5 ) )
% 5.64/5.93 => ( produc4947309494688390418_int_o @ C @ P2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI2
% 5.64/5.93 thf(fact_4985_case__prodI,axiom,
% 5.64/5.93 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.64/5.93 ( ( F @ A @ B )
% 5.64/5.93 => ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI
% 5.64/5.93 thf(fact_4986_case__prodI,axiom,
% 5.64/5.93 ! [F: num > num > $o,A: num,B: num] :
% 5.64/5.93 ( ( F @ A @ B )
% 5.64/5.93 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI
% 5.64/5.93 thf(fact_4987_case__prodI,axiom,
% 5.64/5.93 ! [F: nat > num > $o,A: nat,B: num] :
% 5.64/5.93 ( ( F @ A @ B )
% 5.64/5.93 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI
% 5.64/5.93 thf(fact_4988_case__prodI,axiom,
% 5.64/5.93 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.64/5.93 ( ( F @ A @ B )
% 5.64/5.93 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI
% 5.64/5.93 thf(fact_4989_case__prodI,axiom,
% 5.64/5.93 ! [F: int > int > $o,A: int,B: int] :
% 5.64/5.93 ( ( F @ A @ B )
% 5.64/5.93 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI
% 5.64/5.93 thf(fact_4990_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: produc6271795597528267376eger_o,Z: complex,C: code_integer > $o > set_complex] :
% 5.64/5.93 ( ! [A5: code_integer,B5: $o] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.64/5.93 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4991_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: produc6271795597528267376eger_o,Z: real,C: code_integer > $o > set_real] :
% 5.64/5.93 ( ! [A5: code_integer,B5: $o] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.64/5.93 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4992_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: produc6271795597528267376eger_o,Z: nat,C: code_integer > $o > set_nat] :
% 5.64/5.93 ( ! [A5: code_integer,B5: $o] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.64/5.93 => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4993_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: produc6271795597528267376eger_o,Z: int,C: code_integer > $o > set_int] :
% 5.64/5.93 ( ! [A5: code_integer,B5: $o] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( produc6677183202524767010eger_o @ A5 @ B5 ) )
% 5.64/5.93 => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4994_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 5.64/5.93 ( ! [A5: num,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.64/5.93 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4995_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.64/5.93 ( ! [A5: num,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.64/5.93 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4996_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.64/5.93 ( ! [A5: num,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.64/5.93 => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4997_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.64/5.93 ( ! [A5: num,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_num_num @ A5 @ B5 ) )
% 5.64/5.93 => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4998_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 5.64/5.93 ( ! [A5: nat,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.64/5.93 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_4999_mem__case__prodI2,axiom,
% 5.64/5.93 ! [P2: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.64/5.93 ( ! [A5: nat,B5: num] :
% 5.64/5.93 ( ( P2
% 5.64/5.93 = ( product_Pair_nat_num @ A5 @ B5 ) )
% 5.64/5.93 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.64/5.93 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI2
% 5.64/5.93 thf(fact_5000_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: complex,C: code_integer > $o > set_complex,A: code_integer,B: $o] :
% 5.64/5.93 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5001_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: real,C: code_integer > $o > set_real,A: code_integer,B: $o] :
% 5.64/5.93 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5002_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: nat,C: code_integer > $o > set_nat,A: code_integer,B: $o] :
% 5.64/5.93 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5003_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: int,C: code_integer > $o > set_int,A: code_integer,B: $o] :
% 5.64/5.93 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5004_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 5.64/5.93 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5005_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.64/5.93 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5006_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.64/5.93 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5007_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.64/5.93 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5008_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 5.64/5.93 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5009_mem__case__prodI,axiom,
% 5.64/5.93 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.64/5.93 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.64/5.93 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % mem_case_prodI
% 5.64/5.93 thf(fact_5010_case__prodI2_H,axiom,
% 5.64/5.93 ! [P2: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 5.64/5.93 ( ! [A5: nat,B5: nat] :
% 5.64/5.93 ( ( ( product_Pair_nat_nat @ A5 @ B5 )
% 5.64/5.93 = P2 )
% 5.64/5.93 => ( C @ A5 @ B5 @ X2 ) )
% 5.64/5.93 => ( produc8739625826339149834_nat_o @ C @ P2 @ X2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % case_prodI2'
% 5.64/5.93 thf(fact_5011_of__bool__less__eq__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.64/5.93 = ( P
% 5.64/5.93 => Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_eq_iff
% 5.64/5.93 thf(fact_5012_of__bool__less__eq__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.64/5.93 = ( P
% 5.64/5.93 => Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_eq_iff
% 5.64/5.93 thf(fact_5013_of__bool__less__eq__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.64/5.93 = ( P
% 5.64/5.93 => Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_eq_iff
% 5.64/5.93 thf(fact_5014_of__bool__less__eq__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.64/5.93 = ( P
% 5.64/5.93 => Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_eq_iff
% 5.64/5.93 thf(fact_5015_of__bool__less__eq__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.64/5.93 = ( P
% 5.64/5.93 => Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_eq_iff
% 5.64/5.93 thf(fact_5016_of__bool__less__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.64/5.93 = ( ~ P
% 5.64/5.93 & Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_iff
% 5.64/5.93 thf(fact_5017_of__bool__less__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.64/5.93 = ( ~ P
% 5.64/5.93 & Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_iff
% 5.64/5.93 thf(fact_5018_of__bool__less__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.64/5.93 = ( ~ P
% 5.64/5.93 & Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_iff
% 5.64/5.93 thf(fact_5019_of__bool__less__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.64/5.93 = ( ~ P
% 5.64/5.93 & Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_iff
% 5.64/5.93 thf(fact_5020_of__bool__less__iff,axiom,
% 5.64/5.93 ! [P: $o,Q: $o] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.64/5.93 = ( ~ P
% 5.64/5.93 & Q ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_iff
% 5.64/5.93 thf(fact_5021_of__bool__eq__1__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.64/5.93 = one_one_complex )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq_1_iff
% 5.64/5.93 thf(fact_5022_of__bool__eq__1__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.64/5.93 = one_one_real )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq_1_iff
% 5.64/5.93 thf(fact_5023_of__bool__eq__1__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.64/5.93 = one_one_rat )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq_1_iff
% 5.64/5.93 thf(fact_5024_of__bool__eq__1__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.64/5.93 = one_one_nat )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq_1_iff
% 5.64/5.93 thf(fact_5025_of__bool__eq__1__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.64/5.93 = one_one_int )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq_1_iff
% 5.64/5.93 thf(fact_5026_of__bool__eq__1__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ( zero_n356916108424825756nteger @ P )
% 5.64/5.93 = one_one_Code_integer )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq_1_iff
% 5.64/5.93 thf(fact_5027_of__bool__eq_I2_J,axiom,
% 5.64/5.93 ( ( zero_n1201886186963655149omplex @ $true )
% 5.64/5.93 = one_one_complex ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq(2)
% 5.64/5.93 thf(fact_5028_of__bool__eq_I2_J,axiom,
% 5.64/5.93 ( ( zero_n3304061248610475627l_real @ $true )
% 5.64/5.93 = one_one_real ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq(2)
% 5.64/5.93 thf(fact_5029_of__bool__eq_I2_J,axiom,
% 5.64/5.93 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.64/5.93 = one_one_rat ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq(2)
% 5.64/5.93 thf(fact_5030_of__bool__eq_I2_J,axiom,
% 5.64/5.93 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.64/5.93 = one_one_nat ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq(2)
% 5.64/5.93 thf(fact_5031_of__bool__eq_I2_J,axiom,
% 5.64/5.93 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.64/5.93 = one_one_int ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq(2)
% 5.64/5.93 thf(fact_5032_of__bool__eq_I2_J,axiom,
% 5.64/5.93 ( ( zero_n356916108424825756nteger @ $true )
% 5.64/5.93 = one_one_Code_integer ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_eq(2)
% 5.64/5.93 thf(fact_5033_replicate__eq__replicate,axiom,
% 5.64/5.93 ! [M: nat,X2: vEBT_VEBT,N: nat,Y4: vEBT_VEBT] :
% 5.64/5.93 ( ( ( replicate_VEBT_VEBT @ M @ X2 )
% 5.64/5.93 = ( replicate_VEBT_VEBT @ N @ Y4 ) )
% 5.64/5.93 = ( ( M = N )
% 5.64/5.93 & ( ( M != zero_zero_nat )
% 5.64/5.93 => ( X2 = Y4 ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % replicate_eq_replicate
% 5.64/5.93 thf(fact_5034_length__replicate,axiom,
% 5.64/5.93 ! [N: nat,X2: vEBT_VEBT] :
% 5.64/5.93 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.64/5.93 = N ) ).
% 5.64/5.93
% 5.64/5.93 % length_replicate
% 5.64/5.93 thf(fact_5035_length__replicate,axiom,
% 5.64/5.93 ! [N: nat,X2: $o] :
% 5.64/5.93 ( ( size_size_list_o @ ( replicate_o @ N @ X2 ) )
% 5.64/5.93 = N ) ).
% 5.64/5.93
% 5.64/5.93 % length_replicate
% 5.64/5.93 thf(fact_5036_length__replicate,axiom,
% 5.64/5.93 ! [N: nat,X2: nat] :
% 5.64/5.93 ( ( size_size_list_nat @ ( replicate_nat @ N @ X2 ) )
% 5.64/5.93 = N ) ).
% 5.64/5.93
% 5.64/5.93 % length_replicate
% 5.64/5.93 thf(fact_5037_length__replicate,axiom,
% 5.64/5.93 ! [N: nat,X2: int] :
% 5.64/5.93 ( ( size_size_list_int @ ( replicate_int @ N @ X2 ) )
% 5.64/5.93 = N ) ).
% 5.64/5.93
% 5.64/5.93 % length_replicate
% 5.64/5.93 thf(fact_5038_zero__less__of__bool__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_of_bool_iff
% 5.64/5.93 thf(fact_5039_zero__less__of__bool__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_of_bool_iff
% 5.64/5.93 thf(fact_5040_zero__less__of__bool__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_of_bool_iff
% 5.64/5.93 thf(fact_5041_zero__less__of__bool__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_of_bool_iff
% 5.64/5.93 thf(fact_5042_zero__less__of__bool__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.64/5.93 = P ) ).
% 5.64/5.93
% 5.64/5.93 % zero_less_of_bool_iff
% 5.64/5.93 thf(fact_5043_of__bool__less__one__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.64/5.93 = ~ P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_one_iff
% 5.64/5.93 thf(fact_5044_of__bool__less__one__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.64/5.93 = ~ P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_one_iff
% 5.64/5.93 thf(fact_5045_of__bool__less__one__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.64/5.93 = ~ P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_one_iff
% 5.64/5.93 thf(fact_5046_of__bool__less__one__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.64/5.93 = ~ P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_one_iff
% 5.64/5.93 thf(fact_5047_of__bool__less__one__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.64/5.93 = ~ P ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_less_one_iff
% 5.64/5.93 thf(fact_5048_of__bool__not__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.64/5.93 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_not_iff
% 5.64/5.93 thf(fact_5049_of__bool__not__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.64/5.93 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_not_iff
% 5.64/5.93 thf(fact_5050_of__bool__not__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.64/5.93 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_not_iff
% 5.64/5.93 thf(fact_5051_of__bool__not__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.64/5.93 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_not_iff
% 5.64/5.93 thf(fact_5052_of__bool__not__iff,axiom,
% 5.64/5.93 ! [P: $o] :
% 5.64/5.93 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.64/5.93 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_not_iff
% 5.64/5.93 thf(fact_5053_Suc__0__mod__eq,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.93 = ( zero_n2687167440665602831ol_nat
% 5.64/5.93 @ ( N
% 5.64/5.93 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Suc_0_mod_eq
% 5.64/5.93 thf(fact_5054_signed__take__bit__Suc__1,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.64/5.93 = one_one_int ) ).
% 5.64/5.93
% 5.64/5.93 % signed_take_bit_Suc_1
% 5.64/5.93 thf(fact_5055_signed__take__bit__numeral__of__1,axiom,
% 5.64/5.93 ! [K: num] :
% 5.64/5.93 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.64/5.93 = one_one_int ) ).
% 5.64/5.93
% 5.64/5.93 % signed_take_bit_numeral_of_1
% 5.64/5.93 thf(fact_5056_Ball__set__replicate,axiom,
% 5.64/5.93 ! [N: nat,A: int,P: int > $o] :
% 5.64/5.93 ( ( ! [X: int] :
% 5.64/5.93 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.64/5.93 => ( P @ X ) ) )
% 5.64/5.93 = ( ( P @ A )
% 5.64/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Ball_set_replicate
% 5.64/5.93 thf(fact_5057_Ball__set__replicate,axiom,
% 5.64/5.93 ! [N: nat,A: nat,P: nat > $o] :
% 5.64/5.93 ( ( ! [X: nat] :
% 5.64/5.93 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.64/5.93 => ( P @ X ) ) )
% 5.64/5.93 = ( ( P @ A )
% 5.64/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Ball_set_replicate
% 5.64/5.93 thf(fact_5058_Ball__set__replicate,axiom,
% 5.64/5.93 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.64/5.93 ( ( ! [X: vEBT_VEBT] :
% 5.64/5.93 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.64/5.93 => ( P @ X ) ) )
% 5.64/5.93 = ( ( P @ A )
% 5.64/5.93 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Ball_set_replicate
% 5.64/5.93 thf(fact_5059_Bex__set__replicate,axiom,
% 5.64/5.93 ! [N: nat,A: int,P: int > $o] :
% 5.64/5.93 ( ( ? [X: int] :
% 5.64/5.93 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.64/5.93 & ( P @ X ) ) )
% 5.64/5.93 = ( ( P @ A )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Bex_set_replicate
% 5.64/5.93 thf(fact_5060_Bex__set__replicate,axiom,
% 5.64/5.93 ! [N: nat,A: nat,P: nat > $o] :
% 5.64/5.93 ( ( ? [X: nat] :
% 5.64/5.93 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.64/5.93 & ( P @ X ) ) )
% 5.64/5.93 = ( ( P @ A )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Bex_set_replicate
% 5.64/5.93 thf(fact_5061_Bex__set__replicate,axiom,
% 5.64/5.93 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.64/5.93 ( ( ? [X: vEBT_VEBT] :
% 5.64/5.93 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.64/5.93 & ( P @ X ) ) )
% 5.64/5.93 = ( ( P @ A )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % Bex_set_replicate
% 5.64/5.93 thf(fact_5062_in__set__replicate,axiom,
% 5.64/5.93 ! [X2: product_prod_nat_nat,N: nat,Y4: product_prod_nat_nat] :
% 5.64/5.93 ( ( member8440522571783428010at_nat @ X2 @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N @ Y4 ) ) )
% 5.64/5.93 = ( ( X2 = Y4 )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % in_set_replicate
% 5.64/5.93 thf(fact_5063_in__set__replicate,axiom,
% 5.64/5.93 ! [X2: complex,N: nat,Y4: complex] :
% 5.64/5.93 ( ( member_complex @ X2 @ ( set_complex2 @ ( replicate_complex @ N @ Y4 ) ) )
% 5.64/5.93 = ( ( X2 = Y4 )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % in_set_replicate
% 5.64/5.93 thf(fact_5064_in__set__replicate,axiom,
% 5.64/5.93 ! [X2: real,N: nat,Y4: real] :
% 5.64/5.93 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N @ Y4 ) ) )
% 5.64/5.93 = ( ( X2 = Y4 )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % in_set_replicate
% 5.64/5.93 thf(fact_5065_in__set__replicate,axiom,
% 5.64/5.93 ! [X2: int,N: nat,Y4: int] :
% 5.64/5.93 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N @ Y4 ) ) )
% 5.64/5.93 = ( ( X2 = Y4 )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % in_set_replicate
% 5.64/5.93 thf(fact_5066_in__set__replicate,axiom,
% 5.64/5.93 ! [X2: nat,N: nat,Y4: nat] :
% 5.64/5.93 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N @ Y4 ) ) )
% 5.64/5.93 = ( ( X2 = Y4 )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % in_set_replicate
% 5.64/5.93 thf(fact_5067_in__set__replicate,axiom,
% 5.64/5.93 ! [X2: vEBT_VEBT,N: nat,Y4: vEBT_VEBT] :
% 5.64/5.93 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y4 ) ) )
% 5.64/5.93 = ( ( X2 = Y4 )
% 5.64/5.93 & ( N != zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % in_set_replicate
% 5.64/5.93 thf(fact_5068_nth__replicate,axiom,
% 5.64/5.93 ! [I: nat,N: nat,X2: int] :
% 5.64/5.93 ( ( ord_less_nat @ I @ N )
% 5.64/5.93 => ( ( nth_int @ ( replicate_int @ N @ X2 ) @ I )
% 5.64/5.93 = X2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % nth_replicate
% 5.64/5.93 thf(fact_5069_nth__replicate,axiom,
% 5.64/5.93 ! [I: nat,N: nat,X2: nat] :
% 5.64/5.93 ( ( ord_less_nat @ I @ N )
% 5.64/5.93 => ( ( nth_nat @ ( replicate_nat @ N @ X2 ) @ I )
% 5.64/5.93 = X2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % nth_replicate
% 5.64/5.93 thf(fact_5070_nth__replicate,axiom,
% 5.64/5.93 ! [I: nat,N: nat,X2: vEBT_VEBT] :
% 5.64/5.93 ( ( ord_less_nat @ I @ N )
% 5.64/5.93 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X2 ) @ I )
% 5.64/5.93 = X2 ) ) ).
% 5.64/5.93
% 5.64/5.93 % nth_replicate
% 5.64/5.93 thf(fact_5071_triangle__Suc,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( nat_triangle @ ( suc @ N ) )
% 5.64/5.93 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % triangle_Suc
% 5.64/5.93 thf(fact_5072_signed__take__bit__Suc__bit0,axiom,
% 5.64/5.93 ! [N: nat,K: num] :
% 5.64/5.93 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.64/5.93 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % signed_take_bit_Suc_bit0
% 5.64/5.93 thf(fact_5073_odd__of__bool__self,axiom,
% 5.64/5.93 ! [P2: $o] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.64/5.93 = P2 ) ).
% 5.64/5.93
% 5.64/5.93 % odd_of_bool_self
% 5.64/5.93 thf(fact_5074_odd__of__bool__self,axiom,
% 5.64/5.93 ! [P2: $o] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.64/5.93 = P2 ) ).
% 5.64/5.93
% 5.64/5.93 % odd_of_bool_self
% 5.64/5.93 thf(fact_5075_odd__of__bool__self,axiom,
% 5.64/5.93 ! [P2: $o] :
% 5.64/5.93 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.64/5.93 = P2 ) ).
% 5.64/5.93
% 5.64/5.93 % odd_of_bool_self
% 5.64/5.93 thf(fact_5076_of__bool__half__eq__0,axiom,
% 5.64/5.93 ! [B: $o] :
% 5.64/5.93 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_zero_nat ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_half_eq_0
% 5.64/5.93 thf(fact_5077_of__bool__half__eq__0,axiom,
% 5.64/5.93 ! [B: $o] :
% 5.64/5.93 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_zero_int ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_half_eq_0
% 5.64/5.93 thf(fact_5078_of__bool__half__eq__0,axiom,
% 5.64/5.93 ! [B: $o] :
% 5.64/5.93 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.93 = zero_z3403309356797280102nteger ) ).
% 5.64/5.93
% 5.64/5.93 % of_bool_half_eq_0
% 5.64/5.93 thf(fact_5079_set__decode__0,axiom,
% 5.64/5.93 ! [X2: nat] :
% 5.64/5.93 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.64/5.93 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % set_decode_0
% 5.64/5.93 thf(fact_5080_bits__1__div__exp,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.93 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bits_1_div_exp
% 5.64/5.93 thf(fact_5081_bits__1__div__exp,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.93 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.64/5.93
% 5.64/5.93 % bits_1_div_exp
% 5.64/5.93 thf(fact_5082_bits__1__div__exp,axiom,
% 5.64/5.93 ! [N: nat] :
% 5.64/5.93 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % bits_1_div_exp
% 5.64/5.94 thf(fact_5083_one__div__2__pow__eq,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_div_2_pow_eq
% 5.64/5.94 thf(fact_5084_one__div__2__pow__eq,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_div_2_pow_eq
% 5.64/5.94 thf(fact_5085_one__div__2__pow__eq,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_div_2_pow_eq
% 5.64/5.94 thf(fact_5086_signed__take__bit__Suc__bit1,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.64/5.94 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_Suc_bit1
% 5.64/5.94 thf(fact_5087_one__mod__2__pow__eq,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_mod_2_pow_eq
% 5.64/5.94 thf(fact_5088_one__mod__2__pow__eq,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_mod_2_pow_eq
% 5.64/5.94 thf(fact_5089_one__mod__2__pow__eq,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_mod_2_pow_eq
% 5.64/5.94 thf(fact_5090_dvd__antisym,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ M @ N )
% 5.64/5.94 => ( ( dvd_dvd_nat @ N @ M )
% 5.64/5.94 => ( M = N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_antisym
% 5.64/5.94 thf(fact_5091_of__bool__conj,axiom,
% 5.64/5.94 ! [P: $o,Q: $o] :
% 5.64/5.94 ( ( zero_n3304061248610475627l_real
% 5.64/5.94 @ ( P
% 5.64/5.94 & Q ) )
% 5.64/5.94 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_conj
% 5.64/5.94 thf(fact_5092_of__bool__conj,axiom,
% 5.64/5.94 ! [P: $o,Q: $o] :
% 5.64/5.94 ( ( zero_n2052037380579107095ol_rat
% 5.64/5.94 @ ( P
% 5.64/5.94 & Q ) )
% 5.64/5.94 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_conj
% 5.64/5.94 thf(fact_5093_of__bool__conj,axiom,
% 5.64/5.94 ! [P: $o,Q: $o] :
% 5.64/5.94 ( ( zero_n2687167440665602831ol_nat
% 5.64/5.94 @ ( P
% 5.64/5.94 & Q ) )
% 5.64/5.94 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_conj
% 5.64/5.94 thf(fact_5094_of__bool__conj,axiom,
% 5.64/5.94 ! [P: $o,Q: $o] :
% 5.64/5.94 ( ( zero_n2684676970156552555ol_int
% 5.64/5.94 @ ( P
% 5.64/5.94 & Q ) )
% 5.64/5.94 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_conj
% 5.64/5.94 thf(fact_5095_of__bool__conj,axiom,
% 5.64/5.94 ! [P: $o,Q: $o] :
% 5.64/5.94 ( ( zero_n356916108424825756nteger
% 5.64/5.94 @ ( P
% 5.64/5.94 & Q ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_conj
% 5.64/5.94 thf(fact_5096_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: complex,C: code_integer > $o > set_complex,P2: produc6271795597528267376eger_o] :
% 5.64/5.94 ( ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: code_integer,Y3: $o] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( produc6677183202524767010eger_o @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_complex @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5097_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: real,C: code_integer > $o > set_real,P2: produc6271795597528267376eger_o] :
% 5.64/5.94 ( ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: code_integer,Y3: $o] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( produc6677183202524767010eger_o @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5098_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: nat,C: code_integer > $o > set_nat,P2: produc6271795597528267376eger_o] :
% 5.64/5.94 ( ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: code_integer,Y3: $o] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( produc6677183202524767010eger_o @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_nat @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5099_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: int,C: code_integer > $o > set_int,P2: produc6271795597528267376eger_o] :
% 5.64/5.94 ( ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: code_integer,Y3: $o] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( produc6677183202524767010eger_o @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_int @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5100_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: complex,C: num > num > set_complex,P2: product_prod_num_num] :
% 5.64/5.94 ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: num,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_complex @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5101_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: real,C: num > num > set_real,P2: product_prod_num_num] :
% 5.64/5.94 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: num,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5102_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: nat,C: num > num > set_nat,P2: product_prod_num_num] :
% 5.64/5.94 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: num,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_nat @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5103_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: int,C: num > num > set_int,P2: product_prod_num_num] :
% 5.64/5.94 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: num,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_int @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5104_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: complex,C: nat > num > set_complex,P2: product_prod_nat_num] :
% 5.64/5.94 ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: nat,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_complex @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5105_mem__case__prodE,axiom,
% 5.64/5.94 ! [Z: real,C: nat > num > set_real,P2: product_prod_nat_num] :
% 5.64/5.94 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) )
% 5.64/5.94 => ~ ! [X4: nat,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( member_real @ Z @ ( C @ X4 @ Y3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mem_case_prodE
% 5.64/5.94 thf(fact_5106_signed__take__bit__mult,axiom,
% 5.64/5.94 ! [N: nat,K: int,L: int] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 5.64/5.94 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_mult
% 5.64/5.94 thf(fact_5107_case__prodE,axiom,
% 5.64/5.94 ! [C: code_integer > $o > $o,P2: produc6271795597528267376eger_o] :
% 5.64/5.94 ( ( produc7828578312038201481er_o_o @ C @ P2 )
% 5.64/5.94 => ~ ! [X4: code_integer,Y3: $o] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( produc6677183202524767010eger_o @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodE
% 5.64/5.94 thf(fact_5108_case__prodE,axiom,
% 5.64/5.94 ! [C: num > num > $o,P2: product_prod_num_num] :
% 5.64/5.94 ( ( produc5703948589228662326_num_o @ C @ P2 )
% 5.64/5.94 => ~ ! [X4: num,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_num_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodE
% 5.64/5.94 thf(fact_5109_case__prodE,axiom,
% 5.64/5.94 ! [C: nat > num > $o,P2: product_prod_nat_num] :
% 5.64/5.94 ( ( produc4927758841916487424_num_o @ C @ P2 )
% 5.64/5.94 => ~ ! [X4: nat,Y3: num] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_nat_num @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodE
% 5.64/5.94 thf(fact_5110_case__prodE,axiom,
% 5.64/5.94 ! [C: nat > nat > $o,P2: product_prod_nat_nat] :
% 5.64/5.94 ( ( produc6081775807080527818_nat_o @ C @ P2 )
% 5.64/5.94 => ~ ! [X4: nat,Y3: nat] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodE
% 5.64/5.94 thf(fact_5111_case__prodE,axiom,
% 5.64/5.94 ! [C: int > int > $o,P2: product_prod_int_int] :
% 5.64/5.94 ( ( produc4947309494688390418_int_o @ C @ P2 )
% 5.64/5.94 => ~ ! [X4: int,Y3: int] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_int_int @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( C @ X4 @ Y3 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodE
% 5.64/5.94 thf(fact_5112_case__prodD,axiom,
% 5.64/5.94 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.64/5.94 ( ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) )
% 5.64/5.94 => ( F @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodD
% 5.64/5.94 thf(fact_5113_case__prodD,axiom,
% 5.64/5.94 ! [F: num > num > $o,A: num,B: num] :
% 5.64/5.94 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.64/5.94 => ( F @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodD
% 5.64/5.94 thf(fact_5114_case__prodD,axiom,
% 5.64/5.94 ! [F: nat > num > $o,A: nat,B: num] :
% 5.64/5.94 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.64/5.94 => ( F @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodD
% 5.64/5.94 thf(fact_5115_case__prodD,axiom,
% 5.64/5.94 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.64/5.94 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.64/5.94 => ( F @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodD
% 5.64/5.94 thf(fact_5116_case__prodD,axiom,
% 5.64/5.94 ! [F: int > int > $o,A: int,B: int] :
% 5.64/5.94 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.64/5.94 => ( F @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodD
% 5.64/5.94 thf(fact_5117_case__prodE_H,axiom,
% 5.64/5.94 ! [C: nat > nat > product_prod_nat_nat > $o,P2: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.64/5.94 ( ( produc8739625826339149834_nat_o @ C @ P2 @ Z )
% 5.64/5.94 => ~ ! [X4: nat,Y3: nat] :
% 5.64/5.94 ( ( P2
% 5.64/5.94 = ( product_Pair_nat_nat @ X4 @ Y3 ) )
% 5.64/5.94 => ~ ( C @ X4 @ Y3 @ Z ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodE'
% 5.64/5.94 thf(fact_5118_case__prodD_H,axiom,
% 5.64/5.94 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.64/5.94 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.64/5.94 => ( R @ A @ B @ C ) ) ).
% 5.64/5.94
% 5.64/5.94 % case_prodD'
% 5.64/5.94 thf(fact_5119_zero__less__eq__of__bool,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_less_eq_of_bool
% 5.64/5.94 thf(fact_5120_zero__less__eq__of__bool,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_less_eq_of_bool
% 5.64/5.94 thf(fact_5121_zero__less__eq__of__bool,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_less_eq_of_bool
% 5.64/5.94 thf(fact_5122_zero__less__eq__of__bool,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_less_eq_of_bool
% 5.64/5.94 thf(fact_5123_zero__less__eq__of__bool,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_less_eq_of_bool
% 5.64/5.94 thf(fact_5124_of__bool__less__eq__one,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_less_eq_one
% 5.64/5.94 thf(fact_5125_of__bool__less__eq__one,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_less_eq_one
% 5.64/5.94 thf(fact_5126_of__bool__less__eq__one,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_less_eq_one
% 5.64/5.94 thf(fact_5127_of__bool__less__eq__one,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_less_eq_one
% 5.64/5.94 thf(fact_5128_of__bool__less__eq__one,axiom,
% 5.64/5.94 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_less_eq_one
% 5.64/5.94 thf(fact_5129_of__bool__def,axiom,
% 5.64/5.94 ( zero_n1201886186963655149omplex
% 5.64/5.94 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_def
% 5.64/5.94 thf(fact_5130_of__bool__def,axiom,
% 5.64/5.94 ( zero_n3304061248610475627l_real
% 5.64/5.94 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_def
% 5.64/5.94 thf(fact_5131_of__bool__def,axiom,
% 5.64/5.94 ( zero_n2052037380579107095ol_rat
% 5.64/5.94 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_def
% 5.64/5.94 thf(fact_5132_of__bool__def,axiom,
% 5.64/5.94 ( zero_n2687167440665602831ol_nat
% 5.64/5.94 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_def
% 5.64/5.94 thf(fact_5133_of__bool__def,axiom,
% 5.64/5.94 ( zero_n2684676970156552555ol_int
% 5.64/5.94 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_def
% 5.64/5.94 thf(fact_5134_of__bool__def,axiom,
% 5.64/5.94 ( zero_n356916108424825756nteger
% 5.64/5.94 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_def
% 5.64/5.94 thf(fact_5135_split__of__bool,axiom,
% 5.64/5.94 ! [P: complex > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.64/5.94 = ( ( P2
% 5.64/5.94 => ( P @ one_one_complex ) )
% 5.64/5.94 & ( ~ P2
% 5.64/5.94 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool
% 5.64/5.94 thf(fact_5136_split__of__bool,axiom,
% 5.64/5.94 ! [P: real > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.64/5.94 = ( ( P2
% 5.64/5.94 => ( P @ one_one_real ) )
% 5.64/5.94 & ( ~ P2
% 5.64/5.94 => ( P @ zero_zero_real ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool
% 5.64/5.94 thf(fact_5137_split__of__bool,axiom,
% 5.64/5.94 ! [P: rat > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.64/5.94 = ( ( P2
% 5.64/5.94 => ( P @ one_one_rat ) )
% 5.64/5.94 & ( ~ P2
% 5.64/5.94 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool
% 5.64/5.94 thf(fact_5138_split__of__bool,axiom,
% 5.64/5.94 ! [P: nat > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.64/5.94 = ( ( P2
% 5.64/5.94 => ( P @ one_one_nat ) )
% 5.64/5.94 & ( ~ P2
% 5.64/5.94 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool
% 5.64/5.94 thf(fact_5139_split__of__bool,axiom,
% 5.64/5.94 ! [P: int > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.64/5.94 = ( ( P2
% 5.64/5.94 => ( P @ one_one_int ) )
% 5.64/5.94 & ( ~ P2
% 5.64/5.94 => ( P @ zero_zero_int ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool
% 5.64/5.94 thf(fact_5140_split__of__bool,axiom,
% 5.64/5.94 ! [P: code_integer > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.64/5.94 = ( ( P2
% 5.64/5.94 => ( P @ one_one_Code_integer ) )
% 5.64/5.94 & ( ~ P2
% 5.64/5.94 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool
% 5.64/5.94 thf(fact_5141_split__of__bool__asm,axiom,
% 5.64/5.94 ! [P: complex > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.64/5.94 = ( ~ ( ( P2
% 5.64/5.94 & ~ ( P @ one_one_complex ) )
% 5.64/5.94 | ( ~ P2
% 5.64/5.94 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool_asm
% 5.64/5.94 thf(fact_5142_split__of__bool__asm,axiom,
% 5.64/5.94 ! [P: real > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.64/5.94 = ( ~ ( ( P2
% 5.64/5.94 & ~ ( P @ one_one_real ) )
% 5.64/5.94 | ( ~ P2
% 5.64/5.94 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool_asm
% 5.64/5.94 thf(fact_5143_split__of__bool__asm,axiom,
% 5.64/5.94 ! [P: rat > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.64/5.94 = ( ~ ( ( P2
% 5.64/5.94 & ~ ( P @ one_one_rat ) )
% 5.64/5.94 | ( ~ P2
% 5.64/5.94 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool_asm
% 5.64/5.94 thf(fact_5144_split__of__bool__asm,axiom,
% 5.64/5.94 ! [P: nat > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.64/5.94 = ( ~ ( ( P2
% 5.64/5.94 & ~ ( P @ one_one_nat ) )
% 5.64/5.94 | ( ~ P2
% 5.64/5.94 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool_asm
% 5.64/5.94 thf(fact_5145_split__of__bool__asm,axiom,
% 5.64/5.94 ! [P: int > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.64/5.94 = ( ~ ( ( P2
% 5.64/5.94 & ~ ( P @ one_one_int ) )
% 5.64/5.94 | ( ~ P2
% 5.64/5.94 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool_asm
% 5.64/5.94 thf(fact_5146_split__of__bool__asm,axiom,
% 5.64/5.94 ! [P: code_integer > $o,P2: $o] :
% 5.64/5.94 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.64/5.94 = ( ~ ( ( P2
% 5.64/5.94 & ~ ( P @ one_one_Code_integer ) )
% 5.64/5.94 | ( ~ P2
% 5.64/5.94 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_of_bool_asm
% 5.64/5.94 thf(fact_5147_replicate__length__same,axiom,
% 5.64/5.94 ! [Xs2: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.64/5.94 ( ! [X4: vEBT_VEBT] :
% 5.64/5.94 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.94 => ( X4 = X2 ) )
% 5.64/5.94 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X2 )
% 5.64/5.94 = Xs2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_length_same
% 5.64/5.94 thf(fact_5148_replicate__length__same,axiom,
% 5.64/5.94 ! [Xs2: list_o,X2: $o] :
% 5.64/5.94 ( ! [X4: $o] :
% 5.64/5.94 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 5.64/5.94 => ( X4 = X2 ) )
% 5.64/5.94 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X2 )
% 5.64/5.94 = Xs2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_length_same
% 5.64/5.94 thf(fact_5149_replicate__length__same,axiom,
% 5.64/5.94 ! [Xs2: list_nat,X2: nat] :
% 5.64/5.94 ( ! [X4: nat] :
% 5.64/5.94 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.94 => ( X4 = X2 ) )
% 5.64/5.94 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X2 )
% 5.64/5.94 = Xs2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_length_same
% 5.64/5.94 thf(fact_5150_replicate__length__same,axiom,
% 5.64/5.94 ! [Xs2: list_int,X2: int] :
% 5.64/5.94 ( ! [X4: int] :
% 5.64/5.94 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 5.64/5.94 => ( X4 = X2 ) )
% 5.64/5.94 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X2 )
% 5.64/5.94 = Xs2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_length_same
% 5.64/5.94 thf(fact_5151_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X2: product_prod_nat_nat] :
% 5.64/5.94 ( ( ( size_s5460976970255530739at_nat @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: product_prod_nat_nat] :
% 5.64/5.94 ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replic4235873036481779905at_nat @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5152_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_complex,N: nat,X2: complex] :
% 5.64/5.94 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: complex] :
% 5.64/5.94 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replicate_complex @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5153_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_real,N: nat,X2: real] :
% 5.64/5.94 ( ( ( size_size_list_real @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: real] :
% 5.64/5.94 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replicate_real @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5154_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_VEBT_VEBT,N: nat,X2: vEBT_VEBT] :
% 5.64/5.94 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: vEBT_VEBT] :
% 5.64/5.94 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replicate_VEBT_VEBT @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5155_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_o,N: nat,X2: $o] :
% 5.64/5.94 ( ( ( size_size_list_o @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: $o] :
% 5.64/5.94 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replicate_o @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5156_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_nat,N: nat,X2: nat] :
% 5.64/5.94 ( ( ( size_size_list_nat @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: nat] :
% 5.64/5.94 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replicate_nat @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5157_replicate__eqI,axiom,
% 5.64/5.94 ! [Xs2: list_int,N: nat,X2: int] :
% 5.64/5.94 ( ( ( size_size_list_int @ Xs2 )
% 5.64/5.94 = N )
% 5.64/5.94 => ( ! [Y3: int] :
% 5.64/5.94 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 5.64/5.94 => ( Y3 = X2 ) )
% 5.64/5.94 => ( Xs2
% 5.64/5.94 = ( replicate_int @ N @ X2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % replicate_eqI
% 5.64/5.94 thf(fact_5158_subset__decode__imp__le,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.64/5.94 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % subset_decode_imp_le
% 5.64/5.94 thf(fact_5159_of__bool__odd__eq__mod__2,axiom,
% 5.64/5.94 ! [A: nat] :
% 5.64/5.94 ( ( zero_n2687167440665602831ol_nat
% 5.64/5.94 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.94 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_odd_eq_mod_2
% 5.64/5.94 thf(fact_5160_of__bool__odd__eq__mod__2,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( zero_n2684676970156552555ol_int
% 5.64/5.94 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.94 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_odd_eq_mod_2
% 5.64/5.94 thf(fact_5161_of__bool__odd__eq__mod__2,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( zero_n356916108424825756nteger
% 5.64/5.94 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.64/5.94 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % of_bool_odd_eq_mod_2
% 5.64/5.94 thf(fact_5162_signed__take__bit__int__less__exp,axiom,
% 5.64/5.94 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_int_less_exp
% 5.64/5.94 thf(fact_5163_even__signed__take__bit__iff,axiom,
% 5.64/5.94 ! [M: nat,A: code_integer] :
% 5.64/5.94 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.64/5.94 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % even_signed_take_bit_iff
% 5.64/5.94 thf(fact_5164_even__signed__take__bit__iff,axiom,
% 5.64/5.94 ! [M: nat,A: int] :
% 5.64/5.94 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.64/5.94 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % even_signed_take_bit_iff
% 5.64/5.94 thf(fact_5165_bits__induct,axiom,
% 5.64/5.94 ! [P: nat > $o,A: nat] :
% 5.64/5.94 ( ! [A5: nat] :
% 5.64/5.94 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = A5 )
% 5.64/5.94 => ( P @ A5 ) )
% 5.64/5.94 => ( ! [A5: nat,B5: $o] :
% 5.64/5.94 ( ( P @ A5 )
% 5.64/5.94 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = A5 )
% 5.64/5.94 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.64/5.94 => ( P @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % bits_induct
% 5.64/5.94 thf(fact_5166_bits__induct,axiom,
% 5.64/5.94 ! [P: int > $o,A: int] :
% 5.64/5.94 ( ! [A5: int] :
% 5.64/5.94 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.94 = A5 )
% 5.64/5.94 => ( P @ A5 ) )
% 5.64/5.94 => ( ! [A5: int,B5: $o] :
% 5.64/5.94 ( ( P @ A5 )
% 5.64/5.94 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.94 = A5 )
% 5.64/5.94 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.64/5.94 => ( P @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % bits_induct
% 5.64/5.94 thf(fact_5167_bits__induct,axiom,
% 5.64/5.94 ! [P: code_integer > $o,A: code_integer] :
% 5.64/5.94 ( ! [A5: code_integer] :
% 5.64/5.94 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.94 = A5 )
% 5.64/5.94 => ( P @ A5 ) )
% 5.64/5.94 => ( ! [A5: code_integer,B5: $o] :
% 5.64/5.94 ( ( P @ A5 )
% 5.64/5.94 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.94 = A5 )
% 5.64/5.94 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.64/5.94 => ( P @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % bits_induct
% 5.64/5.94 thf(fact_5168_signed__take__bit__int__less__self__iff,axiom,
% 5.64/5.94 ! [N: nat,K: int] :
% 5.64/5.94 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.64/5.94 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_int_less_self_iff
% 5.64/5.94 thf(fact_5169_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.64/5.94 ! [K: int,N: nat] :
% 5.64/5.94 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.64/5.94 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_int_greater_eq_self_iff
% 5.64/5.94 thf(fact_5170_exp__mod__exp,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % exp_mod_exp
% 5.64/5.94 thf(fact_5171_exp__mod__exp,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % exp_mod_exp
% 5.64/5.94 thf(fact_5172_exp__mod__exp,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % exp_mod_exp
% 5.64/5.94 thf(fact_5173_divmod__nat__def,axiom,
% 5.64/5.94 ( divmod_nat
% 5.64/5.94 = ( ^ [M2: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M2 @ N2 ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divmod_nat_def
% 5.64/5.94 thf(fact_5174_signed__take__bit__int__less__eq,axiom,
% 5.64/5.94 ! [N: nat,K: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.64/5.94 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_int_less_eq
% 5.64/5.94 thf(fact_5175_option_Osize__gen_I1_J,axiom,
% 5.64/5.94 ! [X2: nat > nat] :
% 5.64/5.94 ( ( size_option_nat @ X2 @ none_nat )
% 5.64/5.94 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.94
% 5.64/5.94 % option.size_gen(1)
% 5.64/5.94 thf(fact_5176_option_Osize__gen_I1_J,axiom,
% 5.64/5.94 ! [X2: product_prod_nat_nat > nat] :
% 5.64/5.94 ( ( size_o8335143837870341156at_nat @ X2 @ none_P5556105721700978146at_nat )
% 5.64/5.94 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.94
% 5.64/5.94 % option.size_gen(1)
% 5.64/5.94 thf(fact_5177_option_Osize__gen_I1_J,axiom,
% 5.64/5.94 ! [X2: num > nat] :
% 5.64/5.94 ( ( size_option_num @ X2 @ none_num )
% 5.64/5.94 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.94
% 5.64/5.94 % option.size_gen(1)
% 5.64/5.94 thf(fact_5178_set__decode__def,axiom,
% 5.64/5.94 ( nat_set_decode
% 5.64/5.94 = ( ^ [X: nat] :
% 5.64/5.94 ( collect_nat
% 5.64/5.94 @ ^ [N2: nat] :
% 5.64/5.94 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % set_decode_def
% 5.64/5.94 thf(fact_5179_exp__div__exp__eq,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( times_times_nat
% 5.64/5.94 @ ( zero_n2687167440665602831ol_nat
% 5.64/5.94 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.64/5.94 != zero_zero_nat )
% 5.64/5.94 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.64/5.94 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % exp_div_exp_eq
% 5.64/5.94 thf(fact_5180_exp__div__exp__eq,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( times_times_int
% 5.64/5.94 @ ( zero_n2684676970156552555ol_int
% 5.64/5.94 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.64/5.94 != zero_zero_int )
% 5.64/5.94 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.64/5.94 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % exp_div_exp_eq
% 5.64/5.94 thf(fact_5181_exp__div__exp__eq,axiom,
% 5.64/5.94 ! [M: nat,N: nat] :
% 5.64/5.94 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( times_3573771949741848930nteger
% 5.64/5.94 @ ( zero_n356916108424825756nteger
% 5.64/5.94 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.64/5.94 != zero_z3403309356797280102nteger )
% 5.64/5.94 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.64/5.94 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % exp_div_exp_eq
% 5.64/5.94 thf(fact_5182_vebt__buildup_Osimps_I3_J,axiom,
% 5.64/5.94 ! [Va: nat] :
% 5.64/5.94 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.94 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.94 = ( 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 ) ) ) ) ) ) )
% 5.64/5.94 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.94 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.64/5.94 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % vebt_buildup.simps(3)
% 5.64/5.94 thf(fact_5183_signed__take__bit__Suc__minus__bit1,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.64/5.94 = ( 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 ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_Suc_minus_bit1
% 5.64/5.94 thf(fact_5184_signed__take__bit__rec,axiom,
% 5.64/5.94 ( bit_ri6519982836138164636nteger
% 5.64/5.94 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_rec
% 5.64/5.94 thf(fact_5185_signed__take__bit__rec,axiom,
% 5.64/5.94 ( bit_ri631733984087533419it_int
% 5.64/5.94 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_rec
% 5.64/5.94 thf(fact_5186_signed__take__bit__numeral__bit1,axiom,
% 5.64/5.94 ! [L: num,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.64/5.94 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_numeral_bit1
% 5.64/5.94 thf(fact_5187_vebt__buildup_Opelims,axiom,
% 5.64/5.94 ! [X2: nat,Y4: vEBT_VEBT] :
% 5.64/5.94 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.64/5.94 = Y4 )
% 5.64/5.94 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.64/5.94 => ( ( ( X2 = zero_zero_nat )
% 5.64/5.94 => ( ( Y4
% 5.64/5.94 = ( vEBT_Leaf @ $false @ $false ) )
% 5.64/5.94 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.64/5.94 => ( ( ( X2
% 5.64/5.94 = ( suc @ zero_zero_nat ) )
% 5.64/5.94 => ( ( Y4
% 5.64/5.94 = ( vEBT_Leaf @ $false @ $false ) )
% 5.64/5.94 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.64/5.94 => ~ ! [Va2: nat] :
% 5.64/5.94 ( ( X2
% 5.64/5.94 = ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.94 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.94 => ( Y4
% 5.64/5.94 = ( 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 ) ) ) ) ) ) )
% 5.64/5.94 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.64/5.94 => ( Y4
% 5.64/5.94 = ( 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 ) ) ) ) ) ) ) ) )
% 5.64/5.94 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % vebt_buildup.pelims
% 5.64/5.94 thf(fact_5188_int__ge__less__than2__def,axiom,
% 5.64/5.94 ( int_ge_less_than2
% 5.64/5.94 = ( ^ [D2: int] :
% 5.64/5.94 ( collec213857154873943460nt_int
% 5.64/5.94 @ ( produc4947309494688390418_int_o
% 5.64/5.94 @ ^ [Z6: int,Z4: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ D2 @ Z4 )
% 5.64/5.94 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % int_ge_less_than2_def
% 5.64/5.94 thf(fact_5189_int__ge__less__than__def,axiom,
% 5.64/5.94 ( int_ge_less_than
% 5.64/5.94 = ( ^ [D2: int] :
% 5.64/5.94 ( collec213857154873943460nt_int
% 5.64/5.94 @ ( produc4947309494688390418_int_o
% 5.64/5.94 @ ^ [Z6: int,Z4: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ D2 @ Z6 )
% 5.64/5.94 & ( ord_less_int @ Z6 @ Z4 ) ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % int_ge_less_than_def
% 5.64/5.94 thf(fact_5190_diff__shunt__var,axiom,
% 5.64/5.94 ! [X2: set_int,Y4: set_int] :
% 5.64/5.94 ( ( ( minus_minus_set_int @ X2 @ Y4 )
% 5.64/5.94 = bot_bot_set_int )
% 5.64/5.94 = ( ord_less_eq_set_int @ X2 @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_shunt_var
% 5.64/5.94 thf(fact_5191_diff__shunt__var,axiom,
% 5.64/5.94 ! [X2: set_real,Y4: set_real] :
% 5.64/5.94 ( ( ( minus_minus_set_real @ X2 @ Y4 )
% 5.64/5.94 = bot_bot_set_real )
% 5.64/5.94 = ( ord_less_eq_set_real @ X2 @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_shunt_var
% 5.64/5.94 thf(fact_5192_diff__shunt__var,axiom,
% 5.64/5.94 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.94 ( ( ( minus_minus_set_nat @ X2 @ Y4 )
% 5.64/5.94 = bot_bot_set_nat )
% 5.64/5.94 = ( ord_less_eq_set_nat @ X2 @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_shunt_var
% 5.64/5.94 thf(fact_5193_verit__minus__simplify_I4_J,axiom,
% 5.64/5.94 ! [B: int] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(4)
% 5.64/5.94 thf(fact_5194_verit__minus__simplify_I4_J,axiom,
% 5.64/5.94 ! [B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(4)
% 5.64/5.94 thf(fact_5195_verit__minus__simplify_I4_J,axiom,
% 5.64/5.94 ! [B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(4)
% 5.64/5.94 thf(fact_5196_verit__minus__simplify_I4_J,axiom,
% 5.64/5.94 ! [B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(4)
% 5.64/5.94 thf(fact_5197_verit__minus__simplify_I4_J,axiom,
% 5.64/5.94 ! [B: code_integer] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(4)
% 5.64/5.94 thf(fact_5198_add_Oinverse__inverse,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_inverse
% 5.64/5.94 thf(fact_5199_add_Oinverse__inverse,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_inverse
% 5.64/5.94 thf(fact_5200_add_Oinverse__inverse,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_inverse
% 5.64/5.94 thf(fact_5201_add_Oinverse__inverse,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_inverse
% 5.64/5.94 thf(fact_5202_add_Oinverse__inverse,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_inverse
% 5.64/5.94 thf(fact_5203_neg__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ A )
% 5.64/5.94 = ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( A = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_iff_equal
% 5.64/5.94 thf(fact_5204_neg__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ A )
% 5.64/5.94 = ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( A = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_iff_equal
% 5.64/5.94 thf(fact_5205_neg__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ A )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( A = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_iff_equal
% 5.64/5.94 thf(fact_5206_neg__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( A = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_iff_equal
% 5.64/5.94 thf(fact_5207_neg__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( A = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_iff_equal
% 5.64/5.94 thf(fact_5208_split__part,axiom,
% 5.64/5.94 ! [P: $o,Q: int > int > $o] :
% 5.64/5.94 ( ( produc4947309494688390418_int_o
% 5.64/5.94 @ ^ [A3: int,B3: int] :
% 5.64/5.94 ( P
% 5.64/5.94 & ( Q @ A3 @ B3 ) ) )
% 5.64/5.94 = ( ^ [Ab: product_prod_int_int] :
% 5.64/5.94 ( P
% 5.64/5.94 & ( produc4947309494688390418_int_o @ Q @ Ab ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % split_part
% 5.64/5.94 thf(fact_5209_compl__le__compl__iff,axiom,
% 5.64/5.94 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.94 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( uminus5710092332889474511et_nat @ Y4 ) )
% 5.64/5.94 = ( ord_less_eq_set_nat @ Y4 @ X2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % compl_le_compl_iff
% 5.64/5.94 thf(fact_5210_neg__le__iff__le,axiom,
% 5.64/5.94 ! [B: code_integer,A: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_iff_le
% 5.64/5.94 thf(fact_5211_neg__le__iff__le,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_iff_le
% 5.64/5.94 thf(fact_5212_neg__le__iff__le,axiom,
% 5.64/5.94 ! [B: int,A: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_iff_le
% 5.64/5.94 thf(fact_5213_neg__le__iff__le,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_iff_le
% 5.64/5.94 thf(fact_5214_add_Oinverse__neutral,axiom,
% 5.64/5.94 ( ( uminus_uminus_int @ zero_zero_int )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_neutral
% 5.64/5.94 thf(fact_5215_add_Oinverse__neutral,axiom,
% 5.64/5.94 ( ( uminus_uminus_real @ zero_zero_real )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_neutral
% 5.64/5.94 thf(fact_5216_add_Oinverse__neutral,axiom,
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_neutral
% 5.64/5.94 thf(fact_5217_add_Oinverse__neutral,axiom,
% 5.64/5.94 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_neutral
% 5.64/5.94 thf(fact_5218_add_Oinverse__neutral,axiom,
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_neutral
% 5.64/5.94 thf(fact_5219_neg__0__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( zero_zero_int
% 5.64/5.94 = ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( zero_zero_int = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_equal_iff_equal
% 5.64/5.94 thf(fact_5220_neg__0__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( zero_zero_real
% 5.64/5.94 = ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( zero_zero_real = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_equal_iff_equal
% 5.64/5.94 thf(fact_5221_neg__0__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( zero_zero_complex
% 5.64/5.94 = ( uminus1482373934393186551omplex @ A ) )
% 5.64/5.94 = ( zero_zero_complex = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_equal_iff_equal
% 5.64/5.94 thf(fact_5222_neg__0__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( zero_zero_rat
% 5.64/5.94 = ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( zero_zero_rat = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_equal_iff_equal
% 5.64/5.94 thf(fact_5223_neg__0__equal__iff__equal,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( zero_z3403309356797280102nteger
% 5.64/5.94 = ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_equal_iff_equal
% 5.64/5.94 thf(fact_5224_neg__equal__0__iff__equal,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ A )
% 5.64/5.94 = zero_zero_int )
% 5.64/5.94 = ( A = zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_0_iff_equal
% 5.64/5.94 thf(fact_5225_neg__equal__0__iff__equal,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ A )
% 5.64/5.94 = zero_zero_real )
% 5.64/5.94 = ( A = zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_0_iff_equal
% 5.64/5.94 thf(fact_5226_neg__equal__0__iff__equal,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ A )
% 5.64/5.94 = zero_zero_complex )
% 5.64/5.94 = ( A = zero_zero_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_0_iff_equal
% 5.64/5.94 thf(fact_5227_neg__equal__0__iff__equal,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = zero_zero_rat )
% 5.64/5.94 = ( A = zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_0_iff_equal
% 5.64/5.94 thf(fact_5228_neg__equal__0__iff__equal,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = zero_z3403309356797280102nteger )
% 5.64/5.94 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_0_iff_equal
% 5.64/5.94 thf(fact_5229_equal__neg__zero,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( A = zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % equal_neg_zero
% 5.64/5.94 thf(fact_5230_equal__neg__zero,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( A = zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % equal_neg_zero
% 5.64/5.94 thf(fact_5231_equal__neg__zero,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( A = zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % equal_neg_zero
% 5.64/5.94 thf(fact_5232_equal__neg__zero,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % equal_neg_zero
% 5.64/5.94 thf(fact_5233_neg__equal__zero,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ A )
% 5.64/5.94 = A )
% 5.64/5.94 = ( A = zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_zero
% 5.64/5.94 thf(fact_5234_neg__equal__zero,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ A )
% 5.64/5.94 = A )
% 5.64/5.94 = ( A = zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_zero
% 5.64/5.94 thf(fact_5235_neg__equal__zero,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = A )
% 5.64/5.94 = ( A = zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_zero
% 5.64/5.94 thf(fact_5236_neg__equal__zero,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = A )
% 5.64/5.94 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_equal_zero
% 5.64/5.94 thf(fact_5237_neg__less__iff__less,axiom,
% 5.64/5.94 ! [B: int,A: int] :
% 5.64/5.94 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( ord_less_int @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_iff_less
% 5.64/5.94 thf(fact_5238_neg__less__iff__less,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( ord_less_real @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_iff_less
% 5.64/5.94 thf(fact_5239_neg__less__iff__less,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_iff_less
% 5.64/5.94 thf(fact_5240_neg__less__iff__less,axiom,
% 5.64/5.94 ! [B: code_integer,A: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_iff_less
% 5.64/5.94 thf(fact_5241_neg__numeral__eq__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( M = N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_eq_iff
% 5.64/5.94 thf(fact_5242_neg__numeral__eq__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( M = N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_eq_iff
% 5.64/5.94 thf(fact_5243_neg__numeral__eq__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( M = N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_eq_iff
% 5.64/5.94 thf(fact_5244_neg__numeral__eq__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( M = N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_eq_iff
% 5.64/5.94 thf(fact_5245_neg__numeral__eq__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( M = N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_eq_iff
% 5.64/5.94 thf(fact_5246_mult__minus__right,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_right
% 5.64/5.94 thf(fact_5247_mult__minus__right,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_right
% 5.64/5.94 thf(fact_5248_mult__minus__right,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_right
% 5.64/5.94 thf(fact_5249_mult__minus__right,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_right
% 5.64/5.94 thf(fact_5250_mult__minus__right,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_right
% 5.64/5.94 thf(fact_5251_minus__mult__minus,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( times_times_int @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_minus
% 5.64/5.94 thf(fact_5252_minus__mult__minus,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( times_times_real @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_minus
% 5.64/5.94 thf(fact_5253_minus__mult__minus,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( times_times_complex @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_minus
% 5.64/5.94 thf(fact_5254_minus__mult__minus,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( times_times_rat @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_minus
% 5.64/5.94 thf(fact_5255_minus__mult__minus,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_minus
% 5.64/5.94 thf(fact_5256_mult__minus__left,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.94 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_left
% 5.64/5.94 thf(fact_5257_mult__minus__left,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.94 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_left
% 5.64/5.94 thf(fact_5258_mult__minus__left,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_left
% 5.64/5.94 thf(fact_5259_mult__minus__left,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.94 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_left
% 5.64/5.94 thf(fact_5260_mult__minus__left,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus_left
% 5.64/5.94 thf(fact_5261_add__minus__cancel,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % add_minus_cancel
% 5.64/5.94 thf(fact_5262_add__minus__cancel,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % add_minus_cancel
% 5.64/5.94 thf(fact_5263_add__minus__cancel,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % add_minus_cancel
% 5.64/5.94 thf(fact_5264_add__minus__cancel,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % add_minus_cancel
% 5.64/5.94 thf(fact_5265_add__minus__cancel,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % add_minus_cancel
% 5.64/5.94 thf(fact_5266_minus__add__cancel,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_cancel
% 5.64/5.94 thf(fact_5267_minus__add__cancel,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_cancel
% 5.64/5.94 thf(fact_5268_minus__add__cancel,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_cancel
% 5.64/5.94 thf(fact_5269_minus__add__cancel,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_cancel
% 5.64/5.94 thf(fact_5270_minus__add__cancel,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.64/5.94 = B ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_cancel
% 5.64/5.94 thf(fact_5271_minus__add__distrib,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.64/5.94 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_distrib
% 5.64/5.94 thf(fact_5272_minus__add__distrib,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.64/5.94 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_distrib
% 5.64/5.94 thf(fact_5273_minus__add__distrib,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.64/5.94 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_distrib
% 5.64/5.94 thf(fact_5274_minus__add__distrib,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.94 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_distrib
% 5.64/5.94 thf(fact_5275_minus__add__distrib,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_add_distrib
% 5.64/5.94 thf(fact_5276_minus__diff__eq,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.64/5.94 = ( minus_minus_int @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_eq
% 5.64/5.94 thf(fact_5277_minus__diff__eq,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.64/5.94 = ( minus_minus_real @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_eq
% 5.64/5.94 thf(fact_5278_minus__diff__eq,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.64/5.94 = ( minus_minus_complex @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_eq
% 5.64/5.94 thf(fact_5279_minus__diff__eq,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.64/5.94 = ( minus_minus_rat @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_eq
% 5.64/5.94 thf(fact_5280_minus__diff__eq,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.64/5.94 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_eq
% 5.64/5.94 thf(fact_5281_div__minus__minus,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( divide_divide_int @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % div_minus_minus
% 5.64/5.94 thf(fact_5282_div__minus__minus,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % div_minus_minus
% 5.64/5.94 thf(fact_5283_neg__less__eq__nonneg,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_eq_nonneg
% 5.64/5.94 thf(fact_5284_neg__less__eq__nonneg,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.64/5.94 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_eq_nonneg
% 5.64/5.94 thf(fact_5285_neg__less__eq__nonneg,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.64/5.94 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_eq_nonneg
% 5.64/5.94 thf(fact_5286_neg__less__eq__nonneg,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.64/5.94 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_eq_nonneg
% 5.64/5.94 thf(fact_5287_less__eq__neg__nonpos,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_eq_neg_nonpos
% 5.64/5.94 thf(fact_5288_less__eq__neg__nonpos,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_eq_neg_nonpos
% 5.64/5.94 thf(fact_5289_less__eq__neg__nonpos,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_eq_neg_nonpos
% 5.64/5.94 thf(fact_5290_less__eq__neg__nonpos,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_eq_neg_nonpos
% 5.64/5.94 thf(fact_5291_neg__le__0__iff__le,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_0_iff_le
% 5.64/5.94 thf(fact_5292_neg__le__0__iff__le,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.64/5.94 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_0_iff_le
% 5.64/5.94 thf(fact_5293_neg__le__0__iff__le,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.64/5.94 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_0_iff_le
% 5.64/5.94 thf(fact_5294_neg__le__0__iff__le,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.64/5.94 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_le_0_iff_le
% 5.64/5.94 thf(fact_5295_neg__0__le__iff__le,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_le_iff_le
% 5.64/5.94 thf(fact_5296_neg__0__le__iff__le,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_le_iff_le
% 5.64/5.94 thf(fact_5297_neg__0__le__iff__le,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_le_iff_le
% 5.64/5.94 thf(fact_5298_neg__0__le__iff__le,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_le_iff_le
% 5.64/5.94 thf(fact_5299_less__neg__neg,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_neg_neg
% 5.64/5.94 thf(fact_5300_less__neg__neg,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_neg_neg
% 5.64/5.94 thf(fact_5301_less__neg__neg,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_neg_neg
% 5.64/5.94 thf(fact_5302_less__neg__neg,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_neg_neg
% 5.64/5.94 thf(fact_5303_neg__less__pos,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.64/5.94 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_pos
% 5.64/5.94 thf(fact_5304_neg__less__pos,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.64/5.94 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_pos
% 5.64/5.94 thf(fact_5305_neg__less__pos,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.64/5.94 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_pos
% 5.64/5.94 thf(fact_5306_neg__less__pos,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_pos
% 5.64/5.94 thf(fact_5307_neg__0__less__iff__less,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_less_iff_less
% 5.64/5.94 thf(fact_5308_neg__0__less__iff__less,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_less_iff_less
% 5.64/5.94 thf(fact_5309_neg__0__less__iff__less,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_less_iff_less
% 5.64/5.94 thf(fact_5310_neg__0__less__iff__less,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_0_less_iff_less
% 5.64/5.94 thf(fact_5311_neg__less__0__iff__less,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.64/5.94 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_0_iff_less
% 5.64/5.94 thf(fact_5312_neg__less__0__iff__less,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.64/5.94 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_0_iff_less
% 5.64/5.94 thf(fact_5313_neg__less__0__iff__less,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.64/5.94 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_0_iff_less
% 5.64/5.94 thf(fact_5314_neg__less__0__iff__less,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_less_0_iff_less
% 5.64/5.94 thf(fact_5315_ab__left__minus,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % ab_left_minus
% 5.64/5.94 thf(fact_5316_ab__left__minus,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % ab_left_minus
% 5.64/5.94 thf(fact_5317_ab__left__minus,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % ab_left_minus
% 5.64/5.94 thf(fact_5318_ab__left__minus,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % ab_left_minus
% 5.64/5.94 thf(fact_5319_ab__left__minus,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % ab_left_minus
% 5.64/5.94 thf(fact_5320_add_Oright__inverse,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % add.right_inverse
% 5.64/5.94 thf(fact_5321_add_Oright__inverse,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % add.right_inverse
% 5.64/5.94 thf(fact_5322_add_Oright__inverse,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % add.right_inverse
% 5.64/5.94 thf(fact_5323_add_Oright__inverse,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % add.right_inverse
% 5.64/5.94 thf(fact_5324_add_Oright__inverse,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % add.right_inverse
% 5.64/5.94 thf(fact_5325_verit__minus__simplify_I3_J,axiom,
% 5.64/5.94 ! [B: int] :
% 5.64/5.94 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.64/5.94 = ( uminus_uminus_int @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(3)
% 5.64/5.94 thf(fact_5326_verit__minus__simplify_I3_J,axiom,
% 5.64/5.94 ! [B: real] :
% 5.64/5.94 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(3)
% 5.64/5.94 thf(fact_5327_verit__minus__simplify_I3_J,axiom,
% 5.64/5.94 ! [B: complex] :
% 5.64/5.94 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(3)
% 5.64/5.94 thf(fact_5328_verit__minus__simplify_I3_J,axiom,
% 5.64/5.94 ! [B: rat] :
% 5.64/5.94 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(3)
% 5.64/5.94 thf(fact_5329_verit__minus__simplify_I3_J,axiom,
% 5.64/5.94 ! [B: code_integer] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_minus_simplify(3)
% 5.64/5.94 thf(fact_5330_diff__0,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.64/5.94 = ( uminus_uminus_int @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_0
% 5.64/5.94 thf(fact_5331_diff__0,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.64/5.94 = ( uminus_uminus_real @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_0
% 5.64/5.94 thf(fact_5332_diff__0,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_0
% 5.64/5.94 thf(fact_5333_diff__0,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.64/5.94 = ( uminus_uminus_rat @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_0
% 5.64/5.94 thf(fact_5334_diff__0,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_0
% 5.64/5.94 thf(fact_5335_add__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5336_add__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5337_add__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5338_add__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5339_add__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5340_mult__minus1,axiom,
% 5.64/5.94 ! [Z: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.64/5.94 = ( uminus_uminus_int @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1
% 5.64/5.94 thf(fact_5341_mult__minus1,axiom,
% 5.64/5.94 ! [Z: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.64/5.94 = ( uminus_uminus_real @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1
% 5.64/5.94 thf(fact_5342_mult__minus1,axiom,
% 5.64/5.94 ! [Z: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1
% 5.64/5.94 thf(fact_5343_mult__minus1,axiom,
% 5.64/5.94 ! [Z: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.64/5.94 = ( uminus_uminus_rat @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1
% 5.64/5.94 thf(fact_5344_mult__minus1,axiom,
% 5.64/5.94 ! [Z: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1
% 5.64/5.94 thf(fact_5345_mult__minus1__right,axiom,
% 5.64/5.94 ! [Z: int] :
% 5.64/5.94 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( uminus_uminus_int @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1_right
% 5.64/5.94 thf(fact_5346_mult__minus1__right,axiom,
% 5.64/5.94 ! [Z: real] :
% 5.64/5.94 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( uminus_uminus_real @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1_right
% 5.64/5.94 thf(fact_5347_mult__minus1__right,axiom,
% 5.64/5.94 ! [Z: complex] :
% 5.64/5.94 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1_right
% 5.64/5.94 thf(fact_5348_mult__minus1__right,axiom,
% 5.64/5.94 ! [Z: rat] :
% 5.64/5.94 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( uminus_uminus_rat @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1_right
% 5.64/5.94 thf(fact_5349_mult__minus1__right,axiom,
% 5.64/5.94 ! [Z: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_minus1_right
% 5.64/5.94 thf(fact_5350_uminus__add__conv__diff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.94 = ( minus_minus_int @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_add_conv_diff
% 5.64/5.94 thf(fact_5351_uminus__add__conv__diff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.94 = ( minus_minus_real @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_add_conv_diff
% 5.64/5.94 thf(fact_5352_uminus__add__conv__diff,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.64/5.94 = ( minus_minus_complex @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_add_conv_diff
% 5.64/5.94 thf(fact_5353_uminus__add__conv__diff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.94 = ( minus_minus_rat @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_add_conv_diff
% 5.64/5.94 thf(fact_5354_uminus__add__conv__diff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.94 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_add_conv_diff
% 5.64/5.94 thf(fact_5355_diff__minus__eq__add,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( plus_plus_int @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_minus_eq_add
% 5.64/5.94 thf(fact_5356_diff__minus__eq__add,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( plus_plus_real @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_minus_eq_add
% 5.64/5.94 thf(fact_5357_diff__minus__eq__add,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( plus_plus_complex @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_minus_eq_add
% 5.64/5.94 thf(fact_5358_diff__minus__eq__add,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( plus_plus_rat @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_minus_eq_add
% 5.64/5.94 thf(fact_5359_diff__minus__eq__add,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_minus_eq_add
% 5.64/5.94 thf(fact_5360_div__minus1__right,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( uminus_uminus_int @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % div_minus1_right
% 5.64/5.94 thf(fact_5361_div__minus1__right,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % div_minus1_right
% 5.64/5.94 thf(fact_5362_divide__minus1,axiom,
% 5.64/5.94 ! [X2: real] :
% 5.64/5.94 ( ( divide_divide_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( uminus_uminus_real @ X2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_minus1
% 5.64/5.94 thf(fact_5363_divide__minus1,axiom,
% 5.64/5.94 ! [X2: complex] :
% 5.64/5.94 ( ( divide1717551699836669952omplex @ X2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_minus1
% 5.64/5.94 thf(fact_5364_divide__minus1,axiom,
% 5.64/5.94 ! [X2: rat] :
% 5.64/5.94 ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( uminus_uminus_rat @ X2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_minus1
% 5.64/5.94 thf(fact_5365_signed__take__bit__of__minus__1,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_of_minus_1
% 5.64/5.94 thf(fact_5366_signed__take__bit__of__minus__1,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_of_minus_1
% 5.64/5.94 thf(fact_5367_pred__numeral__simps_I1_J,axiom,
% 5.64/5.94 ( ( pred_numeral @ one )
% 5.64/5.94 = zero_zero_nat ) ).
% 5.64/5.94
% 5.64/5.94 % pred_numeral_simps(1)
% 5.64/5.94 thf(fact_5368_Suc__eq__numeral,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( ( suc @ N )
% 5.64/5.94 = ( numeral_numeral_nat @ K ) )
% 5.64/5.94 = ( N
% 5.64/5.94 = ( pred_numeral @ K ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Suc_eq_numeral
% 5.64/5.94 thf(fact_5369_eq__numeral__Suc,axiom,
% 5.64/5.94 ! [K: num,N: nat] :
% 5.64/5.94 ( ( ( numeral_numeral_nat @ K )
% 5.64/5.94 = ( suc @ N ) )
% 5.64/5.94 = ( ( pred_numeral @ K )
% 5.64/5.94 = N ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_numeral_Suc
% 5.64/5.94 thf(fact_5370_dbl__simps_I1_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(1)
% 5.64/5.94 thf(fact_5371_dbl__simps_I1_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(1)
% 5.64/5.94 thf(fact_5372_dbl__simps_I1_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(1)
% 5.64/5.94 thf(fact_5373_dbl__simps_I1_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(1)
% 5.64/5.94 thf(fact_5374_dbl__simps_I1_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(1)
% 5.64/5.94 thf(fact_5375_dbl__inc__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_inc_simps(4)
% 5.64/5.94 thf(fact_5376_dbl__inc__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_inc_simps(4)
% 5.64/5.94 thf(fact_5377_dbl__inc__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_inc_simps(4)
% 5.64/5.94 thf(fact_5378_dbl__inc__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_inc_simps(4)
% 5.64/5.94 thf(fact_5379_dbl__inc__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_inc_simps(4)
% 5.64/5.94 thf(fact_5380_add__neg__numeral__special_I8_J,axiom,
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(8)
% 5.64/5.94 thf(fact_5381_add__neg__numeral__special_I8_J,axiom,
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(8)
% 5.64/5.94 thf(fact_5382_add__neg__numeral__special_I8_J,axiom,
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(8)
% 5.64/5.94 thf(fact_5383_add__neg__numeral__special_I8_J,axiom,
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(8)
% 5.64/5.94 thf(fact_5384_add__neg__numeral__special_I8_J,axiom,
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(8)
% 5.64/5.94 thf(fact_5385_add__neg__numeral__special_I7_J,axiom,
% 5.64/5.94 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(7)
% 5.64/5.94 thf(fact_5386_add__neg__numeral__special_I7_J,axiom,
% 5.64/5.94 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(7)
% 5.64/5.94 thf(fact_5387_add__neg__numeral__special_I7_J,axiom,
% 5.64/5.94 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(7)
% 5.64/5.94 thf(fact_5388_add__neg__numeral__special_I7_J,axiom,
% 5.64/5.94 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(7)
% 5.64/5.94 thf(fact_5389_add__neg__numeral__special_I7_J,axiom,
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(7)
% 5.64/5.94 thf(fact_5390_diff__numeral__special_I12_J,axiom,
% 5.64/5.94 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(12)
% 5.64/5.94 thf(fact_5391_diff__numeral__special_I12_J,axiom,
% 5.64/5.94 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(12)
% 5.64/5.94 thf(fact_5392_diff__numeral__special_I12_J,axiom,
% 5.64/5.94 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(12)
% 5.64/5.94 thf(fact_5393_diff__numeral__special_I12_J,axiom,
% 5.64/5.94 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(12)
% 5.64/5.94 thf(fact_5394_diff__numeral__special_I12_J,axiom,
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(12)
% 5.64/5.94 thf(fact_5395_neg__one__eq__numeral__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ one_one_int )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_eq_numeral_iff
% 5.64/5.94 thf(fact_5396_neg__one__eq__numeral__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ one_one_real )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_eq_numeral_iff
% 5.64/5.94 thf(fact_5397_neg__one__eq__numeral__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_eq_numeral_iff
% 5.64/5.94 thf(fact_5398_neg__one__eq__numeral__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_eq_numeral_iff
% 5.64/5.94 thf(fact_5399_neg__one__eq__numeral__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_eq_numeral_iff
% 5.64/5.94 thf(fact_5400_numeral__eq__neg__one__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_eq_neg_one_iff
% 5.64/5.94 thf(fact_5401_numeral__eq__neg__one__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.64/5.94 = ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_eq_neg_one_iff
% 5.64/5.94 thf(fact_5402_numeral__eq__neg__one__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_eq_neg_one_iff
% 5.64/5.94 thf(fact_5403_numeral__eq__neg__one__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.64/5.94 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_eq_neg_one_iff
% 5.64/5.94 thf(fact_5404_numeral__eq__neg__one__iff,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( N = one ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_eq_neg_one_iff
% 5.64/5.94 thf(fact_5405_minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.64/5.94 = one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % minus_one_mult_self
% 5.64/5.94 thf(fact_5406_minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.64/5.94 = one_one_real ) ).
% 5.64/5.94
% 5.64/5.94 % minus_one_mult_self
% 5.64/5.94 thf(fact_5407_minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.64/5.94 = one_one_complex ) ).
% 5.64/5.94
% 5.64/5.94 % minus_one_mult_self
% 5.64/5.94 thf(fact_5408_minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.64/5.94 = one_one_rat ) ).
% 5.64/5.94
% 5.64/5.94 % minus_one_mult_self
% 5.64/5.94 thf(fact_5409_minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.64/5.94 = one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % minus_one_mult_self
% 5.64/5.94 thf(fact_5410_left__minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat,A: int] :
% 5.64/5.94 ( ( 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 ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % left_minus_one_mult_self
% 5.64/5.94 thf(fact_5411_left__minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat,A: real] :
% 5.64/5.94 ( ( 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 ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % left_minus_one_mult_self
% 5.64/5.94 thf(fact_5412_left__minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat,A: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % left_minus_one_mult_self
% 5.64/5.94 thf(fact_5413_left__minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat,A: rat] :
% 5.64/5.94 ( ( 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 ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % left_minus_one_mult_self
% 5.64/5.94 thf(fact_5414_left__minus__one__mult__self,axiom,
% 5.64/5.94 ! [N: nat,A: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.64/5.94 = A ) ).
% 5.64/5.94
% 5.64/5.94 % left_minus_one_mult_self
% 5.64/5.94 thf(fact_5415_mod__minus1__right,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % mod_minus1_right
% 5.64/5.94 thf(fact_5416_mod__minus1__right,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % mod_minus1_right
% 5.64/5.94 thf(fact_5417_max__number__of_I2_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(2)
% 5.64/5.94 thf(fact_5418_max__number__of_I2_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(2)
% 5.64/5.94 thf(fact_5419_max__number__of_I2_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(2)
% 5.64/5.94 thf(fact_5420_max__number__of_I2_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(2)
% 5.64/5.94 thf(fact_5421_max__number__of_I3_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.64/5.94 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.64/5.94 = ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.64/5.94 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(3)
% 5.64/5.94 thf(fact_5422_max__number__of_I3_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.94 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.94 = ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.94 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(3)
% 5.64/5.94 thf(fact_5423_max__number__of_I3_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.94 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.94 = ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.94 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(3)
% 5.64/5.94 thf(fact_5424_max__number__of_I3_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.94 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.94 = ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.94 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(3)
% 5.64/5.94 thf(fact_5425_max__number__of_I4_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(4)
% 5.64/5.94 thf(fact_5426_max__number__of_I4_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(4)
% 5.64/5.94 thf(fact_5427_max__number__of_I4_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(4)
% 5.64/5.94 thf(fact_5428_max__number__of_I4_J,axiom,
% 5.64/5.94 ! [U: num,V: num] :
% 5.64/5.94 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.64/5.94 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_number_of(4)
% 5.64/5.94 thf(fact_5429_semiring__norm_I168_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: int] :
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(168)
% 5.64/5.94 thf(fact_5430_semiring__norm_I168_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: real] :
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(168)
% 5.64/5.94 thf(fact_5431_semiring__norm_I168_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(168)
% 5.64/5.94 thf(fact_5432_semiring__norm_I168_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(168)
% 5.64/5.94 thf(fact_5433_semiring__norm_I168_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(168)
% 5.64/5.94 thf(fact_5434_diff__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(3)
% 5.64/5.94 thf(fact_5435_diff__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(3)
% 5.64/5.94 thf(fact_5436_diff__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(3)
% 5.64/5.94 thf(fact_5437_diff__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(3)
% 5.64/5.94 thf(fact_5438_diff__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(3)
% 5.64/5.94 thf(fact_5439_diff__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(2)
% 5.64/5.94 thf(fact_5440_diff__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(2)
% 5.64/5.94 thf(fact_5441_diff__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(2)
% 5.64/5.94 thf(fact_5442_diff__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(2)
% 5.64/5.94 thf(fact_5443_diff__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_simps(2)
% 5.64/5.94 thf(fact_5444_semiring__norm_I172_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(172)
% 5.64/5.94 thf(fact_5445_semiring__norm_I172_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(172)
% 5.64/5.94 thf(fact_5446_semiring__norm_I172_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(172)
% 5.64/5.94 thf(fact_5447_semiring__norm_I172_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(172)
% 5.64/5.94 thf(fact_5448_semiring__norm_I172_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(172)
% 5.64/5.94 thf(fact_5449_semiring__norm_I171_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: int] :
% 5.64/5.94 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(171)
% 5.64/5.94 thf(fact_5450_semiring__norm_I171_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: real] :
% 5.64/5.94 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(171)
% 5.64/5.94 thf(fact_5451_semiring__norm_I171_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(171)
% 5.64/5.94 thf(fact_5452_semiring__norm_I171_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(171)
% 5.64/5.94 thf(fact_5453_semiring__norm_I171_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y4 ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(171)
% 5.64/5.94 thf(fact_5454_semiring__norm_I170_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y4 ) )
% 5.64/5.94 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(170)
% 5.64/5.94 thf(fact_5455_semiring__norm_I170_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y4 ) )
% 5.64/5.94 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(170)
% 5.64/5.94 thf(fact_5456_semiring__norm_I170_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y4 ) )
% 5.64/5.94 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(170)
% 5.64/5.94 thf(fact_5457_semiring__norm_I170_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y4 ) )
% 5.64/5.94 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(170)
% 5.64/5.94 thf(fact_5458_semiring__norm_I170_J,axiom,
% 5.64/5.94 ! [V: num,W: num,Y4: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y4 ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % semiring_norm(170)
% 5.64/5.94 thf(fact_5459_mult__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5460_mult__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5461_mult__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5462_mult__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5463_mult__neg__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(3)
% 5.64/5.94 thf(fact_5464_mult__neg__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(2)
% 5.64/5.94 thf(fact_5465_mult__neg__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(2)
% 5.64/5.94 thf(fact_5466_mult__neg__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(2)
% 5.64/5.94 thf(fact_5467_mult__neg__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(2)
% 5.64/5.94 thf(fact_5468_mult__neg__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(2)
% 5.64/5.94 thf(fact_5469_mult__neg__numeral__simps_I1_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(1)
% 5.64/5.94 thf(fact_5470_mult__neg__numeral__simps_I1_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(1)
% 5.64/5.94 thf(fact_5471_mult__neg__numeral__simps_I1_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(1)
% 5.64/5.94 thf(fact_5472_mult__neg__numeral__simps_I1_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(1)
% 5.64/5.94 thf(fact_5473_mult__neg__numeral__simps_I1_J,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_neg_numeral_simps(1)
% 5.64/5.94 thf(fact_5474_less__Suc__numeral,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.64/5.94 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_Suc_numeral
% 5.64/5.94 thf(fact_5475_less__numeral__Suc,axiom,
% 5.64/5.94 ! [K: num,N: nat] :
% 5.64/5.94 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.64/5.94 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_numeral_Suc
% 5.64/5.94 thf(fact_5476_pred__numeral__simps_I3_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.64/5.94 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % pred_numeral_simps(3)
% 5.64/5.94 thf(fact_5477_le__numeral__Suc,axiom,
% 5.64/5.94 ! [K: num,N: nat] :
% 5.64/5.94 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.64/5.94 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_numeral_Suc
% 5.64/5.94 thf(fact_5478_le__Suc__numeral,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.64/5.94 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_Suc_numeral
% 5.64/5.94 thf(fact_5479_neg__numeral__le__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_iff
% 5.64/5.94 thf(fact_5480_neg__numeral__le__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_iff
% 5.64/5.94 thf(fact_5481_neg__numeral__le__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_iff
% 5.64/5.94 thf(fact_5482_neg__numeral__le__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_iff
% 5.64/5.94 thf(fact_5483_diff__Suc__numeral,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.64/5.94 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_Suc_numeral
% 5.64/5.94 thf(fact_5484_diff__numeral__Suc,axiom,
% 5.64/5.94 ! [K: num,N: nat] :
% 5.64/5.94 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.64/5.94 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_Suc
% 5.64/5.94 thf(fact_5485_neg__numeral__less__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( ord_less_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_iff
% 5.64/5.94 thf(fact_5486_neg__numeral__less__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( ord_less_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_iff
% 5.64/5.94 thf(fact_5487_neg__numeral__less__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( ord_less_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_iff
% 5.64/5.94 thf(fact_5488_neg__numeral__less__iff,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( ord_less_num @ N @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_iff
% 5.64/5.94 thf(fact_5489_max__Suc__numeral,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.64/5.94 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_Suc_numeral
% 5.64/5.94 thf(fact_5490_max__numeral__Suc,axiom,
% 5.64/5.94 ! [K: num,N: nat] :
% 5.64/5.94 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.64/5.94 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % max_numeral_Suc
% 5.64/5.94 thf(fact_5491_pred__numeral__simps_I2_J,axiom,
% 5.64/5.94 ! [K: num] :
% 5.64/5.94 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.64/5.94 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % pred_numeral_simps(2)
% 5.64/5.94 thf(fact_5492_not__neg__one__le__neg__numeral__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_le_neg_numeral_iff
% 5.64/5.94 thf(fact_5493_not__neg__one__le__neg__numeral__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_le_neg_numeral_iff
% 5.64/5.94 thf(fact_5494_not__neg__one__le__neg__numeral__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_le_neg_numeral_iff
% 5.64/5.94 thf(fact_5495_not__neg__one__le__neg__numeral__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_le_neg_numeral_iff
% 5.64/5.94 thf(fact_5496_le__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: rat,B: rat,W: num] :
% 5.64/5.94 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.64/5.94 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5497_le__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: real,B: real,W: num] :
% 5.64/5.94 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.64/5.94 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5498_divide__le__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: rat,W: num,A: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.64/5.94 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_le_eq_numeral1(2)
% 5.64/5.94 thf(fact_5499_divide__le__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: real,W: num,A: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.64/5.94 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_le_eq_numeral1(2)
% 5.64/5.94 thf(fact_5500_divide__eq__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: real,W: num,A: real] :
% 5.64/5.94 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.94 = A )
% 5.64/5.94 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.94 != zero_zero_real )
% 5.64/5.94 => ( B
% 5.64/5.94 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.64/5.94 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.94 = zero_zero_real )
% 5.64/5.94 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_eq_eq_numeral1(2)
% 5.64/5.94 thf(fact_5501_divide__eq__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: complex,W: num,A: complex] :
% 5.64/5.94 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.94 = A )
% 5.64/5.94 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.94 != zero_zero_complex )
% 5.64/5.94 => ( B
% 5.64/5.94 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.64/5.94 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.94 = zero_zero_complex )
% 5.64/5.94 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_eq_eq_numeral1(2)
% 5.64/5.94 thf(fact_5502_divide__eq__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: rat,W: num,A: rat] :
% 5.64/5.94 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.94 = A )
% 5.64/5.94 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.94 != zero_zero_rat )
% 5.64/5.94 => ( B
% 5.64/5.94 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.64/5.94 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.94 = zero_zero_rat )
% 5.64/5.94 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_eq_eq_numeral1(2)
% 5.64/5.94 thf(fact_5503_eq__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: real,B: real,W: num] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.64/5.94 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.94 != zero_zero_real )
% 5.64/5.94 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.94 = B ) )
% 5.64/5.94 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.94 = zero_zero_real )
% 5.64/5.94 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5504_eq__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: complex,B: complex,W: num] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.64/5.94 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.94 != zero_zero_complex )
% 5.64/5.94 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.94 = B ) )
% 5.64/5.94 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.94 = zero_zero_complex )
% 5.64/5.94 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5505_eq__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: rat,B: rat,W: num] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.64/5.94 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.94 != zero_zero_rat )
% 5.64/5.94 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.94 = B ) )
% 5.64/5.94 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.94 = zero_zero_rat )
% 5.64/5.94 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5506_neg__numeral__less__neg__one__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_neg_one_iff
% 5.64/5.94 thf(fact_5507_neg__numeral__less__neg__one__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_neg_one_iff
% 5.64/5.94 thf(fact_5508_neg__numeral__less__neg__one__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_neg_one_iff
% 5.64/5.94 thf(fact_5509_neg__numeral__less__neg__one__iff,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( M != one ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_neg_one_iff
% 5.64/5.94 thf(fact_5510_less__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: real,B: real,W: num] :
% 5.64/5.94 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.64/5.94 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5511_less__divide__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [A: rat,B: rat,W: num] :
% 5.64/5.94 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.64/5.94 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_divide_eq_numeral1(2)
% 5.64/5.94 thf(fact_5512_divide__less__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: real,W: num,A: real] :
% 5.64/5.94 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.64/5.94 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_less_eq_numeral1(2)
% 5.64/5.94 thf(fact_5513_divide__less__eq__numeral1_I2_J,axiom,
% 5.64/5.94 ! [B: rat,W: num,A: rat] :
% 5.64/5.94 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.64/5.94 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_less_eq_numeral1(2)
% 5.64/5.94 thf(fact_5514_power2__minus,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power2_minus
% 5.64/5.94 thf(fact_5515_power2__minus,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power2_minus
% 5.64/5.94 thf(fact_5516_power2__minus,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power2_minus
% 5.64/5.94 thf(fact_5517_power2__minus,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power2_minus
% 5.64/5.94 thf(fact_5518_power2__minus,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power2_minus
% 5.64/5.94 thf(fact_5519_add__neg__numeral__special_I9_J,axiom,
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(9)
% 5.64/5.94 thf(fact_5520_add__neg__numeral__special_I9_J,axiom,
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(9)
% 5.64/5.94 thf(fact_5521_add__neg__numeral__special_I9_J,axiom,
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(9)
% 5.64/5.94 thf(fact_5522_add__neg__numeral__special_I9_J,axiom,
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(9)
% 5.64/5.94 thf(fact_5523_add__neg__numeral__special_I9_J,axiom,
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_neg_numeral_special(9)
% 5.64/5.94 thf(fact_5524_diff__numeral__special_I10_J,axiom,
% 5.64/5.94 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(10)
% 5.64/5.94 thf(fact_5525_diff__numeral__special_I10_J,axiom,
% 5.64/5.94 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(10)
% 5.64/5.94 thf(fact_5526_diff__numeral__special_I10_J,axiom,
% 5.64/5.94 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(10)
% 5.64/5.94 thf(fact_5527_diff__numeral__special_I10_J,axiom,
% 5.64/5.94 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(10)
% 5.64/5.94 thf(fact_5528_diff__numeral__special_I10_J,axiom,
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(10)
% 5.64/5.94 thf(fact_5529_diff__numeral__special_I11_J,axiom,
% 5.64/5.94 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(11)
% 5.64/5.94 thf(fact_5530_diff__numeral__special_I11_J,axiom,
% 5.64/5.94 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(11)
% 5.64/5.94 thf(fact_5531_diff__numeral__special_I11_J,axiom,
% 5.64/5.94 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(11)
% 5.64/5.94 thf(fact_5532_diff__numeral__special_I11_J,axiom,
% 5.64/5.94 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(11)
% 5.64/5.94 thf(fact_5533_diff__numeral__special_I11_J,axiom,
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(11)
% 5.64/5.94 thf(fact_5534_minus__1__div__2__eq,axiom,
% 5.64/5.94 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_1_div_2_eq
% 5.64/5.94 thf(fact_5535_minus__1__div__2__eq,axiom,
% 5.64/5.94 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_1_div_2_eq
% 5.64/5.94 thf(fact_5536_bits__minus__1__mod__2__eq,axiom,
% 5.64/5.94 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.94 = one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % bits_minus_1_mod_2_eq
% 5.64/5.94 thf(fact_5537_bits__minus__1__mod__2__eq,axiom,
% 5.64/5.94 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.94 = one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % bits_minus_1_mod_2_eq
% 5.64/5.94 thf(fact_5538_minus__1__mod__2__eq,axiom,
% 5.64/5.94 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.94 = one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % minus_1_mod_2_eq
% 5.64/5.94 thf(fact_5539_minus__1__mod__2__eq,axiom,
% 5.64/5.94 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.94 = one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % minus_1_mod_2_eq
% 5.64/5.94 thf(fact_5540_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [A: int,N: nat] :
% 5.64/5.94 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Power.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5541_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [A: real,N: nat] :
% 5.64/5.94 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Power.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5542_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [A: complex,N: nat] :
% 5.64/5.94 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Power.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5543_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [A: rat,N: nat] :
% 5.64/5.94 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Power.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5544_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [A: code_integer,N: nat] :
% 5.64/5.94 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Power.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5545_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [N: nat,A: int] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.64/5.94 = ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Parity.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5546_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [N: nat,A: real] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.64/5.94 = ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Parity.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5547_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [N: nat,A: complex] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.64/5.94 = ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Parity.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5548_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [N: nat,A: rat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.64/5.94 = ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Parity.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5549_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.64/5.94 ! [N: nat,A: code_integer] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.64/5.94 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Parity.ring_1_class.power_minus_even
% 5.64/5.94 thf(fact_5550_power__minus__odd,axiom,
% 5.64/5.94 ! [N: nat,A: int] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.64/5.94 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_odd
% 5.64/5.94 thf(fact_5551_power__minus__odd,axiom,
% 5.64/5.94 ! [N: nat,A: real] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.64/5.94 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_odd
% 5.64/5.94 thf(fact_5552_power__minus__odd,axiom,
% 5.64/5.94 ! [N: nat,A: complex] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_odd
% 5.64/5.94 thf(fact_5553_power__minus__odd,axiom,
% 5.64/5.94 ! [N: nat,A: rat] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.64/5.94 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_odd
% 5.64/5.94 thf(fact_5554_power__minus__odd,axiom,
% 5.64/5.94 ! [N: nat,A: code_integer] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_odd
% 5.64/5.94 thf(fact_5555_diff__numeral__special_I3_J,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(3)
% 5.64/5.94 thf(fact_5556_diff__numeral__special_I3_J,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(3)
% 5.64/5.94 thf(fact_5557_diff__numeral__special_I3_J,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.94 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(3)
% 5.64/5.94 thf(fact_5558_diff__numeral__special_I3_J,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.94 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(3)
% 5.64/5.94 thf(fact_5559_diff__numeral__special_I3_J,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.94 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(3)
% 5.64/5.94 thf(fact_5560_diff__numeral__special_I4_J,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(4)
% 5.64/5.94 thf(fact_5561_diff__numeral__special_I4_J,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(4)
% 5.64/5.94 thf(fact_5562_diff__numeral__special_I4_J,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(4)
% 5.64/5.94 thf(fact_5563_diff__numeral__special_I4_J,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(4)
% 5.64/5.94 thf(fact_5564_diff__numeral__special_I4_J,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_numeral_special(4)
% 5.64/5.94 thf(fact_5565_dbl__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(4)
% 5.64/5.94 thf(fact_5566_dbl__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(4)
% 5.64/5.94 thf(fact_5567_dbl__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(4)
% 5.64/5.94 thf(fact_5568_dbl__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(4)
% 5.64/5.94 thf(fact_5569_dbl__simps_I4_J,axiom,
% 5.64/5.94 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dbl_simps(4)
% 5.64/5.94 thf(fact_5570_power__minus1__even,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus1_even
% 5.64/5.94 thf(fact_5571_power__minus1__even,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = one_one_real ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus1_even
% 5.64/5.94 thf(fact_5572_power__minus1__even,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = one_one_complex ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus1_even
% 5.64/5.94 thf(fact_5573_power__minus1__even,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = one_one_rat ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus1_even
% 5.64/5.94 thf(fact_5574_power__minus1__even,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.94 = one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus1_even
% 5.64/5.94 thf(fact_5575_neg__one__even__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.64/5.94 = one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_even_power
% 5.64/5.94 thf(fact_5576_neg__one__even__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.64/5.94 = one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_even_power
% 5.64/5.94 thf(fact_5577_neg__one__even__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.64/5.94 = one_one_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_even_power
% 5.64/5.94 thf(fact_5578_neg__one__even__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.64/5.94 = one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_even_power
% 5.64/5.94 thf(fact_5579_neg__one__even__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.64/5.94 = one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_even_power
% 5.64/5.94 thf(fact_5580_neg__one__odd__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_odd_power
% 5.64/5.94 thf(fact_5581_neg__one__odd__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.64/5.94 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_odd_power
% 5.64/5.94 thf(fact_5582_neg__one__odd__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_odd_power
% 5.64/5.94 thf(fact_5583_neg__one__odd__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.64/5.94 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_odd_power
% 5.64/5.94 thf(fact_5584_neg__one__odd__power,axiom,
% 5.64/5.94 ! [N: nat] :
% 5.64/5.94 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.94 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_odd_power
% 5.64/5.94 thf(fact_5585_signed__take__bit__0,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_0
% 5.64/5.94 thf(fact_5586_signed__take__bit__0,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.64/5.94 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_0
% 5.64/5.94 thf(fact_5587_signed__take__bit__Suc__minus__bit0,axiom,
% 5.64/5.94 ! [N: nat,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.64/5.94 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_Suc_minus_bit0
% 5.64/5.94 thf(fact_5588_signed__take__bit__numeral__bit0,axiom,
% 5.64/5.94 ! [L: num,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.64/5.94 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_numeral_bit0
% 5.64/5.94 thf(fact_5589_signed__take__bit__numeral__minus__bit0,axiom,
% 5.64/5.94 ! [L: num,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.64/5.94 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_numeral_minus_bit0
% 5.64/5.94 thf(fact_5590_signed__take__bit__numeral__minus__bit1,axiom,
% 5.64/5.94 ! [L: num,K: num] :
% 5.64/5.94 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.64/5.94 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % signed_take_bit_numeral_minus_bit1
% 5.64/5.94 thf(fact_5591_Collect__case__prod__mono,axiom,
% 5.64/5.94 ! [A4: int > int > $o,B4: int > int > $o] :
% 5.64/5.94 ( ( ord_le6741204236512500942_int_o @ A4 @ B4 )
% 5.64/5.94 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A4 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B4 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % Collect_case_prod_mono
% 5.64/5.94 thf(fact_5592_prod_Odisc__eq__case,axiom,
% 5.64/5.94 ! [Prod: product_prod_int_int] :
% 5.64/5.94 ( produc4947309494688390418_int_o
% 5.64/5.94 @ ^ [Uu3: int,Uv3: int] : $true
% 5.64/5.94 @ Prod ) ).
% 5.64/5.94
% 5.64/5.94 % prod.disc_eq_case
% 5.64/5.94 thf(fact_5593_compl__mono,axiom,
% 5.64/5.94 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.94 ( ( ord_less_eq_set_nat @ X2 @ Y4 )
% 5.64/5.94 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y4 ) @ ( uminus5710092332889474511et_nat @ X2 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % compl_mono
% 5.64/5.94 thf(fact_5594_compl__le__swap1,axiom,
% 5.64/5.94 ! [Y4: set_nat,X2: set_nat] :
% 5.64/5.94 ( ( ord_less_eq_set_nat @ Y4 @ ( uminus5710092332889474511et_nat @ X2 ) )
% 5.64/5.94 => ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y4 ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % compl_le_swap1
% 5.64/5.94 thf(fact_5595_compl__le__swap2,axiom,
% 5.64/5.94 ! [Y4: set_nat,X2: set_nat] :
% 5.64/5.94 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y4 ) @ X2 )
% 5.64/5.94 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y4 ) ) ).
% 5.64/5.94
% 5.64/5.94 % compl_le_swap2
% 5.64/5.94 thf(fact_5596_verit__negate__coefficient_I3_J,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( A = B )
% 5.64/5.94 => ( ( uminus_uminus_int @ A )
% 5.64/5.94 = ( uminus_uminus_int @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(3)
% 5.64/5.94 thf(fact_5597_verit__negate__coefficient_I3_J,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( A = B )
% 5.64/5.94 => ( ( uminus_uminus_real @ A )
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(3)
% 5.64/5.94 thf(fact_5598_verit__negate__coefficient_I3_J,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( A = B )
% 5.64/5.94 => ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(3)
% 5.64/5.94 thf(fact_5599_verit__negate__coefficient_I3_J,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( A = B )
% 5.64/5.94 => ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(3)
% 5.64/5.94 thf(fact_5600_equation__minus__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % equation_minus_iff
% 5.64/5.94 thf(fact_5601_equation__minus__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % equation_minus_iff
% 5.64/5.94 thf(fact_5602_equation__minus__iff,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % equation_minus_iff
% 5.64/5.94 thf(fact_5603_equation__minus__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % equation_minus_iff
% 5.64/5.94 thf(fact_5604_equation__minus__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % equation_minus_iff
% 5.64/5.94 thf(fact_5605_minus__equation__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( uminus_uminus_int @ B )
% 5.64/5.94 = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_equation_iff
% 5.64/5.94 thf(fact_5606_minus__equation__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( uminus_uminus_real @ B )
% 5.64/5.94 = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_equation_iff
% 5.64/5.94 thf(fact_5607_minus__equation__iff,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( uminus1482373934393186551omplex @ B )
% 5.64/5.94 = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_equation_iff
% 5.64/5.94 thf(fact_5608_minus__equation__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( uminus_uminus_rat @ B )
% 5.64/5.94 = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_equation_iff
% 5.64/5.94 thf(fact_5609_minus__equation__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( uminus1351360451143612070nteger @ B )
% 5.64/5.94 = A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_equation_iff
% 5.64/5.94 thf(fact_5610_le__minus__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_iff
% 5.64/5.94 thf(fact_5611_le__minus__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_iff
% 5.64/5.94 thf(fact_5612_le__minus__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_iff
% 5.64/5.94 thf(fact_5613_le__minus__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_iff
% 5.64/5.94 thf(fact_5614_minus__le__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.94 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_le_iff
% 5.64/5.94 thf(fact_5615_minus__le__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.94 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_le_iff
% 5.64/5.94 thf(fact_5616_minus__le__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.94 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_le_iff
% 5.64/5.94 thf(fact_5617_minus__le__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.94 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_le_iff
% 5.64/5.94 thf(fact_5618_le__imp__neg__le,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.64/5.94 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_imp_neg_le
% 5.64/5.94 thf(fact_5619_le__imp__neg__le,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.94 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_imp_neg_le
% 5.64/5.94 thf(fact_5620_le__imp__neg__le,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.94 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_imp_neg_le
% 5.64/5.94 thf(fact_5621_le__imp__neg__le,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.94 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_imp_neg_le
% 5.64/5.94 thf(fact_5622_less__minus__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_iff
% 5.64/5.94 thf(fact_5623_less__minus__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_iff
% 5.64/5.94 thf(fact_5624_less__minus__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_iff
% 5.64/5.94 thf(fact_5625_less__minus__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_iff
% 5.64/5.94 thf(fact_5626_minus__less__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.94 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_less_iff
% 5.64/5.94 thf(fact_5627_minus__less__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.94 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_less_iff
% 5.64/5.94 thf(fact_5628_minus__less__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.94 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_less_iff
% 5.64/5.94 thf(fact_5629_minus__less__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.94 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_less_iff
% 5.64/5.94 thf(fact_5630_verit__negate__coefficient_I2_J,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ord_less_int @ A @ B )
% 5.64/5.94 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(2)
% 5.64/5.94 thf(fact_5631_verit__negate__coefficient_I2_J,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ord_less_real @ A @ B )
% 5.64/5.94 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(2)
% 5.64/5.94 thf(fact_5632_verit__negate__coefficient_I2_J,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ord_less_rat @ A @ B )
% 5.64/5.94 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(2)
% 5.64/5.94 thf(fact_5633_verit__negate__coefficient_I2_J,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.64/5.94 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % verit_negate_coefficient(2)
% 5.64/5.94 thf(fact_5634_numeral__neq__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( numeral_numeral_int @ M )
% 5.64/5.94 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_numeral
% 5.64/5.94 thf(fact_5635_numeral__neq__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( numeral_numeral_real @ M )
% 5.64/5.94 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_numeral
% 5.64/5.94 thf(fact_5636_numeral__neq__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( numera6690914467698888265omplex @ M )
% 5.64/5.94 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_numeral
% 5.64/5.94 thf(fact_5637_numeral__neq__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( numeral_numeral_rat @ M )
% 5.64/5.94 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_numeral
% 5.64/5.94 thf(fact_5638_numeral__neq__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( numera6620942414471956472nteger @ M )
% 5.64/5.94 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_numeral
% 5.64/5.94 thf(fact_5639_neg__numeral__neq__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.64/5.94 != ( numeral_numeral_int @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_neq_numeral
% 5.64/5.94 thf(fact_5640_neg__numeral__neq__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.64/5.94 != ( numeral_numeral_real @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_neq_numeral
% 5.64/5.94 thf(fact_5641_neg__numeral__neq__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.64/5.94 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_neq_numeral
% 5.64/5.94 thf(fact_5642_neg__numeral__neq__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.64/5.94 != ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_neq_numeral
% 5.64/5.94 thf(fact_5643_neg__numeral__neq__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.64/5.94 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_neq_numeral
% 5.64/5.94 thf(fact_5644_minus__mult__commute,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.94 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_commute
% 5.64/5.94 thf(fact_5645_minus__mult__commute,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.94 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_commute
% 5.64/5.94 thf(fact_5646_minus__mult__commute,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.64/5.94 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_commute
% 5.64/5.94 thf(fact_5647_minus__mult__commute,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.94 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_commute
% 5.64/5.94 thf(fact_5648_minus__mult__commute,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.94 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_mult_commute
% 5.64/5.94 thf(fact_5649_square__eq__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ( times_times_int @ A @ A )
% 5.64/5.94 = ( times_times_int @ B @ B ) )
% 5.64/5.94 = ( ( A = B )
% 5.64/5.94 | ( A
% 5.64/5.94 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_iff
% 5.64/5.94 thf(fact_5650_square__eq__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( times_times_real @ A @ A )
% 5.64/5.94 = ( times_times_real @ B @ B ) )
% 5.64/5.94 = ( ( A = B )
% 5.64/5.94 | ( A
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_iff
% 5.64/5.94 thf(fact_5651_square__eq__iff,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( times_times_complex @ A @ A )
% 5.64/5.94 = ( times_times_complex @ B @ B ) )
% 5.64/5.94 = ( ( A = B )
% 5.64/5.94 | ( A
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_iff
% 5.64/5.94 thf(fact_5652_square__eq__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( times_times_rat @ A @ A )
% 5.64/5.94 = ( times_times_rat @ B @ B ) )
% 5.64/5.94 = ( ( A = B )
% 5.64/5.94 | ( A
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_iff
% 5.64/5.94 thf(fact_5653_square__eq__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.64/5.94 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.64/5.94 = ( ( A = B )
% 5.64/5.94 | ( A
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_iff
% 5.64/5.94 thf(fact_5654_one__neq__neg__one,axiom,
% 5.64/5.94 ( one_one_int
% 5.64/5.94 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_one
% 5.64/5.94 thf(fact_5655_one__neq__neg__one,axiom,
% 5.64/5.94 ( one_one_real
% 5.64/5.94 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_one
% 5.64/5.94 thf(fact_5656_one__neq__neg__one,axiom,
% 5.64/5.94 ( one_one_complex
% 5.64/5.94 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_one
% 5.64/5.94 thf(fact_5657_one__neq__neg__one,axiom,
% 5.64/5.94 ( one_one_rat
% 5.64/5.94 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_one
% 5.64/5.94 thf(fact_5658_one__neq__neg__one,axiom,
% 5.64/5.94 ( one_one_Code_integer
% 5.64/5.94 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_one
% 5.64/5.94 thf(fact_5659_is__num__normalize_I8_J,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.64/5.94 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % is_num_normalize(8)
% 5.64/5.94 thf(fact_5660_is__num__normalize_I8_J,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.64/5.94 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % is_num_normalize(8)
% 5.64/5.94 thf(fact_5661_is__num__normalize_I8_J,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.64/5.94 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % is_num_normalize(8)
% 5.64/5.94 thf(fact_5662_is__num__normalize_I8_J,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.94 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % is_num_normalize(8)
% 5.64/5.94 thf(fact_5663_is__num__normalize_I8_J,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % is_num_normalize(8)
% 5.64/5.94 thf(fact_5664_group__cancel_Oneg1,axiom,
% 5.64/5.94 ! [A4: int,K: int,A: int] :
% 5.64/5.94 ( ( A4
% 5.64/5.94 = ( plus_plus_int @ K @ A ) )
% 5.64/5.94 => ( ( uminus_uminus_int @ A4 )
% 5.64/5.94 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.neg1
% 5.64/5.94 thf(fact_5665_group__cancel_Oneg1,axiom,
% 5.64/5.94 ! [A4: real,K: real,A: real] :
% 5.64/5.94 ( ( A4
% 5.64/5.94 = ( plus_plus_real @ K @ A ) )
% 5.64/5.94 => ( ( uminus_uminus_real @ A4 )
% 5.64/5.94 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.neg1
% 5.64/5.94 thf(fact_5666_group__cancel_Oneg1,axiom,
% 5.64/5.94 ! [A4: complex,K: complex,A: complex] :
% 5.64/5.94 ( ( A4
% 5.64/5.94 = ( plus_plus_complex @ K @ A ) )
% 5.64/5.94 => ( ( uminus1482373934393186551omplex @ A4 )
% 5.64/5.94 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.neg1
% 5.64/5.94 thf(fact_5667_group__cancel_Oneg1,axiom,
% 5.64/5.94 ! [A4: rat,K: rat,A: rat] :
% 5.64/5.94 ( ( A4
% 5.64/5.94 = ( plus_plus_rat @ K @ A ) )
% 5.64/5.94 => ( ( uminus_uminus_rat @ A4 )
% 5.64/5.94 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.neg1
% 5.64/5.94 thf(fact_5668_group__cancel_Oneg1,axiom,
% 5.64/5.94 ! [A4: code_integer,K: code_integer,A: code_integer] :
% 5.64/5.94 ( ( A4
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.64/5.94 => ( ( uminus1351360451143612070nteger @ A4 )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.neg1
% 5.64/5.94 thf(fact_5669_add_Oinverse__distrib__swap,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.64/5.94 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_distrib_swap
% 5.64/5.94 thf(fact_5670_add_Oinverse__distrib__swap,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.64/5.94 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_distrib_swap
% 5.64/5.94 thf(fact_5671_add_Oinverse__distrib__swap,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.64/5.94 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_distrib_swap
% 5.64/5.94 thf(fact_5672_add_Oinverse__distrib__swap,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.64/5.94 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_distrib_swap
% 5.64/5.94 thf(fact_5673_add_Oinverse__distrib__swap,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_distrib_swap
% 5.64/5.94 thf(fact_5674_minus__diff__commute,axiom,
% 5.64/5.94 ! [B: int,A: int] :
% 5.64/5.94 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.64/5.94 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_commute
% 5.64/5.94 thf(fact_5675_minus__diff__commute,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.64/5.94 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_commute
% 5.64/5.94 thf(fact_5676_minus__diff__commute,axiom,
% 5.64/5.94 ! [B: complex,A: complex] :
% 5.64/5.94 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.64/5.94 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_commute
% 5.64/5.94 thf(fact_5677_minus__diff__commute,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.64/5.94 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_commute
% 5.64/5.94 thf(fact_5678_minus__diff__commute,axiom,
% 5.64/5.94 ! [B: code_integer,A: code_integer] :
% 5.64/5.94 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.64/5.94 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_diff_commute
% 5.64/5.94 thf(fact_5679_div__minus__right,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % div_minus_right
% 5.64/5.94 thf(fact_5680_div__minus__right,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % div_minus_right
% 5.64/5.94 thf(fact_5681_minus__divide__left,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.94 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_left
% 5.64/5.94 thf(fact_5682_minus__divide__left,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.94 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_left
% 5.64/5.94 thf(fact_5683_minus__divide__left,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.94 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_left
% 5.64/5.94 thf(fact_5684_minus__divide__divide,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( divide_divide_real @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_divide
% 5.64/5.94 thf(fact_5685_minus__divide__divide,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_divide
% 5.64/5.94 thf(fact_5686_minus__divide__divide,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( divide_divide_rat @ A @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_divide
% 5.64/5.94 thf(fact_5687_minus__divide__right,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.94 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_right
% 5.64/5.94 thf(fact_5688_minus__divide__right,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.94 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_right
% 5.64/5.94 thf(fact_5689_minus__divide__right,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.94 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_right
% 5.64/5.94 thf(fact_5690_neg__numeral__le__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_numeral
% 5.64/5.94 thf(fact_5691_neg__numeral__le__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_numeral
% 5.64/5.94 thf(fact_5692_neg__numeral__le__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_numeral
% 5.64/5.94 thf(fact_5693_neg__numeral__le__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_numeral
% 5.64/5.94 thf(fact_5694_not__numeral__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_numeral
% 5.64/5.94 thf(fact_5695_not__numeral__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_numeral
% 5.64/5.94 thf(fact_5696_not__numeral__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_numeral
% 5.64/5.94 thf(fact_5697_not__numeral__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_numeral
% 5.64/5.94 thf(fact_5698_zero__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( zero_zero_int
% 5.64/5.94 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_numeral
% 5.64/5.94 thf(fact_5699_zero__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( zero_zero_real
% 5.64/5.94 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_numeral
% 5.64/5.94 thf(fact_5700_zero__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( zero_zero_complex
% 5.64/5.94 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_numeral
% 5.64/5.94 thf(fact_5701_zero__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( zero_zero_rat
% 5.64/5.94 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_numeral
% 5.64/5.94 thf(fact_5702_zero__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( zero_z3403309356797280102nteger
% 5.64/5.94 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_numeral
% 5.64/5.94 thf(fact_5703_neg__numeral__less__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_numeral
% 5.64/5.94 thf(fact_5704_neg__numeral__less__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_numeral
% 5.64/5.94 thf(fact_5705_neg__numeral__less__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_numeral
% 5.64/5.94 thf(fact_5706_neg__numeral__less__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_numeral
% 5.64/5.94 thf(fact_5707_not__numeral__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_numeral
% 5.64/5.94 thf(fact_5708_not__numeral__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_numeral
% 5.64/5.94 thf(fact_5709_not__numeral__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_numeral
% 5.64/5.94 thf(fact_5710_not__numeral__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num,N: num] :
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_numeral
% 5.64/5.94 thf(fact_5711_le__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(4)
% 5.64/5.94 thf(fact_5712_le__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(4)
% 5.64/5.94 thf(fact_5713_le__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(4)
% 5.64/5.94 thf(fact_5714_le__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(4)
% 5.64/5.94 thf(fact_5715_le__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(2)
% 5.64/5.94 thf(fact_5716_le__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(2)
% 5.64/5.94 thf(fact_5717_le__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(2)
% 5.64/5.94 thf(fact_5718_le__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(2)
% 5.64/5.94 thf(fact_5719_zero__neq__neg__one,axiom,
% 5.64/5.94 ( zero_zero_int
% 5.64/5.94 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_one
% 5.64/5.94 thf(fact_5720_zero__neq__neg__one,axiom,
% 5.64/5.94 ( zero_zero_real
% 5.64/5.94 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_one
% 5.64/5.94 thf(fact_5721_zero__neq__neg__one,axiom,
% 5.64/5.94 ( zero_zero_complex
% 5.64/5.94 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_one
% 5.64/5.94 thf(fact_5722_zero__neq__neg__one,axiom,
% 5.64/5.94 ( zero_zero_rat
% 5.64/5.94 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_one
% 5.64/5.94 thf(fact_5723_zero__neq__neg__one,axiom,
% 5.64/5.94 ( zero_z3403309356797280102nteger
% 5.64/5.94 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % zero_neq_neg_one
% 5.64/5.94 thf(fact_5724_neg__eq__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ( uminus_uminus_int @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( plus_plus_int @ A @ B )
% 5.64/5.94 = zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_eq_iff_add_eq_0
% 5.64/5.94 thf(fact_5725_neg__eq__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( plus_plus_real @ A @ B )
% 5.64/5.94 = zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_eq_iff_add_eq_0
% 5.64/5.94 thf(fact_5726_neg__eq__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( plus_plus_complex @ A @ B )
% 5.64/5.94 = zero_zero_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_eq_iff_add_eq_0
% 5.64/5.94 thf(fact_5727_neg__eq__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( plus_plus_rat @ A @ B )
% 5.64/5.94 = zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_eq_iff_add_eq_0
% 5.64/5.94 thf(fact_5728_neg__eq__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = B )
% 5.64/5.94 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_eq_iff_add_eq_0
% 5.64/5.94 thf(fact_5729_eq__neg__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( ( plus_plus_int @ A @ B )
% 5.64/5.94 = zero_zero_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_neg_iff_add_eq_0
% 5.64/5.94 thf(fact_5730_eq__neg__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( ( plus_plus_real @ A @ B )
% 5.64/5.94 = zero_zero_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_neg_iff_add_eq_0
% 5.64/5.94 thf(fact_5731_eq__neg__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( ( plus_plus_complex @ A @ B )
% 5.64/5.94 = zero_zero_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_neg_iff_add_eq_0
% 5.64/5.94 thf(fact_5732_eq__neg__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( ( plus_plus_rat @ A @ B )
% 5.64/5.94 = zero_zero_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_neg_iff_add_eq_0
% 5.64/5.94 thf(fact_5733_eq__neg__iff__add__eq__0,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_neg_iff_add_eq_0
% 5.64/5.94 thf(fact_5734_add_Oinverse__unique,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ( plus_plus_int @ A @ B )
% 5.64/5.94 = zero_zero_int )
% 5.64/5.94 => ( ( uminus_uminus_int @ A )
% 5.64/5.94 = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_unique
% 5.64/5.94 thf(fact_5735_add_Oinverse__unique,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( plus_plus_real @ A @ B )
% 5.64/5.94 = zero_zero_real )
% 5.64/5.94 => ( ( uminus_uminus_real @ A )
% 5.64/5.94 = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_unique
% 5.64/5.94 thf(fact_5736_add_Oinverse__unique,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( plus_plus_complex @ A @ B )
% 5.64/5.94 = zero_zero_complex )
% 5.64/5.94 => ( ( uminus1482373934393186551omplex @ A )
% 5.64/5.94 = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_unique
% 5.64/5.94 thf(fact_5737_add_Oinverse__unique,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( plus_plus_rat @ A @ B )
% 5.64/5.94 = zero_zero_rat )
% 5.64/5.94 => ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_unique
% 5.64/5.94 thf(fact_5738_add_Oinverse__unique,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.64/5.94 = zero_z3403309356797280102nteger )
% 5.64/5.94 => ( ( uminus1351360451143612070nteger @ A )
% 5.64/5.94 = B ) ) ).
% 5.64/5.94
% 5.64/5.94 % add.inverse_unique
% 5.64/5.94 thf(fact_5739_ab__group__add__class_Oab__left__minus,axiom,
% 5.64/5.94 ! [A: int] :
% 5.64/5.94 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.64/5.94 = zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_left_minus
% 5.64/5.94 thf(fact_5740_ab__group__add__class_Oab__left__minus,axiom,
% 5.64/5.94 ! [A: real] :
% 5.64/5.94 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.64/5.94 = zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_left_minus
% 5.64/5.94 thf(fact_5741_ab__group__add__class_Oab__left__minus,axiom,
% 5.64/5.94 ! [A: complex] :
% 5.64/5.94 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.64/5.94 = zero_zero_complex ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_left_minus
% 5.64/5.94 thf(fact_5742_ab__group__add__class_Oab__left__minus,axiom,
% 5.64/5.94 ! [A: rat] :
% 5.64/5.94 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.64/5.94 = zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_left_minus
% 5.64/5.94 thf(fact_5743_ab__group__add__class_Oab__left__minus,axiom,
% 5.64/5.94 ! [A: code_integer] :
% 5.64/5.94 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.64/5.94 = zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_left_minus
% 5.64/5.94 thf(fact_5744_add__eq__0__iff,axiom,
% 5.64/5.94 ! [A: int,B: int] :
% 5.64/5.94 ( ( ( plus_plus_int @ A @ B )
% 5.64/5.94 = zero_zero_int )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_eq_0_iff
% 5.64/5.94 thf(fact_5745_add__eq__0__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( plus_plus_real @ A @ B )
% 5.64/5.94 = zero_zero_real )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_eq_0_iff
% 5.64/5.94 thf(fact_5746_add__eq__0__iff,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( plus_plus_complex @ A @ B )
% 5.64/5.94 = zero_zero_complex )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_eq_0_iff
% 5.64/5.94 thf(fact_5747_add__eq__0__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( plus_plus_rat @ A @ B )
% 5.64/5.94 = zero_zero_rat )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_eq_0_iff
% 5.64/5.94 thf(fact_5748_add__eq__0__iff,axiom,
% 5.64/5.94 ! [A: code_integer,B: code_integer] :
% 5.64/5.94 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.64/5.94 = zero_z3403309356797280102nteger )
% 5.64/5.94 = ( B
% 5.64/5.94 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % add_eq_0_iff
% 5.64/5.94 thf(fact_5749_less__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(4)
% 5.64/5.94 thf(fact_5750_less__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(4)
% 5.64/5.94 thf(fact_5751_less__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(4)
% 5.64/5.94 thf(fact_5752_less__minus__one__simps_I4_J,axiom,
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(4)
% 5.64/5.94 thf(fact_5753_less__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(2)
% 5.64/5.94 thf(fact_5754_less__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(2)
% 5.64/5.94 thf(fact_5755_less__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(2)
% 5.64/5.94 thf(fact_5756_less__minus__one__simps_I2_J,axiom,
% 5.64/5.94 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(2)
% 5.64/5.94 thf(fact_5757_numeral__times__minus__swap,axiom,
% 5.64/5.94 ! [W: num,X2: int] :
% 5.64/5.94 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X2 ) )
% 5.64/5.94 = ( times_times_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_times_minus_swap
% 5.64/5.94 thf(fact_5758_numeral__times__minus__swap,axiom,
% 5.64/5.94 ! [W: num,X2: real] :
% 5.64/5.94 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X2 ) )
% 5.64/5.94 = ( times_times_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_times_minus_swap
% 5.64/5.94 thf(fact_5759_numeral__times__minus__swap,axiom,
% 5.64/5.94 ! [W: num,X2: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.64/5.94 = ( times_times_complex @ X2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_times_minus_swap
% 5.64/5.94 thf(fact_5760_numeral__times__minus__swap,axiom,
% 5.64/5.94 ! [W: num,X2: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X2 ) )
% 5.64/5.94 = ( times_times_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_times_minus_swap
% 5.64/5.94 thf(fact_5761_numeral__times__minus__swap,axiom,
% 5.64/5.94 ! [W: num,X2: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X2 ) )
% 5.64/5.94 = ( times_3573771949741848930nteger @ X2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_times_minus_swap
% 5.64/5.94 thf(fact_5762_nonzero__minus__divide__divide,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( B != zero_zero_real )
% 5.64/5.94 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_minus_divide_divide
% 5.64/5.94 thf(fact_5763_nonzero__minus__divide__divide,axiom,
% 5.64/5.94 ! [B: complex,A: complex] :
% 5.64/5.94 ( ( B != zero_zero_complex )
% 5.64/5.94 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_minus_divide_divide
% 5.64/5.94 thf(fact_5764_nonzero__minus__divide__divide,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( B != zero_zero_rat )
% 5.64/5.94 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_minus_divide_divide
% 5.64/5.94 thf(fact_5765_nonzero__minus__divide__right,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( B != zero_zero_real )
% 5.64/5.94 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.94 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_minus_divide_right
% 5.64/5.94 thf(fact_5766_nonzero__minus__divide__right,axiom,
% 5.64/5.94 ! [B: complex,A: complex] :
% 5.64/5.94 ( ( B != zero_zero_complex )
% 5.64/5.94 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.94 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_minus_divide_right
% 5.64/5.94 thf(fact_5767_nonzero__minus__divide__right,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( B != zero_zero_rat )
% 5.64/5.94 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.94 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_minus_divide_right
% 5.64/5.94 thf(fact_5768_numeral__neq__neg__one,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( numeral_numeral_int @ N )
% 5.64/5.94 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_one
% 5.64/5.94 thf(fact_5769_numeral__neq__neg__one,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( numeral_numeral_real @ N )
% 5.64/5.94 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_one
% 5.64/5.94 thf(fact_5770_numeral__neq__neg__one,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( numera6690914467698888265omplex @ N )
% 5.64/5.94 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_one
% 5.64/5.94 thf(fact_5771_numeral__neq__neg__one,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( numeral_numeral_rat @ N )
% 5.64/5.94 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_one
% 5.64/5.94 thf(fact_5772_numeral__neq__neg__one,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( ( numera6620942414471956472nteger @ N )
% 5.64/5.94 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_neq_neg_one
% 5.64/5.94 thf(fact_5773_one__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( one_one_int
% 5.64/5.94 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_numeral
% 5.64/5.94 thf(fact_5774_one__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( one_one_real
% 5.64/5.94 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_numeral
% 5.64/5.94 thf(fact_5775_one__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( one_one_complex
% 5.64/5.94 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_numeral
% 5.64/5.94 thf(fact_5776_one__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( one_one_rat
% 5.64/5.94 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_numeral
% 5.64/5.94 thf(fact_5777_one__neq__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ( one_one_Code_integer
% 5.64/5.94 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % one_neq_neg_numeral
% 5.64/5.94 thf(fact_5778_square__eq__1__iff,axiom,
% 5.64/5.94 ! [X2: int] :
% 5.64/5.94 ( ( ( times_times_int @ X2 @ X2 )
% 5.64/5.94 = one_one_int )
% 5.64/5.94 = ( ( X2 = one_one_int )
% 5.64/5.94 | ( X2
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_1_iff
% 5.64/5.94 thf(fact_5779_square__eq__1__iff,axiom,
% 5.64/5.94 ! [X2: real] :
% 5.64/5.94 ( ( ( times_times_real @ X2 @ X2 )
% 5.64/5.94 = one_one_real )
% 5.64/5.94 = ( ( X2 = one_one_real )
% 5.64/5.94 | ( X2
% 5.64/5.94 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_1_iff
% 5.64/5.94 thf(fact_5780_square__eq__1__iff,axiom,
% 5.64/5.94 ! [X2: complex] :
% 5.64/5.94 ( ( ( times_times_complex @ X2 @ X2 )
% 5.64/5.94 = one_one_complex )
% 5.64/5.94 = ( ( X2 = one_one_complex )
% 5.64/5.94 | ( X2
% 5.64/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_1_iff
% 5.64/5.94 thf(fact_5781_square__eq__1__iff,axiom,
% 5.64/5.94 ! [X2: rat] :
% 5.64/5.94 ( ( ( times_times_rat @ X2 @ X2 )
% 5.64/5.94 = one_one_rat )
% 5.64/5.94 = ( ( X2 = one_one_rat )
% 5.64/5.94 | ( X2
% 5.64/5.94 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_1_iff
% 5.64/5.94 thf(fact_5782_square__eq__1__iff,axiom,
% 5.64/5.94 ! [X2: code_integer] :
% 5.64/5.94 ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 5.64/5.94 = one_one_Code_integer )
% 5.64/5.94 = ( ( X2 = one_one_Code_integer )
% 5.64/5.94 | ( X2
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % square_eq_1_iff
% 5.64/5.94 thf(fact_5783_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_int
% 5.64/5.94 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.64/5.94 thf(fact_5784_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_real
% 5.64/5.94 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.64/5.94 thf(fact_5785_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_complex
% 5.64/5.94 = ( ^ [A3: complex,B3: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.64/5.94 thf(fact_5786_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_rat
% 5.64/5.94 = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.64/5.94 thf(fact_5787_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_8373710615458151222nteger
% 5.64/5.94 = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.64/5.94 thf(fact_5788_diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_int
% 5.64/5.94 = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_conv_add_uminus
% 5.64/5.94 thf(fact_5789_diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_real
% 5.64/5.94 = ( ^ [A3: real,B3: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_conv_add_uminus
% 5.64/5.94 thf(fact_5790_diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_complex
% 5.64/5.94 = ( ^ [A3: complex,B3: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_conv_add_uminus
% 5.64/5.94 thf(fact_5791_diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_minus_rat
% 5.64/5.94 = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_conv_add_uminus
% 5.64/5.94 thf(fact_5792_diff__conv__add__uminus,axiom,
% 5.64/5.94 ( minus_8373710615458151222nteger
% 5.64/5.94 = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % diff_conv_add_uminus
% 5.64/5.94 thf(fact_5793_group__cancel_Osub2,axiom,
% 5.64/5.94 ! [B4: int,K: int,B: int,A: int] :
% 5.64/5.94 ( ( B4
% 5.64/5.94 = ( plus_plus_int @ K @ B ) )
% 5.64/5.94 => ( ( minus_minus_int @ A @ B4 )
% 5.64/5.94 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.sub2
% 5.64/5.94 thf(fact_5794_group__cancel_Osub2,axiom,
% 5.64/5.94 ! [B4: real,K: real,B: real,A: real] :
% 5.64/5.94 ( ( B4
% 5.64/5.94 = ( plus_plus_real @ K @ B ) )
% 5.64/5.94 => ( ( minus_minus_real @ A @ B4 )
% 5.64/5.94 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.sub2
% 5.64/5.94 thf(fact_5795_group__cancel_Osub2,axiom,
% 5.64/5.94 ! [B4: complex,K: complex,B: complex,A: complex] :
% 5.64/5.94 ( ( B4
% 5.64/5.94 = ( plus_plus_complex @ K @ B ) )
% 5.64/5.94 => ( ( minus_minus_complex @ A @ B4 )
% 5.64/5.94 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.sub2
% 5.64/5.94 thf(fact_5796_group__cancel_Osub2,axiom,
% 5.64/5.94 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.64/5.94 ( ( B4
% 5.64/5.94 = ( plus_plus_rat @ K @ B ) )
% 5.64/5.94 => ( ( minus_minus_rat @ A @ B4 )
% 5.64/5.94 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.sub2
% 5.64/5.94 thf(fact_5797_group__cancel_Osub2,axiom,
% 5.64/5.94 ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.64/5.94 ( ( B4
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.64/5.94 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 5.64/5.94 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % group_cancel.sub2
% 5.64/5.94 thf(fact_5798_dvd__div__neg,axiom,
% 5.64/5.94 ! [B: int,A: int] :
% 5.64/5.94 ( ( dvd_dvd_int @ B @ A )
% 5.64/5.94 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.94 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_div_neg
% 5.64/5.94 thf(fact_5799_dvd__div__neg,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( dvd_dvd_real @ B @ A )
% 5.64/5.94 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.64/5.94 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_div_neg
% 5.64/5.94 thf(fact_5800_dvd__div__neg,axiom,
% 5.64/5.94 ! [B: complex,A: complex] :
% 5.64/5.94 ( ( dvd_dvd_complex @ B @ A )
% 5.64/5.94 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_div_neg
% 5.64/5.94 thf(fact_5801_dvd__div__neg,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( dvd_dvd_rat @ B @ A )
% 5.64/5.94 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.64/5.94 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_div_neg
% 5.64/5.94 thf(fact_5802_dvd__div__neg,axiom,
% 5.64/5.94 ! [B: code_integer,A: code_integer] :
% 5.64/5.94 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.94 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_div_neg
% 5.64/5.94 thf(fact_5803_dvd__neg__div,axiom,
% 5.64/5.94 ! [B: int,A: int] :
% 5.64/5.94 ( ( dvd_dvd_int @ B @ A )
% 5.64/5.94 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.94 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_neg_div
% 5.64/5.94 thf(fact_5804_dvd__neg__div,axiom,
% 5.64/5.94 ! [B: real,A: real] :
% 5.64/5.94 ( ( dvd_dvd_real @ B @ A )
% 5.64/5.94 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.94 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_neg_div
% 5.64/5.94 thf(fact_5805_dvd__neg__div,axiom,
% 5.64/5.94 ! [B: complex,A: complex] :
% 5.64/5.94 ( ( dvd_dvd_complex @ B @ A )
% 5.64/5.94 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_neg_div
% 5.64/5.94 thf(fact_5806_dvd__neg__div,axiom,
% 5.64/5.94 ! [B: rat,A: rat] :
% 5.64/5.94 ( ( dvd_dvd_rat @ B @ A )
% 5.64/5.94 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.94 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_neg_div
% 5.64/5.94 thf(fact_5807_dvd__neg__div,axiom,
% 5.64/5.94 ! [B: code_integer,A: code_integer] :
% 5.64/5.94 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.64/5.94 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % dvd_neg_div
% 5.64/5.94 thf(fact_5808_real__minus__mult__self__le,axiom,
% 5.64/5.94 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 5.64/5.94
% 5.64/5.94 % real_minus_mult_self_le
% 5.64/5.94 thf(fact_5809_zmult__eq__1__iff,axiom,
% 5.64/5.94 ! [M: int,N: int] :
% 5.64/5.94 ( ( ( times_times_int @ M @ N )
% 5.64/5.94 = one_one_int )
% 5.64/5.94 = ( ( ( M = one_one_int )
% 5.64/5.94 & ( N = one_one_int ) )
% 5.64/5.94 | ( ( M
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.94 & ( N
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % zmult_eq_1_iff
% 5.64/5.94 thf(fact_5810_pos__zmult__eq__1__iff__lemma,axiom,
% 5.64/5.94 ! [M: int,N: int] :
% 5.64/5.94 ( ( ( times_times_int @ M @ N )
% 5.64/5.94 = one_one_int )
% 5.64/5.94 => ( ( M = one_one_int )
% 5.64/5.94 | ( M
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % pos_zmult_eq_1_iff_lemma
% 5.64/5.94 thf(fact_5811_numeral__eq__Suc,axiom,
% 5.64/5.94 ( numeral_numeral_nat
% 5.64/5.94 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % numeral_eq_Suc
% 5.64/5.94 thf(fact_5812_not__zero__le__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_le_neg_numeral
% 5.64/5.94 thf(fact_5813_not__zero__le__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_le_neg_numeral
% 5.64/5.94 thf(fact_5814_not__zero__le__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_le_neg_numeral
% 5.64/5.94 thf(fact_5815_not__zero__le__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_le_neg_numeral
% 5.64/5.94 thf(fact_5816_neg__numeral__le__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_zero
% 5.64/5.94 thf(fact_5817_neg__numeral__le__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_zero
% 5.64/5.94 thf(fact_5818_neg__numeral__le__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_zero
% 5.64/5.94 thf(fact_5819_neg__numeral__le__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_zero
% 5.64/5.94 thf(fact_5820_not__zero__less__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_less_neg_numeral
% 5.64/5.94 thf(fact_5821_not__zero__less__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_less_neg_numeral
% 5.64/5.94 thf(fact_5822_not__zero__less__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_less_neg_numeral
% 5.64/5.94 thf(fact_5823_not__zero__less__neg__numeral,axiom,
% 5.64/5.94 ! [N: num] :
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_zero_less_neg_numeral
% 5.64/5.94 thf(fact_5824_neg__numeral__less__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_zero
% 5.64/5.94 thf(fact_5825_neg__numeral__less__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_zero
% 5.64/5.94 thf(fact_5826_neg__numeral__less__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_zero
% 5.64/5.94 thf(fact_5827_neg__numeral__less__zero,axiom,
% 5.64/5.94 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_zero
% 5.64/5.94 thf(fact_5828_le__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(3)
% 5.64/5.94 thf(fact_5829_le__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(3)
% 5.64/5.94 thf(fact_5830_le__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(3)
% 5.64/5.94 thf(fact_5831_le__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(3)
% 5.64/5.94 thf(fact_5832_le__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(1)
% 5.64/5.94 thf(fact_5833_le__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(1)
% 5.64/5.94 thf(fact_5834_le__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(1)
% 5.64/5.94 thf(fact_5835_le__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.64/5.94
% 5.64/5.94 % le_minus_one_simps(1)
% 5.64/5.94 thf(fact_5836_less__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(1)
% 5.64/5.94 thf(fact_5837_less__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(1)
% 5.64/5.94 thf(fact_5838_less__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(1)
% 5.64/5.94 thf(fact_5839_less__minus__one__simps_I1_J,axiom,
% 5.64/5.94 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(1)
% 5.64/5.94 thf(fact_5840_less__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(3)
% 5.64/5.94 thf(fact_5841_less__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(3)
% 5.64/5.94 thf(fact_5842_less__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(3)
% 5.64/5.94 thf(fact_5843_less__minus__one__simps_I3_J,axiom,
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % less_minus_one_simps(3)
% 5.64/5.94 thf(fact_5844_neg__numeral__le__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_one
% 5.64/5.94 thf(fact_5845_neg__numeral__le__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_one
% 5.64/5.94 thf(fact_5846_neg__numeral__le__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_one
% 5.64/5.94 thf(fact_5847_neg__numeral__le__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_one
% 5.64/5.94 thf(fact_5848_neg__one__le__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_le_numeral
% 5.64/5.94 thf(fact_5849_neg__one__le__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_le_numeral
% 5.64/5.94 thf(fact_5850_neg__one__le__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_le_numeral
% 5.64/5.94 thf(fact_5851_neg__one__le__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_le_numeral
% 5.64/5.94 thf(fact_5852_neg__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_neg_one
% 5.64/5.94 thf(fact_5853_neg__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_neg_one
% 5.64/5.94 thf(fact_5854_neg__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_neg_one
% 5.64/5.94 thf(fact_5855_neg__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_le_neg_one
% 5.64/5.94 thf(fact_5856_not__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_one
% 5.64/5.94 thf(fact_5857_not__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_one
% 5.64/5.94 thf(fact_5858_not__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_one
% 5.64/5.94 thf(fact_5859_not__numeral__le__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_le_neg_one
% 5.64/5.94 thf(fact_5860_not__one__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_le_neg_numeral
% 5.64/5.94 thf(fact_5861_not__one__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_le_neg_numeral
% 5.64/5.94 thf(fact_5862_not__one__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_le_neg_numeral
% 5.64/5.94 thf(fact_5863_not__one__le__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_le_neg_numeral
% 5.64/5.94 thf(fact_5864_not__neg__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_less_neg_numeral
% 5.64/5.94 thf(fact_5865_not__neg__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_less_neg_numeral
% 5.64/5.94 thf(fact_5866_not__neg__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_less_neg_numeral
% 5.64/5.94 thf(fact_5867_not__neg__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_neg_one_less_neg_numeral
% 5.64/5.94 thf(fact_5868_not__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_less_neg_numeral
% 5.64/5.94 thf(fact_5869_not__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_less_neg_numeral
% 5.64/5.94 thf(fact_5870_not__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_less_neg_numeral
% 5.64/5.94 thf(fact_5871_not__one__less__neg__numeral,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_one_less_neg_numeral
% 5.64/5.94 thf(fact_5872_not__numeral__less__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_one
% 5.64/5.94 thf(fact_5873_not__numeral__less__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_one
% 5.64/5.94 thf(fact_5874_not__numeral__less__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_one
% 5.64/5.94 thf(fact_5875_not__numeral__less__neg__one,axiom,
% 5.64/5.94 ! [M: num] :
% 5.64/5.94 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % not_numeral_less_neg_one
% 5.64/5.94 thf(fact_5876_neg__one__less__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_less_numeral
% 5.64/5.94 thf(fact_5877_neg__one__less__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_less_numeral
% 5.64/5.94 thf(fact_5878_neg__one__less__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_less_numeral
% 5.64/5.94 thf(fact_5879_neg__one__less__numeral,axiom,
% 5.64/5.94 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.64/5.94
% 5.64/5.94 % neg_one_less_numeral
% 5.64/5.94 thf(fact_5880_neg__numeral__less__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_one
% 5.64/5.94 thf(fact_5881_neg__numeral__less__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_one
% 5.64/5.94 thf(fact_5882_neg__numeral__less__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_one
% 5.64/5.94 thf(fact_5883_neg__numeral__less__one,axiom,
% 5.64/5.94 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.64/5.94
% 5.64/5.94 % neg_numeral_less_one
% 5.64/5.94 thf(fact_5884_nonzero__neg__divide__eq__eq2,axiom,
% 5.64/5.94 ! [B: real,C: real,A: real] :
% 5.64/5.94 ( ( B != zero_zero_real )
% 5.64/5.94 => ( ( C
% 5.64/5.94 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.64/5.94 = ( ( times_times_real @ C @ B )
% 5.64/5.94 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_neg_divide_eq_eq2
% 5.64/5.94 thf(fact_5885_nonzero__neg__divide__eq__eq2,axiom,
% 5.64/5.94 ! [B: complex,C: complex,A: complex] :
% 5.64/5.94 ( ( B != zero_zero_complex )
% 5.64/5.94 => ( ( C
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/5.94 = ( ( times_times_complex @ C @ B )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_neg_divide_eq_eq2
% 5.64/5.94 thf(fact_5886_nonzero__neg__divide__eq__eq2,axiom,
% 5.64/5.94 ! [B: rat,C: rat,A: rat] :
% 5.64/5.94 ( ( B != zero_zero_rat )
% 5.64/5.94 => ( ( C
% 5.64/5.94 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.64/5.94 = ( ( times_times_rat @ C @ B )
% 5.64/5.94 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_neg_divide_eq_eq2
% 5.64/5.94 thf(fact_5887_nonzero__neg__divide__eq__eq,axiom,
% 5.64/5.94 ! [B: real,A: real,C: real] :
% 5.64/5.94 ( ( B != zero_zero_real )
% 5.64/5.94 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.94 = C )
% 5.64/5.94 = ( ( uminus_uminus_real @ A )
% 5.64/5.94 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_neg_divide_eq_eq
% 5.64/5.94 thf(fact_5888_nonzero__neg__divide__eq__eq,axiom,
% 5.64/5.94 ! [B: complex,A: complex,C: complex] :
% 5.64/5.94 ( ( B != zero_zero_complex )
% 5.64/5.94 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.94 = C )
% 5.64/5.94 = ( ( uminus1482373934393186551omplex @ A )
% 5.64/5.94 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_neg_divide_eq_eq
% 5.64/5.94 thf(fact_5889_nonzero__neg__divide__eq__eq,axiom,
% 5.64/5.94 ! [B: rat,A: rat,C: rat] :
% 5.64/5.94 ( ( B != zero_zero_rat )
% 5.64/5.94 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.94 = C )
% 5.64/5.94 = ( ( uminus_uminus_rat @ A )
% 5.64/5.94 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % nonzero_neg_divide_eq_eq
% 5.64/5.94 thf(fact_5890_minus__divide__eq__eq,axiom,
% 5.64/5.94 ! [B: real,C: real,A: real] :
% 5.64/5.94 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.64/5.94 = A )
% 5.64/5.94 = ( ( ( C != zero_zero_real )
% 5.64/5.94 => ( ( uminus_uminus_real @ B )
% 5.64/5.94 = ( times_times_real @ A @ C ) ) )
% 5.64/5.94 & ( ( C = zero_zero_real )
% 5.64/5.94 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_eq_eq
% 5.64/5.94 thf(fact_5891_minus__divide__eq__eq,axiom,
% 5.64/5.94 ! [B: complex,C: complex,A: complex] :
% 5.64/5.94 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.94 = A )
% 5.64/5.94 = ( ( ( C != zero_zero_complex )
% 5.64/5.94 => ( ( uminus1482373934393186551omplex @ B )
% 5.64/5.94 = ( times_times_complex @ A @ C ) ) )
% 5.64/5.94 & ( ( C = zero_zero_complex )
% 5.64/5.94 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_eq_eq
% 5.64/5.94 thf(fact_5892_minus__divide__eq__eq,axiom,
% 5.64/5.94 ! [B: rat,C: rat,A: rat] :
% 5.64/5.94 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.94 = A )
% 5.64/5.94 = ( ( ( C != zero_zero_rat )
% 5.64/5.94 => ( ( uminus_uminus_rat @ B )
% 5.64/5.94 = ( times_times_rat @ A @ C ) ) )
% 5.64/5.94 & ( ( C = zero_zero_rat )
% 5.64/5.94 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % minus_divide_eq_eq
% 5.64/5.94 thf(fact_5893_eq__minus__divide__eq,axiom,
% 5.64/5.94 ! [A: real,B: real,C: real] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.94 = ( ( ( C != zero_zero_real )
% 5.64/5.94 => ( ( times_times_real @ A @ C )
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) )
% 5.64/5.94 & ( ( C = zero_zero_real )
% 5.64/5.94 => ( A = zero_zero_real ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_minus_divide_eq
% 5.64/5.94 thf(fact_5894_eq__minus__divide__eq,axiom,
% 5.64/5.94 ! [A: complex,B: complex,C: complex] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.64/5.94 = ( ( ( C != zero_zero_complex )
% 5.64/5.94 => ( ( times_times_complex @ A @ C )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.64/5.94 & ( ( C = zero_zero_complex )
% 5.64/5.94 => ( A = zero_zero_complex ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_minus_divide_eq
% 5.64/5.94 thf(fact_5895_eq__minus__divide__eq,axiom,
% 5.64/5.94 ! [A: rat,B: rat,C: rat] :
% 5.64/5.94 ( ( A
% 5.64/5.94 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.94 = ( ( ( C != zero_zero_rat )
% 5.64/5.94 => ( ( times_times_rat @ A @ C )
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) )
% 5.64/5.94 & ( ( C = zero_zero_rat )
% 5.64/5.94 => ( A = zero_zero_rat ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % eq_minus_divide_eq
% 5.64/5.94 thf(fact_5896_mult__1s__ring__1_I1_J,axiom,
% 5.64/5.94 ! [B: int] :
% 5.64/5.94 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.64/5.94 = ( uminus_uminus_int @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(1)
% 5.64/5.94 thf(fact_5897_mult__1s__ring__1_I1_J,axiom,
% 5.64/5.94 ! [B: real] :
% 5.64/5.94 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(1)
% 5.64/5.94 thf(fact_5898_mult__1s__ring__1_I1_J,axiom,
% 5.64/5.94 ! [B: complex] :
% 5.64/5.94 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(1)
% 5.64/5.94 thf(fact_5899_mult__1s__ring__1_I1_J,axiom,
% 5.64/5.94 ! [B: rat] :
% 5.64/5.94 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(1)
% 5.64/5.94 thf(fact_5900_mult__1s__ring__1_I1_J,axiom,
% 5.64/5.94 ! [B: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(1)
% 5.64/5.94 thf(fact_5901_mult__1s__ring__1_I2_J,axiom,
% 5.64/5.94 ! [B: int] :
% 5.64/5.94 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.64/5.94 = ( uminus_uminus_int @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(2)
% 5.64/5.94 thf(fact_5902_mult__1s__ring__1_I2_J,axiom,
% 5.64/5.94 ! [B: real] :
% 5.64/5.94 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(2)
% 5.64/5.94 thf(fact_5903_mult__1s__ring__1_I2_J,axiom,
% 5.64/5.94 ! [B: complex] :
% 5.64/5.94 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(2)
% 5.64/5.94 thf(fact_5904_mult__1s__ring__1_I2_J,axiom,
% 5.64/5.94 ! [B: rat] :
% 5.64/5.94 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(2)
% 5.64/5.94 thf(fact_5905_mult__1s__ring__1_I2_J,axiom,
% 5.64/5.94 ! [B: code_integer] :
% 5.64/5.94 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.64/5.94
% 5.64/5.94 % mult_1s_ring_1(2)
% 5.64/5.94 thf(fact_5906_divide__eq__minus__1__iff,axiom,
% 5.64/5.94 ! [A: real,B: real] :
% 5.64/5.94 ( ( ( divide_divide_real @ A @ B )
% 5.64/5.94 = ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.94 = ( ( B != zero_zero_real )
% 5.64/5.94 & ( A
% 5.64/5.94 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_eq_minus_1_iff
% 5.64/5.94 thf(fact_5907_divide__eq__minus__1__iff,axiom,
% 5.64/5.94 ! [A: complex,B: complex] :
% 5.64/5.94 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.94 = ( ( B != zero_zero_complex )
% 5.64/5.94 & ( A
% 5.64/5.94 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_eq_minus_1_iff
% 5.64/5.94 thf(fact_5908_divide__eq__minus__1__iff,axiom,
% 5.64/5.94 ! [A: rat,B: rat] :
% 5.64/5.94 ( ( ( divide_divide_rat @ A @ B )
% 5.64/5.94 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.94 = ( ( B != zero_zero_rat )
% 5.64/5.94 & ( A
% 5.64/5.94 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % divide_eq_minus_1_iff
% 5.64/5.94 thf(fact_5909_uminus__numeral__One,axiom,
% 5.64/5.94 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.64/5.94 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_numeral_One
% 5.64/5.94 thf(fact_5910_uminus__numeral__One,axiom,
% 5.64/5.94 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.64/5.94 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_numeral_One
% 5.64/5.94 thf(fact_5911_uminus__numeral__One,axiom,
% 5.64/5.94 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.64/5.94 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_numeral_One
% 5.64/5.94 thf(fact_5912_uminus__numeral__One,axiom,
% 5.64/5.94 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.64/5.94 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_numeral_One
% 5.64/5.94 thf(fact_5913_uminus__numeral__One,axiom,
% 5.64/5.94 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.64/5.94 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.94
% 5.64/5.94 % uminus_numeral_One
% 5.64/5.94 thf(fact_5914_power__minus,axiom,
% 5.64/5.94 ! [A: int,N: nat] :
% 5.64/5.94 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.64/5.94 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus
% 5.64/5.94 thf(fact_5915_power__minus,axiom,
% 5.64/5.94 ! [A: real,N: nat] :
% 5.64/5.94 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.64/5.94 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus
% 5.64/5.94 thf(fact_5916_power__minus,axiom,
% 5.64/5.94 ! [A: complex,N: nat] :
% 5.64/5.94 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.64/5.94 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus
% 5.64/5.94 thf(fact_5917_power__minus,axiom,
% 5.64/5.94 ! [A: rat,N: nat] :
% 5.64/5.94 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.64/5.94 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus
% 5.64/5.94 thf(fact_5918_power__minus,axiom,
% 5.64/5.94 ! [A: code_integer,N: nat] :
% 5.64/5.94 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.64/5.94 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus
% 5.64/5.94 thf(fact_5919_power__minus__Bit0,axiom,
% 5.64/5.94 ! [X2: int,K: num] :
% 5.64/5.94 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.94 = ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_Bit0
% 5.64/5.94 thf(fact_5920_power__minus__Bit0,axiom,
% 5.64/5.94 ! [X2: real,K: num] :
% 5.64/5.94 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.94 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_Bit0
% 5.64/5.94 thf(fact_5921_power__minus__Bit0,axiom,
% 5.64/5.94 ! [X2: complex,K: num] :
% 5.64/5.94 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.94 = ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.64/5.94
% 5.64/5.94 % power_minus_Bit0
% 5.64/5.94 thf(fact_5922_power__minus__Bit0,axiom,
% 5.64/5.94 ! [X2: rat,K: num] :
% 5.64/5.95 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.95 = ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit0
% 5.64/5.95 thf(fact_5923_power__minus__Bit0,axiom,
% 5.64/5.95 ! [X2: code_integer,K: num] :
% 5.64/5.95 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit0
% 5.64/5.95 thf(fact_5924_power__minus__Bit1,axiom,
% 5.64/5.95 ! [X2: int,K: num] :
% 5.64/5.95 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit1
% 5.64/5.95 thf(fact_5925_power__minus__Bit1,axiom,
% 5.64/5.95 ! [X2: real,K: num] :
% 5.64/5.95 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit1
% 5.64/5.95 thf(fact_5926_power__minus__Bit1,axiom,
% 5.64/5.95 ! [X2: complex,K: num] :
% 5.64/5.95 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit1
% 5.64/5.95 thf(fact_5927_power__minus__Bit1,axiom,
% 5.64/5.95 ! [X2: rat,K: num] :
% 5.64/5.95 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit1
% 5.64/5.95 thf(fact_5928_power__minus__Bit1,axiom,
% 5.64/5.95 ! [X2: code_integer,K: num] :
% 5.64/5.95 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus_Bit1
% 5.64/5.95 thf(fact_5929_real__add__less__0__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y4 ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_real @ Y4 @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % real_add_less_0_iff
% 5.64/5.95 thf(fact_5930_real__0__less__add__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.95 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % real_0_less_add_iff
% 5.64/5.95 thf(fact_5931_pred__numeral__def,axiom,
% 5.64/5.95 ( pred_numeral
% 5.64/5.95 = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_numeral_def
% 5.64/5.95 thf(fact_5932_pos__minus__divide__less__eq,axiom,
% 5.64/5.95 ! [C: real,B: real,A: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_minus_divide_less_eq
% 5.64/5.95 thf(fact_5933_pos__minus__divide__less__eq,axiom,
% 5.64/5.95 ! [C: rat,B: rat,A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_minus_divide_less_eq
% 5.64/5.95 thf(fact_5934_pos__less__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: real,A: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_less_minus_divide_eq
% 5.64/5.95 thf(fact_5935_pos__less__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_less_minus_divide_eq
% 5.64/5.95 thf(fact_5936_neg__minus__divide__less__eq,axiom,
% 5.64/5.95 ! [C: real,B: real,A: real] :
% 5.64/5.95 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_minus_divide_less_eq
% 5.64/5.95 thf(fact_5937_neg__minus__divide__less__eq,axiom,
% 5.64/5.95 ! [C: rat,B: rat,A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_minus_divide_less_eq
% 5.64/5.95 thf(fact_5938_neg__less__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: real,A: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_less_minus_divide_eq
% 5.64/5.95 thf(fact_5939_neg__less__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_less_minus_divide_eq
% 5.64/5.95 thf(fact_5940_minus__divide__less__eq,axiom,
% 5.64/5.95 ! [B: real,C: real,A: real] :
% 5.64/5.95 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_less_eq
% 5.64/5.95 thf(fact_5941_minus__divide__less__eq,axiom,
% 5.64/5.95 ! [B: rat,C: rat,A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_less_eq
% 5.64/5.95 thf(fact_5942_less__minus__divide__eq,axiom,
% 5.64/5.95 ! [A: real,B: real,C: real] :
% 5.64/5.95 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % less_minus_divide_eq
% 5.64/5.95 thf(fact_5943_less__minus__divide__eq,axiom,
% 5.64/5.95 ! [A: rat,B: rat,C: rat] :
% 5.64/5.95 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % less_minus_divide_eq
% 5.64/5.95 thf(fact_5944_divide__eq__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: real,C: real,W: num] :
% 5.64/5.95 ( ( ( divide_divide_real @ B @ C )
% 5.64/5.95 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.95 = ( ( ( C != zero_zero_real )
% 5.64/5.95 => ( B
% 5.64/5.95 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ( C = zero_zero_real )
% 5.64/5.95 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.95 = zero_zero_real ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_eq_eq_numeral(2)
% 5.64/5.95 thf(fact_5945_divide__eq__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: complex,C: complex,W: num] :
% 5.64/5.95 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.95 = ( ( ( C != zero_zero_complex )
% 5.64/5.95 => ( B
% 5.64/5.95 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ( C = zero_zero_complex )
% 5.64/5.95 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.95 = zero_zero_complex ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_eq_eq_numeral(2)
% 5.64/5.95 thf(fact_5946_divide__eq__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: rat,C: rat,W: num] :
% 5.64/5.95 ( ( ( divide_divide_rat @ B @ C )
% 5.64/5.95 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.95 = ( ( ( C != zero_zero_rat )
% 5.64/5.95 => ( B
% 5.64/5.95 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ( C = zero_zero_rat )
% 5.64/5.95 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.95 = zero_zero_rat ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_eq_eq_numeral(2)
% 5.64/5.95 thf(fact_5947_eq__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: real,C: real] :
% 5.64/5.95 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.95 = ( divide_divide_real @ B @ C ) )
% 5.64/5.95 = ( ( ( C != zero_zero_real )
% 5.64/5.95 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.64/5.95 = B ) )
% 5.64/5.95 & ( ( C = zero_zero_real )
% 5.64/5.95 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.95 = zero_zero_real ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_5948_eq__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: complex,C: complex] :
% 5.64/5.95 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.95 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.64/5.95 = ( ( ( C != zero_zero_complex )
% 5.64/5.95 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.64/5.95 = B ) )
% 5.64/5.95 & ( ( C = zero_zero_complex )
% 5.64/5.95 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.95 = zero_zero_complex ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_5949_eq__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: rat,C: rat] :
% 5.64/5.95 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.95 = ( divide_divide_rat @ B @ C ) )
% 5.64/5.95 = ( ( ( C != zero_zero_rat )
% 5.64/5.95 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.64/5.95 = B ) )
% 5.64/5.95 & ( ( C = zero_zero_rat )
% 5.64/5.95 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.64/5.95 = zero_zero_rat ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_5950_minus__divide__add__eq__iff,axiom,
% 5.64/5.95 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.95 ( ( Z != zero_zero_real )
% 5.64/5.95 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y4 )
% 5.64/5.95 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_add_eq_iff
% 5.64/5.95 thf(fact_5951_minus__divide__add__eq__iff,axiom,
% 5.64/5.95 ! [Z: complex,X2: complex,Y4: complex] :
% 5.64/5.95 ( ( Z != zero_zero_complex )
% 5.64/5.95 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y4 )
% 5.64/5.95 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_add_eq_iff
% 5.64/5.95 thf(fact_5952_minus__divide__add__eq__iff,axiom,
% 5.64/5.95 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.95 ( ( Z != zero_zero_rat )
% 5.64/5.95 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y4 )
% 5.64/5.95 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_add_eq_iff
% 5.64/5.95 thf(fact_5953_add__divide__eq__if__simps_I3_J,axiom,
% 5.64/5.95 ! [Z: real,A: real,B: real] :
% 5.64/5.95 ( ( ( Z = zero_zero_real )
% 5.64/5.95 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.64/5.95 = B ) )
% 5.64/5.95 & ( ( Z != zero_zero_real )
% 5.64/5.95 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.64/5.95 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(3)
% 5.64/5.95 thf(fact_5954_add__divide__eq__if__simps_I3_J,axiom,
% 5.64/5.95 ! [Z: complex,A: complex,B: complex] :
% 5.64/5.95 ( ( ( Z = zero_zero_complex )
% 5.64/5.95 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.64/5.95 = B ) )
% 5.64/5.95 & ( ( Z != zero_zero_complex )
% 5.64/5.95 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.64/5.95 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(3)
% 5.64/5.95 thf(fact_5955_add__divide__eq__if__simps_I3_J,axiom,
% 5.64/5.95 ! [Z: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ( Z = zero_zero_rat )
% 5.64/5.95 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.64/5.95 = B ) )
% 5.64/5.95 & ( ( Z != zero_zero_rat )
% 5.64/5.95 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.64/5.95 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(3)
% 5.64/5.95 thf(fact_5956_add__divide__eq__if__simps_I6_J,axiom,
% 5.64/5.95 ! [Z: real,A: real,B: real] :
% 5.64/5.95 ( ( ( Z = zero_zero_real )
% 5.64/5.95 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.64/5.95 = ( uminus_uminus_real @ B ) ) )
% 5.64/5.95 & ( ( Z != zero_zero_real )
% 5.64/5.95 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.64/5.95 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(6)
% 5.64/5.95 thf(fact_5957_add__divide__eq__if__simps_I6_J,axiom,
% 5.64/5.95 ! [Z: complex,A: complex,B: complex] :
% 5.64/5.95 ( ( ( Z = zero_zero_complex )
% 5.64/5.95 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.64/5.95 & ( ( Z != zero_zero_complex )
% 5.64/5.95 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.64/5.95 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(6)
% 5.64/5.95 thf(fact_5958_add__divide__eq__if__simps_I6_J,axiom,
% 5.64/5.95 ! [Z: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ( Z = zero_zero_rat )
% 5.64/5.95 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.64/5.95 = ( uminus_uminus_rat @ B ) ) )
% 5.64/5.95 & ( ( Z != zero_zero_rat )
% 5.64/5.95 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.64/5.95 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(6)
% 5.64/5.95 thf(fact_5959_add__divide__eq__if__simps_I5_J,axiom,
% 5.64/5.95 ! [Z: real,A: real,B: real] :
% 5.64/5.95 ( ( ( Z = zero_zero_real )
% 5.64/5.95 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.64/5.95 = ( uminus_uminus_real @ B ) ) )
% 5.64/5.95 & ( ( Z != zero_zero_real )
% 5.64/5.95 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.64/5.95 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(5)
% 5.64/5.95 thf(fact_5960_add__divide__eq__if__simps_I5_J,axiom,
% 5.64/5.95 ! [Z: complex,A: complex,B: complex] :
% 5.64/5.95 ( ( ( Z = zero_zero_complex )
% 5.64/5.95 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.64/5.95 & ( ( Z != zero_zero_complex )
% 5.64/5.95 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.64/5.95 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(5)
% 5.64/5.95 thf(fact_5961_add__divide__eq__if__simps_I5_J,axiom,
% 5.64/5.95 ! [Z: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ( Z = zero_zero_rat )
% 5.64/5.95 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.64/5.95 = ( uminus_uminus_rat @ B ) ) )
% 5.64/5.95 & ( ( Z != zero_zero_rat )
% 5.64/5.95 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.64/5.95 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_divide_eq_if_simps(5)
% 5.64/5.95 thf(fact_5962_minus__divide__diff__eq__iff,axiom,
% 5.64/5.95 ! [Z: real,X2: real,Y4: real] :
% 5.64/5.95 ( ( Z != zero_zero_real )
% 5.64/5.95 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y4 )
% 5.64/5.95 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_diff_eq_iff
% 5.64/5.95 thf(fact_5963_minus__divide__diff__eq__iff,axiom,
% 5.64/5.95 ! [Z: complex,X2: complex,Y4: complex] :
% 5.64/5.95 ( ( Z != zero_zero_complex )
% 5.64/5.95 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y4 )
% 5.64/5.95 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_diff_eq_iff
% 5.64/5.95 thf(fact_5964_minus__divide__diff__eq__iff,axiom,
% 5.64/5.95 ! [Z: rat,X2: rat,Y4: rat] :
% 5.64/5.95 ( ( Z != zero_zero_rat )
% 5.64/5.95 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y4 )
% 5.64/5.95 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y4 @ Z ) ) @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_diff_eq_iff
% 5.64/5.95 thf(fact_5965_even__minus,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.64/5.95 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_minus
% 5.64/5.95 thf(fact_5966_even__minus,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.95 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_minus
% 5.64/5.95 thf(fact_5967_power2__eq__iff,axiom,
% 5.64/5.95 ! [X2: int,Y4: int] :
% 5.64/5.95 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ( X2 = Y4 )
% 5.64/5.95 | ( X2
% 5.64/5.95 = ( uminus_uminus_int @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_iff
% 5.64/5.95 thf(fact_5968_power2__eq__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ( X2 = Y4 )
% 5.64/5.95 | ( X2
% 5.64/5.95 = ( uminus_uminus_real @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_iff
% 5.64/5.95 thf(fact_5969_power2__eq__iff,axiom,
% 5.64/5.95 ! [X2: complex,Y4: complex] :
% 5.64/5.95 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_complex @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ( X2 = Y4 )
% 5.64/5.95 | ( X2
% 5.64/5.95 = ( uminus1482373934393186551omplex @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_iff
% 5.64/5.95 thf(fact_5970_power2__eq__iff,axiom,
% 5.64/5.95 ! [X2: rat,Y4: rat] :
% 5.64/5.95 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ( X2 = Y4 )
% 5.64/5.95 | ( X2
% 5.64/5.95 = ( uminus_uminus_rat @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_iff
% 5.64/5.95 thf(fact_5971_power2__eq__iff,axiom,
% 5.64/5.95 ! [X2: code_integer,Y4: code_integer] :
% 5.64/5.95 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ( X2 = Y4 )
% 5.64/5.95 | ( X2
% 5.64/5.95 = ( uminus1351360451143612070nteger @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_iff
% 5.64/5.95 thf(fact_5972_verit__less__mono__div__int2,axiom,
% 5.64/5.95 ! [A4: int,B4: int,N: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.64/5.95 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N ) @ ( divide_divide_int @ A4 @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % verit_less_mono_div_int2
% 5.64/5.95 thf(fact_5973_div__eq__minus1,axiom,
% 5.64/5.95 ! [B: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.95 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % div_eq_minus1
% 5.64/5.95 thf(fact_5974_pos__minus__divide__le__eq,axiom,
% 5.64/5.95 ! [C: rat,B: rat,A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_minus_divide_le_eq
% 5.64/5.95 thf(fact_5975_pos__minus__divide__le__eq,axiom,
% 5.64/5.95 ! [C: real,B: real,A: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_minus_divide_le_eq
% 5.64/5.95 thf(fact_5976_pos__le__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_le_minus_divide_eq
% 5.64/5.95 thf(fact_5977_pos__le__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: real,A: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % pos_le_minus_divide_eq
% 5.64/5.95 thf(fact_5978_neg__minus__divide__le__eq,axiom,
% 5.64/5.95 ! [C: rat,B: rat,A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_minus_divide_le_eq
% 5.64/5.95 thf(fact_5979_neg__minus__divide__le__eq,axiom,
% 5.64/5.95 ! [C: real,B: real,A: real] :
% 5.64/5.95 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.64/5.95 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_minus_divide_le_eq
% 5.64/5.95 thf(fact_5980_neg__le__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: rat,A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_le_minus_divide_eq
% 5.64/5.95 thf(fact_5981_neg__le__minus__divide__eq,axiom,
% 5.64/5.95 ! [C: real,A: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.95 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_le_minus_divide_eq
% 5.64/5.95 thf(fact_5982_minus__divide__le__eq,axiom,
% 5.64/5.95 ! [B: rat,C: rat,A: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_le_eq
% 5.64/5.95 thf(fact_5983_minus__divide__le__eq,axiom,
% 5.64/5.95 ! [B: real,C: real,A: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_divide_le_eq
% 5.64/5.95 thf(fact_5984_le__minus__divide__eq,axiom,
% 5.64/5.95 ! [A: rat,B: rat,C: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % le_minus_divide_eq
% 5.64/5.95 thf(fact_5985_le__minus__divide__eq,axiom,
% 5.64/5.95 ! [A: real,B: real,C: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % le_minus_divide_eq
% 5.64/5.95 thf(fact_5986_less__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: real,C: real] :
% 5.64/5.95 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % less_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_5987_less__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: rat,C: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % less_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_5988_divide__less__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: real,C: real,W: num] :
% 5.64/5.95 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_less_eq_numeral(2)
% 5.64/5.95 thf(fact_5989_divide__less__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: rat,C: rat,W: num] :
% 5.64/5.95 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_less_eq_numeral(2)
% 5.64/5.95 thf(fact_5990_power2__eq__1__iff,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_int )
% 5.64/5.95 = ( ( A = one_one_int )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_1_iff
% 5.64/5.95 thf(fact_5991_power2__eq__1__iff,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_real )
% 5.64/5.95 = ( ( A = one_one_real )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_1_iff
% 5.64/5.95 thf(fact_5992_power2__eq__1__iff,axiom,
% 5.64/5.95 ! [A: complex] :
% 5.64/5.95 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_complex )
% 5.64/5.95 = ( ( A = one_one_complex )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_1_iff
% 5.64/5.95 thf(fact_5993_power2__eq__1__iff,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_rat )
% 5.64/5.95 = ( ( A = one_one_rat )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_1_iff
% 5.64/5.95 thf(fact_5994_power2__eq__1__iff,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_Code_integer )
% 5.64/5.95 = ( ( A = one_one_Code_integer )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_eq_1_iff
% 5.64/5.95 thf(fact_5995_uminus__power__if,axiom,
% 5.64/5.95 ! [N: nat,A: int] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.64/5.95 = ( power_power_int @ A @ N ) ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.64/5.95 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % uminus_power_if
% 5.64/5.95 thf(fact_5996_uminus__power__if,axiom,
% 5.64/5.95 ! [N: nat,A: real] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.64/5.95 = ( power_power_real @ A @ N ) ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.64/5.95 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % uminus_power_if
% 5.64/5.95 thf(fact_5997_uminus__power__if,axiom,
% 5.64/5.95 ! [N: nat,A: complex] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.64/5.95 = ( power_power_complex @ A @ N ) ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % uminus_power_if
% 5.64/5.95 thf(fact_5998_uminus__power__if,axiom,
% 5.64/5.95 ! [N: nat,A: rat] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.64/5.95 = ( power_power_rat @ A @ N ) ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.64/5.95 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % uminus_power_if
% 5.64/5.95 thf(fact_5999_uminus__power__if,axiom,
% 5.64/5.95 ! [N: nat,A: code_integer] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.64/5.95 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % uminus_power_if
% 5.64/5.95 thf(fact_6000_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.64/5.95 ! [K: nat,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.95 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_one_power_add_eq_neg_one_power_diff
% 5.64/5.95 thf(fact_6001_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.64/5.95 ! [K: nat,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.95 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.64/5.95 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_one_power_add_eq_neg_one_power_diff
% 5.64/5.95 thf(fact_6002_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.64/5.95 ! [K: nat,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.95 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.64/5.95 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_one_power_add_eq_neg_one_power_diff
% 5.64/5.95 thf(fact_6003_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.64/5.95 ! [K: nat,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.95 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.64/5.95 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_one_power_add_eq_neg_one_power_diff
% 5.64/5.95 thf(fact_6004_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.64/5.95 ! [K: nat,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_one_power_add_eq_neg_one_power_diff
% 5.64/5.95 thf(fact_6005_realpow__square__minus__le,axiom,
% 5.64/5.95 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % realpow_square_minus_le
% 5.64/5.95 thf(fact_6006_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.64/5.95 ! [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 ) ) ).
% 5.64/5.95
% 5.64/5.95 % signed_take_bit_int_greater_eq_minus_exp
% 5.64/5.95 thf(fact_6007_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.64/5.95 ! [N: nat,K: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.64/5.95 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % signed_take_bit_int_less_eq_self_iff
% 5.64/5.95 thf(fact_6008_signed__take__bit__int__greater__self__iff,axiom,
% 5.64/5.95 ! [K: int,N: nat] :
% 5.64/5.95 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.64/5.95 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % signed_take_bit_int_greater_self_iff
% 5.64/5.95 thf(fact_6009_zmod__minus1,axiom,
% 5.64/5.95 ! [B: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/5.95 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.64/5.95 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zmod_minus1
% 5.64/5.95 thf(fact_6010_zdiv__zminus2__eq__if,axiom,
% 5.64/5.95 ! [B: int,A: int] :
% 5.64/5.95 ( ( B != zero_zero_int )
% 5.64/5.95 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.64/5.95 & ( ( ( modulo_modulo_int @ A @ B )
% 5.64/5.95 != zero_zero_int )
% 5.64/5.95 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.64/5.95 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zdiv_zminus2_eq_if
% 5.64/5.95 thf(fact_6011_zdiv__zminus1__eq__if,axiom,
% 5.64/5.95 ! [B: int,A: int] :
% 5.64/5.95 ( ( B != zero_zero_int )
% 5.64/5.95 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.95 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.64/5.95 & ( ( ( modulo_modulo_int @ A @ B )
% 5.64/5.95 != zero_zero_int )
% 5.64/5.95 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.95 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zdiv_zminus1_eq_if
% 5.64/5.95 thf(fact_6012_le__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: rat,C: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % le_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_6013_le__divide__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [W: num,B: real,C: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % le_divide_eq_numeral(2)
% 5.64/5.95 thf(fact_6014_divide__le__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: rat,C: rat,W: num] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.64/5.95 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.64/5.95 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_le_eq_numeral(2)
% 5.64/5.95 thf(fact_6015_divide__le__eq__numeral_I2_J,axiom,
% 5.64/5.95 ! [B: real,C: real,W: num] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.95 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.64/5.95 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.64/5.95 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_le_eq_numeral(2)
% 5.64/5.95 thf(fact_6016_square__le__1,axiom,
% 5.64/5.95 ! [X2: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.64/5.95 => ( ( ord_le3102999989581377725nteger @ X2 @ one_one_Code_integer )
% 5.64/5.95 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % square_le_1
% 5.64/5.95 thf(fact_6017_square__le__1,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 5.64/5.95 => ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % square_le_1
% 5.64/5.95 thf(fact_6018_square__le__1,axiom,
% 5.64/5.95 ! [X2: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_int @ X2 @ one_one_int )
% 5.64/5.95 => ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % square_le_1
% 5.64/5.95 thf(fact_6019_square__le__1,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % square_le_1
% 5.64/5.95 thf(fact_6020_minus__power__mult__self,axiom,
% 5.64/5.95 ! [A: int,N: nat] :
% 5.64/5.95 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.64/5.95 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_power_mult_self
% 5.64/5.95 thf(fact_6021_minus__power__mult__self,axiom,
% 5.64/5.95 ! [A: real,N: nat] :
% 5.64/5.95 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.64/5.95 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_power_mult_self
% 5.64/5.95 thf(fact_6022_minus__power__mult__self,axiom,
% 5.64/5.95 ! [A: complex,N: nat] :
% 5.64/5.95 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.64/5.95 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_power_mult_self
% 5.64/5.95 thf(fact_6023_minus__power__mult__self,axiom,
% 5.64/5.95 ! [A: rat,N: nat] :
% 5.64/5.95 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.64/5.95 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_power_mult_self
% 5.64/5.95 thf(fact_6024_minus__power__mult__self,axiom,
% 5.64/5.95 ! [A: code_integer,N: nat] :
% 5.64/5.95 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_power_mult_self
% 5.64/5.95 thf(fact_6025_minus__one__power__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.64/5.95 = one_one_int ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_one_power_iff
% 5.64/5.95 thf(fact_6026_minus__one__power__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.64/5.95 = one_one_real ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.64/5.95 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_one_power_iff
% 5.64/5.95 thf(fact_6027_minus__one__power__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.64/5.95 = one_one_complex ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_one_power_iff
% 5.64/5.95 thf(fact_6028_minus__one__power__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.64/5.95 = one_one_rat ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.64/5.95 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_one_power_iff
% 5.64/5.95 thf(fact_6029_minus__one__power__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.64/5.95 = one_one_Code_integer ) )
% 5.64/5.95 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_one_power_iff
% 5.64/5.95 thf(fact_6030_signed__take__bit__int__eq__self,axiom,
% 5.64/5.95 ! [N: nat,K: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.64/5.95 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.95 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.64/5.95 = K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % signed_take_bit_int_eq_self
% 5.64/5.95 thf(fact_6031_signed__take__bit__int__eq__self__iff,axiom,
% 5.64/5.95 ! [N: nat,K: int] :
% 5.64/5.95 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.64/5.95 = K )
% 5.64/5.95 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.64/5.95 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % signed_take_bit_int_eq_self_iff
% 5.64/5.95 thf(fact_6032_minus__1__div__exp__eq__int,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_1_div_exp_eq_int
% 5.64/5.95 thf(fact_6033_div__pos__neg__trivial,axiom,
% 5.64/5.95 ! [K: int,L: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.95 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.64/5.95 => ( ( divide_divide_int @ K @ L )
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % div_pos_neg_trivial
% 5.64/5.95 thf(fact_6034_power__minus1__odd,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus1_odd
% 5.64/5.95 thf(fact_6035_power__minus1__odd,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus1_odd
% 5.64/5.95 thf(fact_6036_power__minus1__odd,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus1_odd
% 5.64/5.95 thf(fact_6037_power__minus1__odd,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus1_odd
% 5.64/5.95 thf(fact_6038_power__minus1__odd,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_minus1_odd
% 5.64/5.95 thf(fact_6039_int__bit__induct,axiom,
% 5.64/5.95 ! [P: int > $o,K: int] :
% 5.64/5.95 ( ( P @ zero_zero_int )
% 5.64/5.95 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.95 => ( ! [K3: int] :
% 5.64/5.95 ( ( P @ K3 )
% 5.64/5.95 => ( ( K3 != zero_zero_int )
% 5.64/5.95 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.95 => ( ! [K3: int] :
% 5.64/5.95 ( ( P @ K3 )
% 5.64/5.95 => ( ( K3
% 5.64/5.95 != ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.95 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.64/5.95 => ( P @ K ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % int_bit_induct
% 5.64/5.95 thf(fact_6040_signed__take__bit__int__greater__eq,axiom,
% 5.64/5.95 ! [K: int,N: nat] :
% 5.64/5.95 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % signed_take_bit_int_greater_eq
% 5.64/5.95 thf(fact_6041_minus__one__div__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_one_div_numeral
% 5.64/5.95 thf(fact_6042_one__div__minus__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % one_div_minus_numeral
% 5.64/5.95 thf(fact_6043_minus__numeral__div__numeral,axiom,
% 5.64/5.95 ! [M: num,N: num] :
% 5.64/5.95 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % minus_numeral_div_numeral
% 5.64/5.95 thf(fact_6044_numeral__div__minus__numeral,axiom,
% 5.64/5.95 ! [M: num,N: num] :
% 5.64/5.95 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_div_minus_numeral
% 5.64/5.95 thf(fact_6045_dbl__dec__simps_I4_J,axiom,
% 5.64/5.95 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(4)
% 5.64/5.95 thf(fact_6046_dbl__dec__simps_I4_J,axiom,
% 5.64/5.95 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.95 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(4)
% 5.64/5.95 thf(fact_6047_dbl__dec__simps_I4_J,axiom,
% 5.64/5.95 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(4)
% 5.64/5.95 thf(fact_6048_dbl__dec__simps_I4_J,axiom,
% 5.64/5.95 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.95 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(4)
% 5.64/5.95 thf(fact_6049_dbl__dec__simps_I4_J,axiom,
% 5.64/5.95 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(4)
% 5.64/5.95 thf(fact_6050_of__int__code__if,axiom,
% 5.64/5.95 ( ring_1_of_int_int
% 5.64/5.95 = ( ^ [K2: int] :
% 5.64/5.95 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 5.64/5.95 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.64/5.95 @ ( if_int
% 5.64/5.95 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_code_if
% 5.64/5.95 thf(fact_6051_of__int__code__if,axiom,
% 5.64/5.95 ( ring_1_of_int_real
% 5.64/5.95 = ( ^ [K2: int] :
% 5.64/5.95 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 5.64/5.95 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 5.64/5.95 @ ( if_real
% 5.64/5.95 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_code_if
% 5.64/5.95 thf(fact_6052_of__int__code__if,axiom,
% 5.64/5.95 ( ring_17405671764205052669omplex
% 5.64/5.95 = ( ^ [K2: int] :
% 5.64/5.95 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 5.64/5.95 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 5.64/5.95 @ ( if_complex
% 5.64/5.95 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_code_if
% 5.64/5.95 thf(fact_6053_of__int__code__if,axiom,
% 5.64/5.95 ( ring_1_of_int_rat
% 5.64/5.95 = ( ^ [K2: int] :
% 5.64/5.95 ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 5.64/5.95 @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 5.64/5.95 @ ( if_rat
% 5.64/5.95 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_code_if
% 5.64/5.95 thf(fact_6054_of__int__code__if,axiom,
% 5.64/5.95 ( ring_18347121197199848620nteger
% 5.64/5.95 = ( ^ [K2: int] :
% 5.64/5.95 ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.64/5.95 @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 5.64/5.95 @ ( if_Code_integer
% 5.64/5.95 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_code_if
% 5.64/5.95 thf(fact_6055_dbl__dec__simps_I3_J,axiom,
% 5.64/5.95 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.64/5.95 = one_one_complex ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(3)
% 5.64/5.95 thf(fact_6056_dbl__dec__simps_I3_J,axiom,
% 5.64/5.95 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.64/5.95 = one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(3)
% 5.64/5.95 thf(fact_6057_dbl__dec__simps_I3_J,axiom,
% 5.64/5.95 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.64/5.95 = one_one_rat ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(3)
% 5.64/5.95 thf(fact_6058_dbl__dec__simps_I3_J,axiom,
% 5.64/5.95 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(3)
% 5.64/5.95 thf(fact_6059_of__int__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.64/5.95 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral
% 5.64/5.95 thf(fact_6060_of__int__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.64/5.95 = ( numeral_numeral_real @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral
% 5.64/5.95 thf(fact_6061_of__int__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.64/5.95 = ( numeral_numeral_rat @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral
% 5.64/5.95 thf(fact_6062_of__int__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.64/5.95 = ( numeral_numeral_int @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral
% 5.64/5.95 thf(fact_6063_of__int__eq__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.64/5.95 = ( numera6690914467698888265omplex @ N ) )
% 5.64/5.95 = ( Z
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_iff
% 5.64/5.95 thf(fact_6064_of__int__eq__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ( ring_1_of_int_real @ Z )
% 5.64/5.95 = ( numeral_numeral_real @ N ) )
% 5.64/5.95 = ( Z
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_iff
% 5.64/5.95 thf(fact_6065_of__int__eq__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ( ring_1_of_int_rat @ Z )
% 5.64/5.95 = ( numeral_numeral_rat @ N ) )
% 5.64/5.95 = ( Z
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_iff
% 5.64/5.95 thf(fact_6066_of__int__eq__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ( ring_1_of_int_int @ Z )
% 5.64/5.95 = ( numeral_numeral_int @ N ) )
% 5.64/5.95 = ( Z
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_iff
% 5.64/5.95 thf(fact_6067_of__int__le__iff,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_iff
% 5.64/5.95 thf(fact_6068_of__int__le__iff,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_iff
% 5.64/5.95 thf(fact_6069_of__int__le__iff,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_iff
% 5.64/5.95 thf(fact_6070_of__int__less__iff,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_int @ W @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_iff
% 5.64/5.95 thf(fact_6071_of__int__less__iff,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_int @ W @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_iff
% 5.64/5.95 thf(fact_6072_of__int__less__iff,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_int @ W @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_iff
% 5.64/5.95 thf(fact_6073_of__int__eq__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.64/5.95 = one_one_complex )
% 5.64/5.95 = ( Z = one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_1_iff
% 5.64/5.95 thf(fact_6074_of__int__eq__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ( ring_1_of_int_int @ Z )
% 5.64/5.95 = one_one_int )
% 5.64/5.95 = ( Z = one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_1_iff
% 5.64/5.95 thf(fact_6075_of__int__eq__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ( ring_1_of_int_real @ Z )
% 5.64/5.95 = one_one_real )
% 5.64/5.95 = ( Z = one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_1_iff
% 5.64/5.95 thf(fact_6076_of__int__eq__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ( ring_1_of_int_rat @ Z )
% 5.64/5.95 = one_one_rat )
% 5.64/5.95 = ( Z = one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_1_iff
% 5.64/5.95 thf(fact_6077_of__int__1,axiom,
% 5.64/5.95 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.64/5.95 = one_one_complex ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1
% 5.64/5.95 thf(fact_6078_of__int__1,axiom,
% 5.64/5.95 ( ( ring_1_of_int_int @ one_one_int )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1
% 5.64/5.95 thf(fact_6079_of__int__1,axiom,
% 5.64/5.95 ( ( ring_1_of_int_real @ one_one_int )
% 5.64/5.95 = one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1
% 5.64/5.95 thf(fact_6080_of__int__1,axiom,
% 5.64/5.95 ( ( ring_1_of_int_rat @ one_one_int )
% 5.64/5.95 = one_one_rat ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1
% 5.64/5.95 thf(fact_6081_of__int__mult,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.64/5.95 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_mult
% 5.64/5.95 thf(fact_6082_of__int__mult,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.64/5.95 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_mult
% 5.64/5.95 thf(fact_6083_of__int__mult,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.64/5.95 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_mult
% 5.64/5.95 thf(fact_6084_of__int__add,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.64/5.95 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_add
% 5.64/5.95 thf(fact_6085_of__int__add,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.64/5.95 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_add
% 5.64/5.95 thf(fact_6086_of__int__add,axiom,
% 5.64/5.95 ! [W: int,Z: int] :
% 5.64/5.95 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.64/5.95 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_add
% 5.64/5.95 thf(fact_6087_of__int__power,axiom,
% 5.64/5.95 ! [Z: int,N: nat] :
% 5.64/5.95 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.64/5.95 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power
% 5.64/5.95 thf(fact_6088_of__int__power,axiom,
% 5.64/5.95 ! [Z: int,N: nat] :
% 5.64/5.95 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.64/5.95 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power
% 5.64/5.95 thf(fact_6089_of__int__power,axiom,
% 5.64/5.95 ! [Z: int,N: nat] :
% 5.64/5.95 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.64/5.95 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power
% 5.64/5.95 thf(fact_6090_of__int__power,axiom,
% 5.64/5.95 ! [Z: int,N: nat] :
% 5.64/5.95 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.64/5.95 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power
% 5.64/5.95 thf(fact_6091_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.64/5.95 = ( ring_1_of_int_rat @ X2 ) )
% 5.64/5.95 = ( ( power_power_int @ B @ W )
% 5.64/5.95 = X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6092_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.64/5.95 = ( ring_1_of_int_real @ X2 ) )
% 5.64/5.95 = ( ( power_power_int @ B @ W )
% 5.64/5.95 = X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6093_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.64/5.95 = ( ring_1_of_int_int @ X2 ) )
% 5.64/5.95 = ( ( power_power_int @ B @ W )
% 5.64/5.95 = X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6094_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.64/5.95 = ( ring_17405671764205052669omplex @ X2 ) )
% 5.64/5.95 = ( ( power_power_int @ B @ W )
% 5.64/5.95 = X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6095_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_rat @ X2 )
% 5.64/5.95 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.64/5.95 = ( X2
% 5.64/5.95 = ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6096_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_real @ X2 )
% 5.64/5.95 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.64/5.95 = ( X2
% 5.64/5.95 = ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6097_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_int @ X2 )
% 5.64/5.95 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.64/5.95 = ( X2
% 5.64/5.95 = ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6098_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ( ring_17405671764205052669omplex @ X2 )
% 5.64/5.95 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.64/5.95 = ( X2
% 5.64/5.95 = ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6099_dbl__dec__simps_I5_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.64/5.95 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(5)
% 5.64/5.95 thf(fact_6100_dbl__dec__simps_I5_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.64/5.95 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(5)
% 5.64/5.95 thf(fact_6101_dbl__dec__simps_I5_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.64/5.95 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(5)
% 5.64/5.95 thf(fact_6102_dbl__dec__simps_I5_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.64/5.95 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(5)
% 5.64/5.95 thf(fact_6103_dbl__dec__simps_I2_J,axiom,
% 5.64/5.95 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.64/5.95 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(2)
% 5.64/5.95 thf(fact_6104_dbl__dec__simps_I2_J,axiom,
% 5.64/5.95 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.64/5.95 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(2)
% 5.64/5.95 thf(fact_6105_dbl__dec__simps_I2_J,axiom,
% 5.64/5.95 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(2)
% 5.64/5.95 thf(fact_6106_dbl__dec__simps_I2_J,axiom,
% 5.64/5.95 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.64/5.95 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(2)
% 5.64/5.95 thf(fact_6107_dbl__dec__simps_I2_J,axiom,
% 5.64/5.95 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(2)
% 5.64/5.95 thf(fact_6108_dbl__inc__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_inc_simps(1)
% 5.64/5.95 thf(fact_6109_dbl__inc__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_inc_simps(1)
% 5.64/5.95 thf(fact_6110_dbl__inc__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_inc_simps(1)
% 5.64/5.95 thf(fact_6111_dbl__inc__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_inc_simps(1)
% 5.64/5.95 thf(fact_6112_dbl__inc__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_inc_simps(1)
% 5.64/5.95 thf(fact_6113_dbl__dec__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(1)
% 5.64/5.95 thf(fact_6114_dbl__dec__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(1)
% 5.64/5.95 thf(fact_6115_dbl__dec__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(1)
% 5.64/5.95 thf(fact_6116_dbl__dec__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(1)
% 5.64/5.95 thf(fact_6117_dbl__dec__simps_I1_J,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_simps(1)
% 5.64/5.95 thf(fact_6118_of__int__0__le__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_0_le_iff
% 5.64/5.95 thf(fact_6119_of__int__0__le__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_0_le_iff
% 5.64/5.95 thf(fact_6120_of__int__0__le__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_0_le_iff
% 5.64/5.95 thf(fact_6121_of__int__le__0__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_0_iff
% 5.64/5.95 thf(fact_6122_of__int__le__0__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_0_iff
% 5.64/5.95 thf(fact_6123_of__int__le__0__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_0_iff
% 5.64/5.95 thf(fact_6124_of__int__0__less__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_0_less_iff
% 5.64/5.95 thf(fact_6125_of__int__0__less__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_0_less_iff
% 5.64/5.95 thf(fact_6126_of__int__0__less__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_0_less_iff
% 5.64/5.95 thf(fact_6127_of__int__less__0__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_0_iff
% 5.64/5.95 thf(fact_6128_of__int__less__0__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.64/5.95 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_0_iff
% 5.64/5.95 thf(fact_6129_of__int__less__0__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.64/5.95 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_0_iff
% 5.64/5.95 thf(fact_6130_of__int__le__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_numeral_iff
% 5.64/5.95 thf(fact_6131_of__int__le__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_numeral_iff
% 5.64/5.95 thf(fact_6132_of__int__le__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_numeral_iff
% 5.64/5.95 thf(fact_6133_of__int__numeral__le__iff,axiom,
% 5.64/5.95 ! [N: num,Z: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral_le_iff
% 5.64/5.95 thf(fact_6134_of__int__numeral__le__iff,axiom,
% 5.64/5.95 ! [N: num,Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral_le_iff
% 5.64/5.95 thf(fact_6135_of__int__numeral__le__iff,axiom,
% 5.64/5.95 ! [N: num,Z: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral_le_iff
% 5.64/5.95 thf(fact_6136_of__int__less__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.95 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_numeral_iff
% 5.64/5.95 thf(fact_6137_of__int__less__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.95 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_numeral_iff
% 5.64/5.95 thf(fact_6138_of__int__less__numeral__iff,axiom,
% 5.64/5.95 ! [Z: int,N: num] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.95 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_numeral_iff
% 5.64/5.95 thf(fact_6139_of__int__numeral__less__iff,axiom,
% 5.64/5.95 ! [N: num,Z: int] :
% 5.64/5.95 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral_less_iff
% 5.64/5.95 thf(fact_6140_of__int__numeral__less__iff,axiom,
% 5.64/5.95 ! [N: num,Z: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral_less_iff
% 5.64/5.95 thf(fact_6141_of__int__numeral__less__iff,axiom,
% 5.64/5.95 ! [N: num,Z: int] :
% 5.64/5.95 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_numeral_less_iff
% 5.64/5.95 thf(fact_6142_of__int__le__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_1_iff
% 5.64/5.95 thf(fact_6143_of__int__le__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_1_iff
% 5.64/5.95 thf(fact_6144_of__int__le__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.64/5.95 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_1_iff
% 5.64/5.95 thf(fact_6145_of__int__1__le__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1_le_iff
% 5.64/5.95 thf(fact_6146_of__int__1__le__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1_le_iff
% 5.64/5.95 thf(fact_6147_of__int__1__le__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1_le_iff
% 5.64/5.95 thf(fact_6148_of__int__less__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.64/5.95 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_1_iff
% 5.64/5.95 thf(fact_6149_of__int__less__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.64/5.95 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_1_iff
% 5.64/5.95 thf(fact_6150_of__int__less__1__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.64/5.95 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_1_iff
% 5.64/5.95 thf(fact_6151_of__int__1__less__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.95 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1_less_iff
% 5.64/5.95 thf(fact_6152_of__int__1__less__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.95 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1_less_iff
% 5.64/5.95 thf(fact_6153_of__int__1__less__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.64/5.95 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_1_less_iff
% 5.64/5.95 thf(fact_6154_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.64/5.95 = ( ring_17405671764205052669omplex @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6155_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.64/5.95 = ( ring_1_of_int_real @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6156_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.64/5.95 = ( ring_1_of_int_rat @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6157_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.95 = ( ring_1_of_int_int @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6158_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_17405671764205052669omplex @ Y4 )
% 5.64/5.95 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6159_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_real @ Y4 )
% 5.64/5.95 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6160_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_rat @ Y4 )
% 5.64/5.95 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6161_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_int @ Y4 )
% 5.64/5.95 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6162_of__int__le__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6163_of__int__le__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6164_of__int__le__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6165_of__int__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.64/5.95 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6166_of__int__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.64/5.95 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6167_of__int__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.64/5.95 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6168_of__int__less__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6169_of__int__less__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6170_of__int__less__of__int__power__cancel__iff,axiom,
% 5.64/5.95 ! [B: int,W: nat,X2: int] :
% 5.64/5.95 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_of_int_power_cancel_iff
% 5.64/5.95 thf(fact_6171_of__int__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.64/5.95 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6172_of__int__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.64/5.95 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6173_of__int__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: int,B: int,W: nat] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.64/5.95 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6174_numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6175_numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6176_numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6177_of__int__le__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6178_of__int__le__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6179_of__int__le__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6180_numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6181_numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6182_numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6183_of__int__less__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6184_of__int__less__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6185_of__int__less__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6186_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.64/5.95 = ( ring_1_of_int_int @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6187_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N )
% 5.64/5.95 = ( ring_1_of_int_real @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6188_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N )
% 5.64/5.95 = ( ring_17405671764205052669omplex @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6189_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N )
% 5.64/5.95 = ( ring_1_of_int_rat @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6190_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.95 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N )
% 5.64/5.95 = ( ring_18347121197199848620nteger @ Y4 ) )
% 5.64/5.95 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N )
% 5.64/5.95 = Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_eq_of_int_cancel_iff
% 5.64/5.95 thf(fact_6191_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_int @ Y4 )
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6192_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_real @ Y4 )
% 5.64/5.95 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6193_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_17405671764205052669omplex @ Y4 )
% 5.64/5.95 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6194_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_1_of_int_rat @ Y4 )
% 5.64/5.95 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6195_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ( ring_18347121197199848620nteger @ Y4 )
% 5.64/5.95 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.64/5.95 = ( Y4
% 5.64/5.95 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_eq_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6196_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6197_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6198_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6199_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_le_of_int_cancel_iff
% 5.64/5.95 thf(fact_6200_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6201_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6202_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6203_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_le_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6204_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6205_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6206_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6207_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.64/5.95 ! [X2: num,N: nat,A: int] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.64/5.95 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % neg_numeral_power_less_of_int_cancel_iff
% 5.64/5.95 thf(fact_6208_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6209_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6210_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6211_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.64/5.95 ! [A: int,X2: num,N: nat] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N ) )
% 5.64/5.95 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_less_neg_numeral_power_cancel_iff
% 5.64/5.95 thf(fact_6212_mult__of__int__commute,axiom,
% 5.64/5.95 ! [X2: int,Y4: real] :
% 5.64/5.95 ( ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ Y4 )
% 5.64/5.95 = ( times_times_real @ Y4 @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % mult_of_int_commute
% 5.64/5.95 thf(fact_6213_mult__of__int__commute,axiom,
% 5.64/5.95 ! [X2: int,Y4: rat] :
% 5.64/5.95 ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y4 )
% 5.64/5.95 = ( times_times_rat @ Y4 @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % mult_of_int_commute
% 5.64/5.95 thf(fact_6214_mult__of__int__commute,axiom,
% 5.64/5.95 ! [X2: int,Y4: int] :
% 5.64/5.95 ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y4 )
% 5.64/5.95 = ( times_times_int @ Y4 @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % mult_of_int_commute
% 5.64/5.95 thf(fact_6215_real__of__int__div4,axiom,
% 5.64/5.95 ! [N: int,X2: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % real_of_int_div4
% 5.64/5.95 thf(fact_6216_real__of__int__div,axiom,
% 5.64/5.95 ! [D: int,N: int] :
% 5.64/5.95 ( ( dvd_dvd_int @ D @ N )
% 5.64/5.95 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.64/5.95 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % real_of_int_div
% 5.64/5.95 thf(fact_6217_of__int__nonneg,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.95 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_nonneg
% 5.64/5.95 thf(fact_6218_of__int__nonneg,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.95 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_nonneg
% 5.64/5.95 thf(fact_6219_of__int__nonneg,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.95 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_nonneg
% 5.64/5.95 thf(fact_6220_of__int__pos,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.95 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_pos
% 5.64/5.95 thf(fact_6221_of__int__pos,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.95 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_pos
% 5.64/5.95 thf(fact_6222_of__int__pos,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.95 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_pos
% 5.64/5.95 thf(fact_6223_of__int__neg__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_neg_numeral
% 5.64/5.95 thf(fact_6224_of__int__neg__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_neg_numeral
% 5.64/5.95 thf(fact_6225_of__int__neg__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_neg_numeral
% 5.64/5.95 thf(fact_6226_of__int__neg__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_neg_numeral
% 5.64/5.95 thf(fact_6227_of__int__neg__numeral,axiom,
% 5.64/5.95 ! [K: num] :
% 5.64/5.95 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_neg_numeral
% 5.64/5.95 thf(fact_6228_int__le__real__less,axiom,
% 5.64/5.95 ( ord_less_eq_int
% 5.64/5.95 = ( ^ [N2: int,M2: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M2 ) @ one_one_real ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % int_le_real_less
% 5.64/5.95 thf(fact_6229_int__less__real__le,axiom,
% 5.64/5.95 ( ord_less_int
% 5.64/5.95 = ( ^ [N2: int,M2: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % int_less_real_le
% 5.64/5.95 thf(fact_6230_real__of__int__div__aux,axiom,
% 5.64/5.95 ! [X2: int,D: int] :
% 5.64/5.95 ( ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ D ) )
% 5.64/5.95 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X2 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X2 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % real_of_int_div_aux
% 5.64/5.95 thf(fact_6231_real__of__int__div2,axiom,
% 5.64/5.95 ! [N: int,X2: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % real_of_int_div2
% 5.64/5.95 thf(fact_6232_real__of__int__div3,axiom,
% 5.64/5.95 ! [N: int,X2: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % real_of_int_div3
% 5.64/5.95 thf(fact_6233_even__of__int__iff,axiom,
% 5.64/5.95 ! [K: int] :
% 5.64/5.95 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.64/5.95 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_of_int_iff
% 5.64/5.95 thf(fact_6234_even__of__int__iff,axiom,
% 5.64/5.95 ! [K: int] :
% 5.64/5.95 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.64/5.95 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_of_int_iff
% 5.64/5.95 thf(fact_6235_dbl__dec__def,axiom,
% 5.64/5.95 ( neg_nu6511756317524482435omplex
% 5.64/5.95 = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_def
% 5.64/5.95 thf(fact_6236_dbl__dec__def,axiom,
% 5.64/5.95 ( neg_nu6075765906172075777c_real
% 5.64/5.95 = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_def
% 5.64/5.95 thf(fact_6237_dbl__dec__def,axiom,
% 5.64/5.95 ( neg_nu3179335615603231917ec_rat
% 5.64/5.95 = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_def
% 5.64/5.95 thf(fact_6238_dbl__dec__def,axiom,
% 5.64/5.95 ( neg_nu3811975205180677377ec_int
% 5.64/5.95 = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % dbl_dec_def
% 5.64/5.95 thf(fact_6239_floor__exists,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ? [Z2: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 )
% 5.64/5.95 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % floor_exists
% 5.64/5.95 thf(fact_6240_floor__exists,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ? [Z2: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X2 )
% 5.64/5.95 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % floor_exists
% 5.64/5.95 thf(fact_6241_floor__exists1,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ? [X4: int] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ X2 )
% 5.64/5.95 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.64/5.95 & ! [Y5: int] :
% 5.64/5.95 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X2 )
% 5.64/5.95 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.64/5.95 => ( Y5 = X4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % floor_exists1
% 5.64/5.95 thf(fact_6242_floor__exists1,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ? [X4: int] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ X2 )
% 5.64/5.95 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X4 @ one_one_int ) ) )
% 5.64/5.95 & ! [Y5: int] :
% 5.64/5.95 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X2 )
% 5.64/5.95 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.64/5.95 => ( Y5 = X4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % floor_exists1
% 5.64/5.95 thf(fact_6243_pred__subset__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr448751882837621926eger_o,S3: set_Pr448751882837621926eger_o] :
% 5.64/5.95 ( ( ord_le2162486998276636481er_o_o
% 5.64/5.95 @ ^ [X: code_integer,Y: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y ) @ R )
% 5.64/5.95 @ ^ [X: code_integer,Y: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y ) @ S3 ) )
% 5.64/5.95 = ( ord_le8980329558974975238eger_o @ R @ S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_subset_eq2
% 5.64/5.95 thf(fact_6244_pred__subset__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr8218934625190621173um_num,S3: set_Pr8218934625190621173um_num] :
% 5.64/5.95 ( ( ord_le6124364862034508274_num_o
% 5.64/5.95 @ ^ [X: num,Y: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y ) @ R )
% 5.64/5.95 @ ^ [X: num,Y: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y ) @ S3 ) )
% 5.64/5.95 = ( ord_le880128212290418581um_num @ R @ S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_subset_eq2
% 5.64/5.95 thf(fact_6245_pred__subset__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr6200539531224447659at_num,S3: set_Pr6200539531224447659at_num] :
% 5.64/5.95 ( ( ord_le3404735783095501756_num_o
% 5.64/5.95 @ ^ [X: nat,Y: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R )
% 5.64/5.95 @ ^ [X: nat,Y: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ S3 ) )
% 5.64/5.95 = ( ord_le8085105155179020875at_num @ R @ S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_subset_eq2
% 5.64/5.95 thf(fact_6246_pred__subset__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.64/5.95 ( ( ord_le2646555220125990790_nat_o
% 5.64/5.95 @ ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 5.64/5.95 @ ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ S3 ) )
% 5.64/5.95 = ( ord_le3146513528884898305at_nat @ R @ S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_subset_eq2
% 5.64/5.95 thf(fact_6247_pred__subset__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.64/5.95 ( ( ord_le6741204236512500942_int_o
% 5.64/5.95 @ ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R )
% 5.64/5.95 @ ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ S3 ) )
% 5.64/5.95 = ( ord_le2843351958646193337nt_int @ R @ S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_subset_eq2
% 5.64/5.95 thf(fact_6248_ln__one__minus__pos__lower__bound,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.95 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_one_minus_pos_lower_bound
% 5.64/5.95 thf(fact_6249_add__scale__eq__noteq,axiom,
% 5.64/5.95 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.64/5.95 ( ( R2 != zero_zero_complex )
% 5.64/5.95 => ( ( ( A = B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 5.64/5.95 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_scale_eq_noteq
% 5.64/5.95 thf(fact_6250_add__scale__eq__noteq,axiom,
% 5.64/5.95 ! [R2: real,A: real,B: real,C: real,D: real] :
% 5.64/5.95 ( ( R2 != zero_zero_real )
% 5.64/5.95 => ( ( ( A = B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 5.64/5.95 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_scale_eq_noteq
% 5.64/5.95 thf(fact_6251_add__scale__eq__noteq,axiom,
% 5.64/5.95 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.95 ( ( R2 != zero_zero_rat )
% 5.64/5.95 => ( ( ( A = B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 5.64/5.95 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_scale_eq_noteq
% 5.64/5.95 thf(fact_6252_add__scale__eq__noteq,axiom,
% 5.64/5.95 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.95 ( ( R2 != zero_zero_nat )
% 5.64/5.95 => ( ( ( A = B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 5.64/5.95 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_scale_eq_noteq
% 5.64/5.95 thf(fact_6253_add__scale__eq__noteq,axiom,
% 5.64/5.95 ! [R2: int,A: int,B: int,C: int,D: int] :
% 5.64/5.95 ( ( R2 != zero_zero_int )
% 5.64/5.95 => ( ( ( A = B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 5.64/5.95 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_scale_eq_noteq
% 5.64/5.95 thf(fact_6254_artanh__def,axiom,
% 5.64/5.95 ( artanh_real
% 5.64/5.95 = ( ^ [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 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % artanh_def
% 5.64/5.95 thf(fact_6255_ln__one,axiom,
% 5.64/5.95 ( ( ln_ln_real @ one_one_real )
% 5.64/5.95 = zero_zero_real ) ).
% 5.64/5.95
% 5.64/5.95 % ln_one
% 5.64/5.95 thf(fact_6256_ln__less__cancel__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y4 ) )
% 5.64/5.95 = ( ord_less_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_less_cancel_iff
% 5.64/5.95 thf(fact_6257_ln__inj__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( ( ln_ln_real @ X2 )
% 5.64/5.95 = ( ln_ln_real @ Y4 ) )
% 5.64/5.95 = ( X2 = Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_inj_iff
% 5.64/5.95 thf(fact_6258_ln__le__cancel__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y4 ) )
% 5.64/5.95 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_le_cancel_iff
% 5.64/5.95 thf(fact_6259_ln__eq__zero__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ( ln_ln_real @ X2 )
% 5.64/5.95 = zero_zero_real )
% 5.64/5.95 = ( X2 = one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_eq_zero_iff
% 5.64/5.95 thf(fact_6260_ln__gt__zero__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.95 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_gt_zero_iff
% 5.64/5.95 thf(fact_6261_ln__less__zero__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_less_zero_iff
% 5.64/5.95 thf(fact_6262_ln__le__zero__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_le_zero_iff
% 5.64/5.95 thf(fact_6263_ln__ge__zero__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.95 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_ge_zero_iff
% 5.64/5.95 thf(fact_6264_ln__less__self,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_less_self
% 5.64/5.95 thf(fact_6265_ln__bound,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_bound
% 5.64/5.95 thf(fact_6266_ln__gt__zero,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.95 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_gt_zero
% 5.64/5.95 thf(fact_6267_ln__less__zero,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/5.95 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_less_zero
% 5.64/5.95 thf(fact_6268_ln__gt__zero__imp__gt__one,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_gt_zero_imp_gt_one
% 5.64/5.95 thf(fact_6269_ln__ge__zero__imp__ge__one,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_ge_zero_imp_ge_one
% 5.64/5.95 thf(fact_6270_ln__mult,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.95 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y4 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_mult
% 5.64/5.95 thf(fact_6271_ln__eq__minus__one,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ( ln_ln_real @ X2 )
% 5.64/5.95 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.64/5.95 => ( X2 = one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_eq_minus_one
% 5.64/5.95 thf(fact_6272_ln__div,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( ln_ln_real @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.95 = ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y4 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_div
% 5.64/5.95 thf(fact_6273_ln__2__less__1,axiom,
% 5.64/5.95 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.64/5.95
% 5.64/5.95 % ln_2_less_1
% 5.64/5.95 thf(fact_6274_pred__equals__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr448751882837621926eger_o,S3: set_Pr448751882837621926eger_o] :
% 5.64/5.95 ( ( ( ^ [X: code_integer,Y: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y ) @ R ) )
% 5.64/5.95 = ( ^ [X: code_integer,Y: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y ) @ S3 ) ) )
% 5.64/5.95 = ( R = S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_equals_eq2
% 5.64/5.95 thf(fact_6275_pred__equals__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr8218934625190621173um_num,S3: set_Pr8218934625190621173um_num] :
% 5.64/5.95 ( ( ( ^ [X: num,Y: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y ) @ R ) )
% 5.64/5.95 = ( ^ [X: num,Y: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y ) @ S3 ) ) )
% 5.64/5.95 = ( R = S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_equals_eq2
% 5.64/5.95 thf(fact_6276_pred__equals__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr6200539531224447659at_num,S3: set_Pr6200539531224447659at_num] :
% 5.64/5.95 ( ( ( ^ [X: nat,Y: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ R ) )
% 5.64/5.95 = ( ^ [X: nat,Y: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ S3 ) ) )
% 5.64/5.95 = ( R = S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_equals_eq2
% 5.64/5.95 thf(fact_6277_pred__equals__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.64/5.95 ( ( ( ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R ) )
% 5.64/5.95 = ( ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ S3 ) ) )
% 5.64/5.95 = ( R = S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_equals_eq2
% 5.64/5.95 thf(fact_6278_pred__equals__eq2,axiom,
% 5.64/5.95 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.64/5.95 ( ( ( ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R ) )
% 5.64/5.95 = ( ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ S3 ) ) )
% 5.64/5.95 = ( R = S3 ) ) ).
% 5.64/5.95
% 5.64/5.95 % pred_equals_eq2
% 5.64/5.95 thf(fact_6279_bot__empty__eq2,axiom,
% 5.64/5.95 ( bot_bo4731626569425807221er_o_o
% 5.64/5.95 = ( ^ [X: code_integer,Y: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y ) @ bot_bo5379713665208646970eger_o ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % bot_empty_eq2
% 5.64/5.95 thf(fact_6280_bot__empty__eq2,axiom,
% 5.64/5.95 ( bot_bot_num_num_o
% 5.64/5.95 = ( ^ [X: num,Y: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y ) @ bot_bo9056780473022590049um_num ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % bot_empty_eq2
% 5.64/5.95 thf(fact_6281_bot__empty__eq2,axiom,
% 5.64/5.95 ( bot_bot_nat_num_o
% 5.64/5.95 = ( ^ [X: nat,Y: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y ) @ bot_bo7038385379056416535at_num ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % bot_empty_eq2
% 5.64/5.95 thf(fact_6282_bot__empty__eq2,axiom,
% 5.64/5.95 ( bot_bot_nat_nat_o
% 5.64/5.95 = ( ^ [X: nat,Y: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % bot_empty_eq2
% 5.64/5.95 thf(fact_6283_bot__empty__eq2,axiom,
% 5.64/5.95 ( bot_bot_int_int_o
% 5.64/5.95 = ( ^ [X: int,Y: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % bot_empty_eq2
% 5.64/5.95 thf(fact_6284_ln__le__minus__one,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_le_minus_one
% 5.64/5.95 thf(fact_6285_ln__diff__le,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y4 ) ) @ ( divide_divide_real @ ( minus_minus_real @ X2 @ Y4 ) @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_diff_le
% 5.64/5.95 thf(fact_6286_ln__add__one__self__le__self2,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.95 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_add_one_self_le_self2
% 5.64/5.95 thf(fact_6287_ln__one__minus__pos__upper__bound,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_one_minus_pos_upper_bound
% 5.64/5.95 thf(fact_6288_add__0__iff,axiom,
% 5.64/5.95 ! [B: complex,A: complex] :
% 5.64/5.95 ( ( B
% 5.64/5.95 = ( plus_plus_complex @ B @ A ) )
% 5.64/5.95 = ( A = zero_zero_complex ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_0_iff
% 5.64/5.95 thf(fact_6289_add__0__iff,axiom,
% 5.64/5.95 ! [B: real,A: real] :
% 5.64/5.95 ( ( B
% 5.64/5.95 = ( plus_plus_real @ B @ A ) )
% 5.64/5.95 = ( A = zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_0_iff
% 5.64/5.95 thf(fact_6290_add__0__iff,axiom,
% 5.64/5.95 ! [B: rat,A: rat] :
% 5.64/5.95 ( ( B
% 5.64/5.95 = ( plus_plus_rat @ B @ A ) )
% 5.64/5.95 = ( A = zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_0_iff
% 5.64/5.95 thf(fact_6291_add__0__iff,axiom,
% 5.64/5.95 ! [B: nat,A: nat] :
% 5.64/5.95 ( ( B
% 5.64/5.95 = ( plus_plus_nat @ B @ A ) )
% 5.64/5.95 = ( A = zero_zero_nat ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_0_iff
% 5.64/5.95 thf(fact_6292_add__0__iff,axiom,
% 5.64/5.95 ! [B: int,A: int] :
% 5.64/5.95 ( ( B
% 5.64/5.95 = ( plus_plus_int @ B @ A ) )
% 5.64/5.95 = ( A = zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % add_0_iff
% 5.64/5.95 thf(fact_6293_crossproduct__eq,axiom,
% 5.64/5.95 ! [W: real,Y4: real,X2: real,Z: real] :
% 5.64/5.95 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y4 ) @ ( times_times_real @ X2 @ Z ) )
% 5.64/5.95 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X2 @ Y4 ) ) )
% 5.64/5.95 = ( ( W = X2 )
% 5.64/5.95 | ( Y4 = Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_eq
% 5.64/5.95 thf(fact_6294_crossproduct__eq,axiom,
% 5.64/5.95 ! [W: rat,Y4: rat,X2: rat,Z: rat] :
% 5.64/5.95 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y4 ) @ ( times_times_rat @ X2 @ Z ) )
% 5.64/5.95 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X2 @ Y4 ) ) )
% 5.64/5.95 = ( ( W = X2 )
% 5.64/5.95 | ( Y4 = Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_eq
% 5.64/5.95 thf(fact_6295_crossproduct__eq,axiom,
% 5.64/5.95 ! [W: nat,Y4: nat,X2: nat,Z: nat] :
% 5.64/5.95 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y4 ) @ ( times_times_nat @ X2 @ Z ) )
% 5.64/5.95 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X2 @ Y4 ) ) )
% 5.64/5.95 = ( ( W = X2 )
% 5.64/5.95 | ( Y4 = Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_eq
% 5.64/5.95 thf(fact_6296_crossproduct__eq,axiom,
% 5.64/5.95 ! [W: int,Y4: int,X2: int,Z: int] :
% 5.64/5.95 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y4 ) @ ( times_times_int @ X2 @ Z ) )
% 5.64/5.95 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X2 @ Y4 ) ) )
% 5.64/5.95 = ( ( W = X2 )
% 5.64/5.95 | ( Y4 = Z ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_eq
% 5.64/5.95 thf(fact_6297_crossproduct__noteq,axiom,
% 5.64/5.95 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.95 ( ( ( A != B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.64/5.95 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_noteq
% 5.64/5.95 thf(fact_6298_crossproduct__noteq,axiom,
% 5.64/5.95 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.64/5.95 ( ( ( A != B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.64/5.95 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_noteq
% 5.64/5.95 thf(fact_6299_crossproduct__noteq,axiom,
% 5.64/5.95 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.64/5.95 ( ( ( A != B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.64/5.95 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_noteq
% 5.64/5.95 thf(fact_6300_crossproduct__noteq,axiom,
% 5.64/5.95 ! [A: int,B: int,C: int,D: int] :
% 5.64/5.95 ( ( ( A != B )
% 5.64/5.95 & ( C != D ) )
% 5.64/5.95 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.64/5.95 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % crossproduct_noteq
% 5.64/5.95 thf(fact_6301_exists__least__lemma,axiom,
% 5.64/5.95 ! [P: nat > $o] :
% 5.64/5.95 ( ~ ( P @ zero_zero_nat )
% 5.64/5.95 => ( ? [X_1: nat] : ( P @ X_1 )
% 5.64/5.95 => ? [N3: nat] :
% 5.64/5.95 ( ~ ( P @ N3 )
% 5.64/5.95 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % exists_least_lemma
% 5.64/5.95 thf(fact_6302_ex__le__of__int,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ? [Z2: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ex_le_of_int
% 5.64/5.95 thf(fact_6303_ex__le__of__int,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ? [Z2: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ex_le_of_int
% 5.64/5.95 thf(fact_6304_ex__of__int__less,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X2 ) ).
% 5.64/5.95
% 5.64/5.95 % ex_of_int_less
% 5.64/5.95 thf(fact_6305_ex__of__int__less,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X2 ) ).
% 5.64/5.95
% 5.64/5.95 % ex_of_int_less
% 5.64/5.95 thf(fact_6306_ex__less__of__int,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ? [Z2: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ex_less_of_int
% 5.64/5.95 thf(fact_6307_ex__less__of__int,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ? [Z2: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % ex_less_of_int
% 5.64/5.95 thf(fact_6308_subrelI,axiom,
% 5.64/5.95 ! [R2: set_Pr448751882837621926eger_o,S2: set_Pr448751882837621926eger_o] :
% 5.64/5.95 ( ! [X4: code_integer,Y3: $o] :
% 5.64/5.95 ( ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X4 @ Y3 ) @ R2 )
% 5.64/5.95 => ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X4 @ Y3 ) @ S2 ) )
% 5.64/5.95 => ( ord_le8980329558974975238eger_o @ R2 @ S2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % subrelI
% 5.64/5.95 thf(fact_6309_subrelI,axiom,
% 5.64/5.95 ! [R2: set_Pr8218934625190621173um_num,S2: set_Pr8218934625190621173um_num] :
% 5.64/5.95 ( ! [X4: num,Y3: num] :
% 5.64/5.95 ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ X4 @ Y3 ) @ R2 )
% 5.64/5.95 => ( member7279096912039735102um_num @ ( product_Pair_num_num @ X4 @ Y3 ) @ S2 ) )
% 5.64/5.95 => ( ord_le880128212290418581um_num @ R2 @ S2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % subrelI
% 5.64/5.95 thf(fact_6310_subrelI,axiom,
% 5.64/5.95 ! [R2: set_Pr6200539531224447659at_num,S2: set_Pr6200539531224447659at_num] :
% 5.64/5.95 ( ! [X4: nat,Y3: num] :
% 5.64/5.95 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y3 ) @ R2 )
% 5.64/5.95 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X4 @ Y3 ) @ S2 ) )
% 5.64/5.95 => ( ord_le8085105155179020875at_num @ R2 @ S2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % subrelI
% 5.64/5.95 thf(fact_6311_subrelI,axiom,
% 5.64/5.95 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.64/5.95 ( ! [X4: nat,Y3: nat] :
% 5.64/5.95 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ R2 )
% 5.64/5.95 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y3 ) @ S2 ) )
% 5.64/5.95 => ( ord_le3146513528884898305at_nat @ R2 @ S2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % subrelI
% 5.64/5.95 thf(fact_6312_subrelI,axiom,
% 5.64/5.95 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 5.64/5.95 ( ! [X4: int,Y3: int] :
% 5.64/5.95 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y3 ) @ R2 )
% 5.64/5.95 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y3 ) @ S2 ) )
% 5.64/5.95 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % subrelI
% 5.64/5.95 thf(fact_6313_ln__one__plus__pos__lower__bound,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % ln_one_plus_pos_lower_bound
% 5.64/5.95 thf(fact_6314_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.64/5.95 thf(fact_6315_round__unique,axiom,
% 5.64/5.95 ! [X2: rat,Y4: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y4 ) )
% 5.64/5.95 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.64/5.95 = Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_unique
% 5.64/5.95 thf(fact_6316_round__unique,axiom,
% 5.64/5.95 ! [X2: real,Y4: int] :
% 5.64/5.95 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y4 ) )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 => ( ( archim8280529875227126926d_real @ X2 )
% 5.64/5.95 = Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_unique
% 5.64/5.95 thf(fact_6317_tanh__ln__real,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.95 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % tanh_ln_real
% 5.64/5.95 thf(fact_6318_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ln_one_plus_x_minus_x_bound
% 5.64/5.95 thf(fact_6319_of__int__round__gt,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_gt
% 5.64/5.95 thf(fact_6320_of__int__round__gt,axiom,
% 5.64/5.95 ! [X2: rat] : ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_gt
% 5.64/5.95 thf(fact_6321_of__int__round__ge,axiom,
% 5.64/5.95 ! [X2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_ge
% 5.64/5.95 thf(fact_6322_of__int__round__ge,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_ge
% 5.64/5.95 thf(fact_6323_abs__idempotent,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.64/5.95 = ( abs_abs_real @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_idempotent
% 5.64/5.95 thf(fact_6324_abs__idempotent,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.64/5.95 = ( abs_abs_int @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_idempotent
% 5.64/5.95 thf(fact_6325_abs__idempotent,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.64/5.95 = ( abs_abs_rat @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_idempotent
% 5.64/5.95 thf(fact_6326_abs__idempotent,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.64/5.95 = ( abs_abs_Code_integer @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_idempotent
% 5.64/5.95 thf(fact_6327_abs__zero,axiom,
% 5.64/5.95 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.64/5.95 = zero_z3403309356797280102nteger ) ).
% 5.64/5.95
% 5.64/5.95 % abs_zero
% 5.64/5.95 thf(fact_6328_abs__zero,axiom,
% 5.64/5.95 ( ( abs_abs_real @ zero_zero_real )
% 5.64/5.95 = zero_zero_real ) ).
% 5.64/5.95
% 5.64/5.95 % abs_zero
% 5.64/5.95 thf(fact_6329_abs__zero,axiom,
% 5.64/5.95 ( ( abs_abs_rat @ zero_zero_rat )
% 5.64/5.95 = zero_zero_rat ) ).
% 5.64/5.95
% 5.64/5.95 % abs_zero
% 5.64/5.95 thf(fact_6330_abs__zero,axiom,
% 5.64/5.95 ( ( abs_abs_int @ zero_zero_int )
% 5.64/5.95 = zero_zero_int ) ).
% 5.64/5.95
% 5.64/5.95 % abs_zero
% 5.64/5.95 thf(fact_6331_abs__eq__0,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ( abs_abs_Code_integer @ A )
% 5.64/5.95 = zero_z3403309356797280102nteger )
% 5.64/5.95 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_0
% 5.64/5.95 thf(fact_6332_abs__eq__0,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ( abs_abs_real @ A )
% 5.64/5.95 = zero_zero_real )
% 5.64/5.95 = ( A = zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_0
% 5.64/5.95 thf(fact_6333_abs__eq__0,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ( abs_abs_rat @ A )
% 5.64/5.95 = zero_zero_rat )
% 5.64/5.95 = ( A = zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_0
% 5.64/5.95 thf(fact_6334_abs__eq__0,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ( abs_abs_int @ A )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 = ( A = zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_0
% 5.64/5.95 thf(fact_6335_abs__0__eq,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( zero_z3403309356797280102nteger
% 5.64/5.95 = ( abs_abs_Code_integer @ A ) )
% 5.64/5.95 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_0_eq
% 5.64/5.95 thf(fact_6336_abs__0__eq,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( zero_zero_real
% 5.64/5.95 = ( abs_abs_real @ A ) )
% 5.64/5.95 = ( A = zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_0_eq
% 5.64/5.95 thf(fact_6337_abs__0__eq,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( zero_zero_rat
% 5.64/5.95 = ( abs_abs_rat @ A ) )
% 5.64/5.95 = ( A = zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_0_eq
% 5.64/5.95 thf(fact_6338_abs__0__eq,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( zero_zero_int
% 5.64/5.95 = ( abs_abs_int @ A ) )
% 5.64/5.95 = ( A = zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_0_eq
% 5.64/5.95 thf(fact_6339_abs__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.64/5.95 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_numeral
% 5.64/5.95 thf(fact_6340_abs__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.64/5.95 = ( numeral_numeral_real @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_numeral
% 5.64/5.95 thf(fact_6341_abs__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.64/5.95 = ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_numeral
% 5.64/5.95 thf(fact_6342_abs__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_numeral
% 5.64/5.95 thf(fact_6343_abs__mult__self__eq,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.64/5.95 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_self_eq
% 5.64/5.95 thf(fact_6344_abs__mult__self__eq,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.64/5.95 = ( times_times_real @ A @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_self_eq
% 5.64/5.95 thf(fact_6345_abs__mult__self__eq,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.64/5.95 = ( times_times_rat @ A @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_self_eq
% 5.64/5.95 thf(fact_6346_abs__mult__self__eq,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.64/5.95 = ( times_times_int @ A @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_self_eq
% 5.64/5.95 thf(fact_6347_abs__1,axiom,
% 5.64/5.95 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.64/5.95 = one_one_Code_integer ) ).
% 5.64/5.95
% 5.64/5.95 % abs_1
% 5.64/5.95 thf(fact_6348_abs__1,axiom,
% 5.64/5.95 ( ( abs_abs_complex @ one_one_complex )
% 5.64/5.95 = one_one_complex ) ).
% 5.64/5.95
% 5.64/5.95 % abs_1
% 5.64/5.95 thf(fact_6349_abs__1,axiom,
% 5.64/5.95 ( ( abs_abs_real @ one_one_real )
% 5.64/5.95 = one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % abs_1
% 5.64/5.95 thf(fact_6350_abs__1,axiom,
% 5.64/5.95 ( ( abs_abs_rat @ one_one_rat )
% 5.64/5.95 = one_one_rat ) ).
% 5.64/5.95
% 5.64/5.95 % abs_1
% 5.64/5.95 thf(fact_6351_abs__1,axiom,
% 5.64/5.95 ( ( abs_abs_int @ one_one_int )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % abs_1
% 5.64/5.95 thf(fact_6352_abs__add__abs,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.64/5.95 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_abs
% 5.64/5.95 thf(fact_6353_abs__add__abs,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.64/5.95 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_abs
% 5.64/5.95 thf(fact_6354_abs__add__abs,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.64/5.95 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_abs
% 5.64/5.95 thf(fact_6355_abs__add__abs,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.64/5.95 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_abs
% 5.64/5.95 thf(fact_6356_abs__divide,axiom,
% 5.64/5.95 ! [A: complex,B: complex] :
% 5.64/5.95 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.95 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_divide
% 5.64/5.95 thf(fact_6357_abs__divide,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.95 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_divide
% 5.64/5.95 thf(fact_6358_abs__divide,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.95 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_divide
% 5.64/5.95 thf(fact_6359_abs__minus__cancel,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.64/5.95 = ( abs_abs_int @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_cancel
% 5.64/5.95 thf(fact_6360_abs__minus__cancel,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.64/5.95 = ( abs_abs_real @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_cancel
% 5.64/5.95 thf(fact_6361_abs__minus__cancel,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.64/5.95 = ( abs_abs_rat @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_cancel
% 5.64/5.95 thf(fact_6362_abs__minus__cancel,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.64/5.95 = ( abs_abs_Code_integer @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_cancel
% 5.64/5.95 thf(fact_6363_tanh__real__less__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ ( tanh_real @ X2 ) @ ( tanh_real @ Y4 ) )
% 5.64/5.95 = ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % tanh_real_less_iff
% 5.64/5.95 thf(fact_6364_abs__of__nonneg,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.95 => ( ( abs_abs_Code_integer @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonneg
% 5.64/5.95 thf(fact_6365_abs__of__nonneg,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.95 => ( ( abs_abs_rat @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonneg
% 5.64/5.95 thf(fact_6366_abs__of__nonneg,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.95 => ( ( abs_abs_int @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonneg
% 5.64/5.95 thf(fact_6367_abs__of__nonneg,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.95 => ( ( abs_abs_real @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonneg
% 5.64/5.95 thf(fact_6368_abs__le__self__iff,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.64/5.95 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_self_iff
% 5.64/5.95 thf(fact_6369_abs__le__self__iff,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.64/5.95 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_self_iff
% 5.64/5.95 thf(fact_6370_abs__le__self__iff,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.64/5.95 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_self_iff
% 5.64/5.95 thf(fact_6371_abs__le__self__iff,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.64/5.95 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_self_iff
% 5.64/5.95 thf(fact_6372_abs__le__zero__iff,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.64/5.95 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_zero_iff
% 5.64/5.95 thf(fact_6373_abs__le__zero__iff,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.64/5.95 = ( A = zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_zero_iff
% 5.64/5.95 thf(fact_6374_abs__le__zero__iff,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.64/5.95 = ( A = zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_zero_iff
% 5.64/5.95 thf(fact_6375_abs__le__zero__iff,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.64/5.95 = ( A = zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_zero_iff
% 5.64/5.95 thf(fact_6376_zero__less__abs__iff,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.64/5.95 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_abs_iff
% 5.64/5.95 thf(fact_6377_zero__less__abs__iff,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.64/5.95 = ( A != zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_abs_iff
% 5.64/5.95 thf(fact_6378_zero__less__abs__iff,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.64/5.95 = ( A != zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_abs_iff
% 5.64/5.95 thf(fact_6379_zero__less__abs__iff,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.64/5.95 = ( A != zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_abs_iff
% 5.64/5.95 thf(fact_6380_abs__neg__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_numeral
% 5.64/5.95 thf(fact_6381_abs__neg__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.95 = ( numeral_numeral_real @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_numeral
% 5.64/5.95 thf(fact_6382_abs__neg__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.95 = ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_numeral
% 5.64/5.95 thf(fact_6383_abs__neg__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.95 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_numeral
% 5.64/5.95 thf(fact_6384_abs__neg__one,axiom,
% 5.64/5.95 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_one
% 5.64/5.95 thf(fact_6385_abs__neg__one,axiom,
% 5.64/5.95 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.95 = one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_one
% 5.64/5.95 thf(fact_6386_abs__neg__one,axiom,
% 5.64/5.95 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.95 = one_one_rat ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_one
% 5.64/5.95 thf(fact_6387_abs__neg__one,axiom,
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.95 = one_one_Code_integer ) ).
% 5.64/5.95
% 5.64/5.95 % abs_neg_one
% 5.64/5.95 thf(fact_6388_abs__power__minus,axiom,
% 5.64/5.95 ! [A: int,N: nat] :
% 5.64/5.95 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.64/5.95 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power_minus
% 5.64/5.95 thf(fact_6389_abs__power__minus,axiom,
% 5.64/5.95 ! [A: real,N: nat] :
% 5.64/5.95 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.64/5.95 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power_minus
% 5.64/5.95 thf(fact_6390_abs__power__minus,axiom,
% 5.64/5.95 ! [A: rat,N: nat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.64/5.95 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power_minus
% 5.64/5.95 thf(fact_6391_abs__power__minus,axiom,
% 5.64/5.95 ! [A: code_integer,N: nat] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.64/5.95 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power_minus
% 5.64/5.95 thf(fact_6392_tanh__real__pos__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X2 ) )
% 5.64/5.95 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % tanh_real_pos_iff
% 5.64/5.95 thf(fact_6393_tanh__real__neg__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( tanh_real @ X2 ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % tanh_real_neg_iff
% 5.64/5.95 thf(fact_6394_round__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_numeral
% 5.64/5.95 thf(fact_6395_round__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.64/5.95 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_numeral
% 5.64/5.95 thf(fact_6396_round__1,axiom,
% 5.64/5.95 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % round_1
% 5.64/5.95 thf(fact_6397_round__1,axiom,
% 5.64/5.95 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % round_1
% 5.64/5.95 thf(fact_6398_divide__le__0__abs__iff,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.64/5.95 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.95 | ( B = zero_zero_rat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_le_0_abs_iff
% 5.64/5.95 thf(fact_6399_divide__le__0__abs__iff,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.64/5.95 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.95 | ( B = zero_zero_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % divide_le_0_abs_iff
% 5.64/5.95 thf(fact_6400_zero__le__divide__abs__iff,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.64/5.95 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.95 | ( B = zero_zero_rat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_le_divide_abs_iff
% 5.64/5.95 thf(fact_6401_zero__le__divide__abs__iff,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.64/5.95 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.95 | ( B = zero_zero_real ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_le_divide_abs_iff
% 5.64/5.95 thf(fact_6402_abs__of__nonpos,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.64/5.95 => ( ( abs_abs_Code_integer @ A )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonpos
% 5.64/5.95 thf(fact_6403_abs__of__nonpos,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.64/5.95 => ( ( abs_abs_rat @ A )
% 5.64/5.95 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonpos
% 5.64/5.95 thf(fact_6404_abs__of__nonpos,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.64/5.95 => ( ( abs_abs_int @ A )
% 5.64/5.95 = ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonpos
% 5.64/5.95 thf(fact_6405_abs__of__nonpos,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.95 => ( ( abs_abs_real @ A )
% 5.64/5.95 = ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_nonpos
% 5.64/5.95 thf(fact_6406_artanh__minus__real,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.95 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.64/5.95 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % artanh_minus_real
% 5.64/5.95 thf(fact_6407_zero__less__power__abs__iff,axiom,
% 5.64/5.95 ! [A: code_integer,N: nat] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.64/5.95 = ( ( A != zero_z3403309356797280102nteger )
% 5.64/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_power_abs_iff
% 5.64/5.95 thf(fact_6408_zero__less__power__abs__iff,axiom,
% 5.64/5.95 ! [A: real,N: nat] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.64/5.95 = ( ( A != zero_zero_real )
% 5.64/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_power_abs_iff
% 5.64/5.95 thf(fact_6409_zero__less__power__abs__iff,axiom,
% 5.64/5.95 ! [A: rat,N: nat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.64/5.95 = ( ( A != zero_zero_rat )
% 5.64/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_power_abs_iff
% 5.64/5.95 thf(fact_6410_zero__less__power__abs__iff,axiom,
% 5.64/5.95 ! [A: int,N: nat] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.64/5.95 = ( ( A != zero_zero_int )
% 5.64/5.95 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_power_abs_iff
% 5.64/5.95 thf(fact_6411_abs__power2,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power2
% 5.64/5.95 thf(fact_6412_abs__power2,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power2
% 5.64/5.95 thf(fact_6413_abs__power2,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power2
% 5.64/5.95 thf(fact_6414_abs__power2,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_power2
% 5.64/5.95 thf(fact_6415_power2__abs,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_abs
% 5.64/5.95 thf(fact_6416_power2__abs,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_abs
% 5.64/5.95 thf(fact_6417_power2__abs,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_abs
% 5.64/5.95 thf(fact_6418_power2__abs,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_abs
% 5.64/5.95 thf(fact_6419_round__neg__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_neg_numeral
% 5.64/5.95 thf(fact_6420_round__neg__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.95 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_neg_numeral
% 5.64/5.95 thf(fact_6421_power__even__abs__numeral,axiom,
% 5.64/5.95 ! [W: num,A: rat] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs_numeral
% 5.64/5.95 thf(fact_6422_power__even__abs__numeral,axiom,
% 5.64/5.95 ! [W: num,A: code_integer] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs_numeral
% 5.64/5.95 thf(fact_6423_power__even__abs__numeral,axiom,
% 5.64/5.95 ! [W: num,A: real] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs_numeral
% 5.64/5.95 thf(fact_6424_power__even__abs__numeral,axiom,
% 5.64/5.95 ! [W: num,A: int] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.64/5.95 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs_numeral
% 5.64/5.95 thf(fact_6425_abs__ge__self,axiom,
% 5.64/5.95 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_self
% 5.64/5.95 thf(fact_6426_abs__ge__self,axiom,
% 5.64/5.95 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_self
% 5.64/5.95 thf(fact_6427_abs__ge__self,axiom,
% 5.64/5.95 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_self
% 5.64/5.95 thf(fact_6428_abs__ge__self,axiom,
% 5.64/5.95 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_self
% 5.64/5.95 thf(fact_6429_abs__le__D1,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.64/5.95 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D1
% 5.64/5.95 thf(fact_6430_abs__le__D1,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D1
% 5.64/5.95 thf(fact_6431_abs__le__D1,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D1
% 5.64/5.95 thf(fact_6432_abs__le__D1,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D1
% 5.64/5.95 thf(fact_6433_abs__mult,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.64/5.95 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult
% 5.64/5.95 thf(fact_6434_abs__mult,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.64/5.95 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult
% 5.64/5.95 thf(fact_6435_abs__mult,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.95 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult
% 5.64/5.95 thf(fact_6436_abs__mult,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.64/5.95 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult
% 5.64/5.95 thf(fact_6437_abs__one,axiom,
% 5.64/5.95 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.64/5.95 = one_one_Code_integer ) ).
% 5.64/5.95
% 5.64/5.95 % abs_one
% 5.64/5.95 thf(fact_6438_abs__one,axiom,
% 5.64/5.95 ( ( abs_abs_real @ one_one_real )
% 5.64/5.95 = one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % abs_one
% 5.64/5.95 thf(fact_6439_abs__one,axiom,
% 5.64/5.95 ( ( abs_abs_rat @ one_one_rat )
% 5.64/5.95 = one_one_rat ) ).
% 5.64/5.95
% 5.64/5.95 % abs_one
% 5.64/5.95 thf(fact_6440_abs__one,axiom,
% 5.64/5.95 ( ( abs_abs_int @ one_one_int )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % abs_one
% 5.64/5.95 thf(fact_6441_abs__minus__commute,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.64/5.95 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_commute
% 5.64/5.95 thf(fact_6442_abs__minus__commute,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.64/5.95 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_commute
% 5.64/5.95 thf(fact_6443_abs__minus__commute,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.64/5.95 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_commute
% 5.64/5.95 thf(fact_6444_abs__minus__commute,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.64/5.95 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_commute
% 5.64/5.95 thf(fact_6445_power__abs,axiom,
% 5.64/5.95 ! [A: rat,N: nat] :
% 5.64/5.95 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.64/5.95 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_abs
% 5.64/5.95 thf(fact_6446_power__abs,axiom,
% 5.64/5.95 ! [A: code_integer,N: nat] :
% 5.64/5.95 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.64/5.95 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_abs
% 5.64/5.95 thf(fact_6447_power__abs,axiom,
% 5.64/5.95 ! [A: real,N: nat] :
% 5.64/5.95 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.64/5.95 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_abs
% 5.64/5.95 thf(fact_6448_power__abs,axiom,
% 5.64/5.95 ! [A: int,N: nat] :
% 5.64/5.95 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.64/5.95 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_abs
% 5.64/5.95 thf(fact_6449_round__diff__minimal,axiom,
% 5.64/5.95 ! [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 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_diff_minimal
% 5.64/5.95 thf(fact_6450_round__diff__minimal,axiom,
% 5.64/5.95 ! [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 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_diff_minimal
% 5.64/5.95 thf(fact_6451_abs__ge__zero,axiom,
% 5.64/5.95 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_zero
% 5.64/5.95 thf(fact_6452_abs__ge__zero,axiom,
% 5.64/5.95 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_zero
% 5.64/5.95 thf(fact_6453_abs__ge__zero,axiom,
% 5.64/5.95 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_zero
% 5.64/5.95 thf(fact_6454_abs__ge__zero,axiom,
% 5.64/5.95 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_zero
% 5.64/5.95 thf(fact_6455_abs__not__less__zero,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.64/5.95
% 5.64/5.95 % abs_not_less_zero
% 5.64/5.95 thf(fact_6456_abs__not__less__zero,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.64/5.95
% 5.64/5.95 % abs_not_less_zero
% 5.64/5.95 thf(fact_6457_abs__not__less__zero,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.64/5.95
% 5.64/5.95 % abs_not_less_zero
% 5.64/5.95 thf(fact_6458_abs__not__less__zero,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.64/5.95
% 5.64/5.95 % abs_not_less_zero
% 5.64/5.95 thf(fact_6459_abs__of__pos,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.95 => ( ( abs_abs_Code_integer @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_pos
% 5.64/5.95 thf(fact_6460_abs__of__pos,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.95 => ( ( abs_abs_real @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_pos
% 5.64/5.95 thf(fact_6461_abs__of__pos,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.64/5.95 => ( ( abs_abs_rat @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_pos
% 5.64/5.95 thf(fact_6462_abs__of__pos,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/5.95 => ( ( abs_abs_int @ A )
% 5.64/5.95 = A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_pos
% 5.64/5.95 thf(fact_6463_abs__triangle__ineq,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq
% 5.64/5.95 thf(fact_6464_abs__triangle__ineq,axiom,
% 5.64/5.95 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq
% 5.64/5.95 thf(fact_6465_abs__triangle__ineq,axiom,
% 5.64/5.95 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq
% 5.64/5.95 thf(fact_6466_abs__triangle__ineq,axiom,
% 5.64/5.95 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq
% 5.64/5.95 thf(fact_6467_abs__mult__less,axiom,
% 5.64/5.95 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.64/5.95 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.64/5.95 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_less
% 5.64/5.95 thf(fact_6468_abs__mult__less,axiom,
% 5.64/5.95 ! [A: real,C: real,B: real,D: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.64/5.95 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.64/5.95 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_less
% 5.64/5.95 thf(fact_6469_abs__mult__less,axiom,
% 5.64/5.95 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.64/5.95 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.64/5.95 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_less
% 5.64/5.95 thf(fact_6470_abs__mult__less,axiom,
% 5.64/5.95 ! [A: int,C: int,B: int,D: int] :
% 5.64/5.95 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.64/5.95 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.64/5.95 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_less
% 5.64/5.95 thf(fact_6471_abs__triangle__ineq2__sym,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2_sym
% 5.64/5.95 thf(fact_6472_abs__triangle__ineq2__sym,axiom,
% 5.64/5.95 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2_sym
% 5.64/5.95 thf(fact_6473_abs__triangle__ineq2__sym,axiom,
% 5.64/5.95 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2_sym
% 5.64/5.95 thf(fact_6474_abs__triangle__ineq2__sym,axiom,
% 5.64/5.95 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2_sym
% 5.64/5.95 thf(fact_6475_abs__triangle__ineq3,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq3
% 5.64/5.95 thf(fact_6476_abs__triangle__ineq3,axiom,
% 5.64/5.95 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq3
% 5.64/5.95 thf(fact_6477_abs__triangle__ineq3,axiom,
% 5.64/5.95 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq3
% 5.64/5.95 thf(fact_6478_abs__triangle__ineq3,axiom,
% 5.64/5.95 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq3
% 5.64/5.95 thf(fact_6479_abs__triangle__ineq2,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2
% 5.64/5.95 thf(fact_6480_abs__triangle__ineq2,axiom,
% 5.64/5.95 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2
% 5.64/5.95 thf(fact_6481_abs__triangle__ineq2,axiom,
% 5.64/5.95 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2
% 5.64/5.95 thf(fact_6482_abs__triangle__ineq2,axiom,
% 5.64/5.95 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq2
% 5.64/5.95 thf(fact_6483_nonzero__abs__divide,axiom,
% 5.64/5.95 ! [B: real,A: real] :
% 5.64/5.95 ( ( B != zero_zero_real )
% 5.64/5.95 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.95 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % nonzero_abs_divide
% 5.64/5.95 thf(fact_6484_nonzero__abs__divide,axiom,
% 5.64/5.95 ! [B: rat,A: rat] :
% 5.64/5.95 ( ( B != zero_zero_rat )
% 5.64/5.95 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.64/5.95 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % nonzero_abs_divide
% 5.64/5.95 thf(fact_6485_abs__ge__minus__self,axiom,
% 5.64/5.95 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_minus_self
% 5.64/5.95 thf(fact_6486_abs__ge__minus__self,axiom,
% 5.64/5.95 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_minus_self
% 5.64/5.95 thf(fact_6487_abs__ge__minus__self,axiom,
% 5.64/5.95 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_minus_self
% 5.64/5.95 thf(fact_6488_abs__ge__minus__self,axiom,
% 5.64/5.95 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ge_minus_self
% 5.64/5.95 thf(fact_6489_abs__le__iff,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.64/5.95 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.64/5.95 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_iff
% 5.64/5.95 thf(fact_6490_abs__le__iff,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.64/5.95 = ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.95 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_iff
% 5.64/5.95 thf(fact_6491_abs__le__iff,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.64/5.95 = ( ( ord_less_eq_int @ A @ B )
% 5.64/5.95 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_iff
% 5.64/5.95 thf(fact_6492_abs__le__iff,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.64/5.95 = ( ( ord_less_eq_real @ A @ B )
% 5.64/5.95 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_iff
% 5.64/5.95 thf(fact_6493_abs__le__D2,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.64/5.95 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D2
% 5.64/5.95 thf(fact_6494_abs__le__D2,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D2
% 5.64/5.95 thf(fact_6495_abs__le__D2,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D2
% 5.64/5.95 thf(fact_6496_abs__le__D2,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_D2
% 5.64/5.95 thf(fact_6497_abs__leI,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.64/5.95 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.64/5.95 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_leI
% 5.64/5.95 thf(fact_6498_abs__leI,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ A @ B )
% 5.64/5.95 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_leI
% 5.64/5.95 thf(fact_6499_abs__leI,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ A @ B )
% 5.64/5.95 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_leI
% 5.64/5.95 thf(fact_6500_abs__leI,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ A @ B )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.64/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_leI
% 5.64/5.95 thf(fact_6501_abs__less__iff,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.64/5.95 = ( ( ord_less_int @ A @ B )
% 5.64/5.95 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_less_iff
% 5.64/5.95 thf(fact_6502_abs__less__iff,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.64/5.95 = ( ( ord_less_real @ A @ B )
% 5.64/5.95 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_less_iff
% 5.64/5.95 thf(fact_6503_abs__less__iff,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.64/5.95 = ( ( ord_less_rat @ A @ B )
% 5.64/5.95 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_less_iff
% 5.64/5.95 thf(fact_6504_abs__less__iff,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.64/5.95 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.64/5.95 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_less_iff
% 5.64/5.95 thf(fact_6505_tanh__real__lt__1,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.64/5.95
% 5.64/5.95 % tanh_real_lt_1
% 5.64/5.95 thf(fact_6506_dense__eq0__I,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ( ! [E2: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E2 ) )
% 5.64/5.95 => ( X2 = zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % dense_eq0_I
% 5.64/5.95 thf(fact_6507_dense__eq0__I,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ! [E2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.64/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ E2 ) )
% 5.64/5.95 => ( X2 = zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % dense_eq0_I
% 5.64/5.95 thf(fact_6508_abs__mult__pos,axiom,
% 5.64/5.95 ! [X2: code_integer,Y4: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.64/5.95 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y4 ) @ X2 )
% 5.64/5.95 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y4 @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_pos
% 5.64/5.95 thf(fact_6509_abs__mult__pos,axiom,
% 5.64/5.95 ! [X2: rat,Y4: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.64/5.95 => ( ( times_times_rat @ ( abs_abs_rat @ Y4 ) @ X2 )
% 5.64/5.95 = ( abs_abs_rat @ ( times_times_rat @ Y4 @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_pos
% 5.64/5.95 thf(fact_6510_abs__mult__pos,axiom,
% 5.64/5.95 ! [X2: int,Y4: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.95 => ( ( times_times_int @ ( abs_abs_int @ Y4 ) @ X2 )
% 5.64/5.95 = ( abs_abs_int @ ( times_times_int @ Y4 @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_pos
% 5.64/5.95 thf(fact_6511_abs__mult__pos,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( times_times_real @ ( abs_abs_real @ Y4 ) @ X2 )
% 5.64/5.95 = ( abs_abs_real @ ( times_times_real @ Y4 @ X2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_mult_pos
% 5.64/5.95 thf(fact_6512_abs__eq__mult,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.95 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.64/5.95 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.95 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.64/5.95 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.64/5.95 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_mult
% 5.64/5.95 thf(fact_6513_abs__eq__mult,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.95 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.64/5.95 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.95 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.64/5.95 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.64/5.95 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_mult
% 5.64/5.95 thf(fact_6514_abs__eq__mult,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.95 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.64/5.95 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.95 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.64/5.95 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.64/5.95 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_mult
% 5.64/5.95 thf(fact_6515_abs__eq__mult,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.95 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.64/5.95 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.95 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.64/5.95 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.64/5.95 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_mult
% 5.64/5.95 thf(fact_6516_abs__eq__iff_H,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( ( abs_abs_Code_integer @ A )
% 5.64/5.95 = B )
% 5.64/5.95 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.64/5.95 & ( ( A = B )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_iff'
% 5.64/5.95 thf(fact_6517_abs__eq__iff_H,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( ( abs_abs_rat @ A )
% 5.64/5.95 = B )
% 5.64/5.95 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.95 & ( ( A = B )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_iff'
% 5.64/5.95 thf(fact_6518_abs__eq__iff_H,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( ( abs_abs_int @ A )
% 5.64/5.95 = B )
% 5.64/5.95 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.95 & ( ( A = B )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_iff'
% 5.64/5.95 thf(fact_6519_abs__eq__iff_H,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( ( abs_abs_real @ A )
% 5.64/5.95 = B )
% 5.64/5.95 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.95 & ( ( A = B )
% 5.64/5.95 | ( A
% 5.64/5.95 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_eq_iff'
% 5.64/5.95 thf(fact_6520_eq__abs__iff_H,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( A
% 5.64/5.95 = ( abs_abs_Code_integer @ B ) )
% 5.64/5.95 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.64/5.95 & ( ( B = A )
% 5.64/5.95 | ( B
% 5.64/5.95 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_abs_iff'
% 5.64/5.95 thf(fact_6521_eq__abs__iff_H,axiom,
% 5.64/5.95 ! [A: rat,B: rat] :
% 5.64/5.95 ( ( A
% 5.64/5.95 = ( abs_abs_rat @ B ) )
% 5.64/5.95 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.95 & ( ( B = A )
% 5.64/5.95 | ( B
% 5.64/5.95 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_abs_iff'
% 5.64/5.95 thf(fact_6522_eq__abs__iff_H,axiom,
% 5.64/5.95 ! [A: int,B: int] :
% 5.64/5.95 ( ( A
% 5.64/5.95 = ( abs_abs_int @ B ) )
% 5.64/5.95 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.64/5.95 & ( ( B = A )
% 5.64/5.95 | ( B
% 5.64/5.95 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_abs_iff'
% 5.64/5.95 thf(fact_6523_eq__abs__iff_H,axiom,
% 5.64/5.95 ! [A: real,B: real] :
% 5.64/5.95 ( ( A
% 5.64/5.95 = ( abs_abs_real @ B ) )
% 5.64/5.95 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.95 & ( ( B = A )
% 5.64/5.95 | ( B
% 5.64/5.95 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % eq_abs_iff'
% 5.64/5.95 thf(fact_6524_abs__minus__le__zero,axiom,
% 5.64/5.95 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_le_zero
% 5.64/5.95 thf(fact_6525_abs__minus__le__zero,axiom,
% 5.64/5.95 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_le_zero
% 5.64/5.95 thf(fact_6526_abs__minus__le__zero,axiom,
% 5.64/5.95 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_le_zero
% 5.64/5.95 thf(fact_6527_abs__minus__le__zero,axiom,
% 5.64/5.95 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.64/5.95
% 5.64/5.95 % abs_minus_le_zero
% 5.64/5.95 thf(fact_6528_abs__div__pos,axiom,
% 5.64/5.95 ! [Y4: real,X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( divide_divide_real @ ( abs_abs_real @ X2 ) @ Y4 )
% 5.64/5.95 = ( abs_abs_real @ ( divide_divide_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_div_pos
% 5.64/5.95 thf(fact_6529_abs__div__pos,axiom,
% 5.64/5.95 ! [Y4: rat,X2: rat] :
% 5.64/5.95 ( ( ord_less_rat @ zero_zero_rat @ Y4 )
% 5.64/5.95 => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y4 )
% 5.64/5.95 = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_div_pos
% 5.64/5.95 thf(fact_6530_zero__le__power__abs,axiom,
% 5.64/5.95 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_le_power_abs
% 5.64/5.95 thf(fact_6531_zero__le__power__abs,axiom,
% 5.64/5.95 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_le_power_abs
% 5.64/5.95 thf(fact_6532_zero__le__power__abs,axiom,
% 5.64/5.95 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_le_power_abs
% 5.64/5.95 thf(fact_6533_zero__le__power__abs,axiom,
% 5.64/5.95 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_le_power_abs
% 5.64/5.95 thf(fact_6534_abs__if,axiom,
% 5.64/5.95 ( abs_abs_int
% 5.64/5.95 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if
% 5.64/5.95 thf(fact_6535_abs__if,axiom,
% 5.64/5.95 ( abs_abs_real
% 5.64/5.95 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if
% 5.64/5.95 thf(fact_6536_abs__if,axiom,
% 5.64/5.95 ( abs_abs_rat
% 5.64/5.95 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if
% 5.64/5.95 thf(fact_6537_abs__if,axiom,
% 5.64/5.95 ( abs_abs_Code_integer
% 5.64/5.95 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if
% 5.64/5.95 thf(fact_6538_abs__if__raw,axiom,
% 5.64/5.95 ( abs_abs_int
% 5.64/5.95 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if_raw
% 5.64/5.95 thf(fact_6539_abs__if__raw,axiom,
% 5.64/5.95 ( abs_abs_real
% 5.64/5.95 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if_raw
% 5.64/5.95 thf(fact_6540_abs__if__raw,axiom,
% 5.64/5.95 ( abs_abs_rat
% 5.64/5.95 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if_raw
% 5.64/5.95 thf(fact_6541_abs__if__raw,axiom,
% 5.64/5.95 ( abs_abs_Code_integer
% 5.64/5.95 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_if_raw
% 5.64/5.95 thf(fact_6542_abs__of__neg,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( ord_less_int @ A @ zero_zero_int )
% 5.64/5.95 => ( ( abs_abs_int @ A )
% 5.64/5.95 = ( uminus_uminus_int @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_neg
% 5.64/5.95 thf(fact_6543_abs__of__neg,axiom,
% 5.64/5.95 ! [A: real] :
% 5.64/5.95 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.95 => ( ( abs_abs_real @ A )
% 5.64/5.95 = ( uminus_uminus_real @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_neg
% 5.64/5.95 thf(fact_6544_abs__of__neg,axiom,
% 5.64/5.95 ! [A: rat] :
% 5.64/5.95 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.64/5.95 => ( ( abs_abs_rat @ A )
% 5.64/5.95 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_neg
% 5.64/5.95 thf(fact_6545_abs__of__neg,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.64/5.95 => ( ( abs_abs_Code_integer @ A )
% 5.64/5.95 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_of_neg
% 5.64/5.95 thf(fact_6546_abs__diff__le__iff,axiom,
% 5.64/5.95 ! [X2: code_integer,A: code_integer,R2: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_le_iff
% 5.64/5.95 thf(fact_6547_abs__diff__le__iff,axiom,
% 5.64/5.95 ! [X2: rat,A: rat,R2: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_le_iff
% 5.64/5.95 thf(fact_6548_abs__diff__le__iff,axiom,
% 5.64/5.95 ! [X2: int,A: int,R2: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_le_iff
% 5.64/5.95 thf(fact_6549_abs__diff__le__iff,axiom,
% 5.64/5.95 ! [X2: real,A: real,R2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_le_iff
% 5.64/5.95 thf(fact_6550_abs__diff__triangle__ineq,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_triangle_ineq
% 5.64/5.95 thf(fact_6551_abs__diff__triangle__ineq,axiom,
% 5.64/5.95 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_triangle_ineq
% 5.64/5.95 thf(fact_6552_abs__diff__triangle__ineq,axiom,
% 5.64/5.95 ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_triangle_ineq
% 5.64/5.95 thf(fact_6553_abs__diff__triangle__ineq,axiom,
% 5.64/5.95 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_triangle_ineq
% 5.64/5.95 thf(fact_6554_abs__triangle__ineq4,axiom,
% 5.64/5.95 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq4
% 5.64/5.95 thf(fact_6555_abs__triangle__ineq4,axiom,
% 5.64/5.95 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq4
% 5.64/5.95 thf(fact_6556_abs__triangle__ineq4,axiom,
% 5.64/5.95 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq4
% 5.64/5.95 thf(fact_6557_abs__triangle__ineq4,axiom,
% 5.64/5.95 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_triangle_ineq4
% 5.64/5.95 thf(fact_6558_abs__diff__less__iff,axiom,
% 5.64/5.95 ! [X2: code_integer,A: code_integer,R2: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_less_iff
% 5.64/5.95 thf(fact_6559_abs__diff__less__iff,axiom,
% 5.64/5.95 ! [X2: real,A: real,R2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_less_real @ X2 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_less_iff
% 5.64/5.95 thf(fact_6560_abs__diff__less__iff,axiom,
% 5.64/5.95 ! [X2: rat,A: rat,R2: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_less_iff
% 5.64/5.95 thf(fact_6561_abs__diff__less__iff,axiom,
% 5.64/5.95 ! [X2: int,A: int,R2: int] :
% 5.64/5.95 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R2 )
% 5.64/5.95 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X2 )
% 5.64/5.95 & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_diff_less_iff
% 5.64/5.95 thf(fact_6562_round__mono,axiom,
% 5.64/5.95 ! [X2: rat,Y4: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.95 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_mono
% 5.64/5.95 thf(fact_6563_round__mono,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.95 => ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X2 ) @ ( archim8280529875227126926d_real @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_mono
% 5.64/5.95 thf(fact_6564_abs__real__def,axiom,
% 5.64/5.95 ( abs_abs_real
% 5.64/5.95 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_real_def
% 5.64/5.95 thf(fact_6565_lemma__interval__lt,axiom,
% 5.64/5.95 ! [A: real,X2: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ A @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ X2 @ B )
% 5.64/5.95 => ? [D3: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/5.95 & ! [Y5: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y5 ) ) @ D3 )
% 5.64/5.95 => ( ( ord_less_real @ A @ Y5 )
% 5.64/5.95 & ( ord_less_real @ Y5 @ B ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % lemma_interval_lt
% 5.64/5.95 thf(fact_6566_tanh__real__gt__neg1,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % tanh_real_gt_neg1
% 5.64/5.95 thf(fact_6567_abs__add__one__gt__zero,axiom,
% 5.64/5.95 ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_one_gt_zero
% 5.64/5.95 thf(fact_6568_abs__add__one__gt__zero,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_one_gt_zero
% 5.64/5.95 thf(fact_6569_abs__add__one__gt__zero,axiom,
% 5.64/5.95 ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_one_gt_zero
% 5.64/5.95 thf(fact_6570_abs__add__one__gt__zero,axiom,
% 5.64/5.95 ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_add_one_gt_zero
% 5.64/5.95 thf(fact_6571_of__int__leD,axiom,
% 5.64/5.95 ! [N: int,X2: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_leD
% 5.64/5.95 thf(fact_6572_of__int__leD,axiom,
% 5.64/5.95 ! [N: int,X2: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_leD
% 5.64/5.95 thf(fact_6573_of__int__leD,axiom,
% 5.64/5.95 ! [N: int,X2: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_leD
% 5.64/5.95 thf(fact_6574_of__int__leD,axiom,
% 5.64/5.95 ! [N: int,X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_leD
% 5.64/5.95 thf(fact_6575_of__int__lessD,axiom,
% 5.64/5.95 ! [N: int,X2: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_lessD
% 5.64/5.95 thf(fact_6576_of__int__lessD,axiom,
% 5.64/5.95 ! [N: int,X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_lessD
% 5.64/5.95 thf(fact_6577_of__int__lessD,axiom,
% 5.64/5.95 ! [N: int,X2: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_lessD
% 5.64/5.95 thf(fact_6578_of__int__lessD,axiom,
% 5.64/5.95 ! [N: int,X2: int] :
% 5.64/5.95 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X2 )
% 5.64/5.95 => ( ( N = zero_zero_int )
% 5.64/5.95 | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_lessD
% 5.64/5.95 thf(fact_6579_lemma__interval,axiom,
% 5.64/5.95 ! [A: real,X2: real,B: real] :
% 5.64/5.95 ( ( ord_less_real @ A @ X2 )
% 5.64/5.95 => ( ( ord_less_real @ X2 @ B )
% 5.64/5.95 => ? [D3: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/5.95 & ! [Y5: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y5 ) ) @ D3 )
% 5.64/5.95 => ( ( ord_less_eq_real @ A @ Y5 )
% 5.64/5.95 & ( ord_less_eq_real @ Y5 @ B ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % lemma_interval
% 5.64/5.95 thf(fact_6580_of__int__round__abs__le,axiom,
% 5.64/5.95 ! [X2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ X2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_abs_le
% 5.64/5.95 thf(fact_6581_of__int__round__abs__le,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ X2 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_abs_le
% 5.64/5.95 thf(fact_6582_round__unique_H,axiom,
% 5.64/5.95 ! [X2: real,N: int] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.95 => ( ( archim8280529875227126926d_real @ X2 )
% 5.64/5.95 = N ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_unique'
% 5.64/5.95 thf(fact_6583_round__unique_H,axiom,
% 5.64/5.95 ! [X2: rat,N: int] :
% 5.64/5.95 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.64/5.95 = N ) ) ).
% 5.64/5.95
% 5.64/5.95 % round_unique'
% 5.64/5.95 thf(fact_6584_abs__le__square__iff,axiom,
% 5.64/5.95 ! [X2: code_integer,Y4: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ Y4 ) )
% 5.64/5.95 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_square_iff
% 5.64/5.95 thf(fact_6585_abs__le__square__iff,axiom,
% 5.64/5.95 ! [X2: rat,Y4: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ ( abs_abs_rat @ Y4 ) )
% 5.64/5.95 = ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_square_iff
% 5.64/5.95 thf(fact_6586_abs__le__square__iff,axiom,
% 5.64/5.95 ! [X2: int,Y4: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y4 ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_square_iff
% 5.64/5.95 thf(fact_6587_abs__le__square__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y4 ) )
% 5.64/5.95 = ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_le_square_iff
% 5.64/5.95 thf(fact_6588_abs__square__eq__1,axiom,
% 5.64/5.95 ! [X2: code_integer] :
% 5.64/5.95 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_Code_integer )
% 5.64/5.95 = ( ( abs_abs_Code_integer @ X2 )
% 5.64/5.95 = one_one_Code_integer ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_eq_1
% 5.64/5.95 thf(fact_6589_abs__square__eq__1,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_rat )
% 5.64/5.95 = ( ( abs_abs_rat @ X2 )
% 5.64/5.95 = one_one_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_eq_1
% 5.64/5.95 thf(fact_6590_abs__square__eq__1,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_real )
% 5.64/5.95 = ( ( abs_abs_real @ X2 )
% 5.64/5.95 = one_one_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_eq_1
% 5.64/5.95 thf(fact_6591_abs__square__eq__1,axiom,
% 5.64/5.95 ! [X2: int] :
% 5.64/5.95 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = one_one_int )
% 5.64/5.95 = ( ( abs_abs_int @ X2 )
% 5.64/5.95 = one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_eq_1
% 5.64/5.95 thf(fact_6592_power__even__abs,axiom,
% 5.64/5.95 ! [N: nat,A: rat] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.64/5.95 = ( power_power_rat @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs
% 5.64/5.95 thf(fact_6593_power__even__abs,axiom,
% 5.64/5.95 ! [N: nat,A: code_integer] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.64/5.95 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs
% 5.64/5.95 thf(fact_6594_power__even__abs,axiom,
% 5.64/5.95 ! [N: nat,A: real] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.64/5.95 = ( power_power_real @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs
% 5.64/5.95 thf(fact_6595_power__even__abs,axiom,
% 5.64/5.95 ! [N: nat,A: int] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.64/5.95 = ( power_power_int @ A @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_even_abs
% 5.64/5.95 thf(fact_6596_power2__le__iff__abs__le,axiom,
% 5.64/5.95 ! [Y4: code_integer,X2: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y4 )
% 5.64/5.95 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_le_iff_abs_le
% 5.64/5.95 thf(fact_6597_power2__le__iff__abs__le,axiom,
% 5.64/5.95 ! [Y4: rat,X2: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ Y4 )
% 5.64/5.95 => ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_le_iff_abs_le
% 5.64/5.95 thf(fact_6598_power2__le__iff__abs__le,axiom,
% 5.64/5.95 ! [Y4: int,X2: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.95 => ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_le_iff_abs_le
% 5.64/5.95 thf(fact_6599_power2__le__iff__abs__le,axiom,
% 5.64/5.95 ! [Y4: real,X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.95 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power2_le_iff_abs_le
% 5.64/5.95 thf(fact_6600_abs__sqrt__wlog,axiom,
% 5.64/5.95 ! [P: code_integer > code_integer > $o,X2: code_integer] :
% 5.64/5.95 ( ! [X4: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.64/5.95 => ( P @ X4 @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 => ( P @ ( abs_abs_Code_integer @ X2 ) @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_sqrt_wlog
% 5.64/5.95 thf(fact_6601_abs__sqrt__wlog,axiom,
% 5.64/5.95 ! [P: rat > rat > $o,X2: rat] :
% 5.64/5.95 ( ! [X4: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.64/5.95 => ( P @ X4 @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 => ( P @ ( abs_abs_rat @ X2 ) @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_sqrt_wlog
% 5.64/5.95 thf(fact_6602_abs__sqrt__wlog,axiom,
% 5.64/5.95 ! [P: int > int > $o,X2: int] :
% 5.64/5.95 ( ! [X4: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.64/5.95 => ( P @ X4 @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 => ( P @ ( abs_abs_int @ X2 ) @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_sqrt_wlog
% 5.64/5.95 thf(fact_6603_abs__sqrt__wlog,axiom,
% 5.64/5.95 ! [P: real > real > $o,X2: real] :
% 5.64/5.95 ( ! [X4: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.64/5.95 => ( P @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.95 => ( P @ ( abs_abs_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_sqrt_wlog
% 5.64/5.95 thf(fact_6604_abs__square__le__1,axiom,
% 5.64/5.95 ! [X2: code_integer] :
% 5.64/5.95 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.64/5.95 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_le_1
% 5.64/5.95 thf(fact_6605_abs__square__le__1,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.64/5.95 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_le_1
% 5.64/5.95 thf(fact_6606_abs__square__le__1,axiom,
% 5.64/5.95 ! [X2: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.64/5.95 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_le_1
% 5.64/5.95 thf(fact_6607_abs__square__le__1,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.64/5.95 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_le_1
% 5.64/5.95 thf(fact_6608_abs__square__less__1,axiom,
% 5.64/5.95 ! [X2: code_integer] :
% 5.64/5.95 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.64/5.95 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_less_1
% 5.64/5.95 thf(fact_6609_abs__square__less__1,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.64/5.95 = ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_less_1
% 5.64/5.95 thf(fact_6610_abs__square__less__1,axiom,
% 5.64/5.95 ! [X2: rat] :
% 5.64/5.95 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.64/5.95 = ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_less_1
% 5.64/5.95 thf(fact_6611_abs__square__less__1,axiom,
% 5.64/5.95 ! [X2: int] :
% 5.64/5.95 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.64/5.95 = ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_square_less_1
% 5.64/5.95 thf(fact_6612_power__mono__even,axiom,
% 5.64/5.95 ! [N: nat,A: code_integer,B: code_integer] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.64/5.95 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_mono_even
% 5.64/5.95 thf(fact_6613_power__mono__even,axiom,
% 5.64/5.95 ! [N: nat,A: rat,B: rat] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_mono_even
% 5.64/5.95 thf(fact_6614_power__mono__even,axiom,
% 5.64/5.95 ! [N: nat,A: int,B: int] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_mono_even
% 5.64/5.95 thf(fact_6615_power__mono__even,axiom,
% 5.64/5.95 ! [N: nat,A: real,B: real] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.95 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.64/5.95 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % power_mono_even
% 5.64/5.95 thf(fact_6616_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.95 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.95 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.64/5.95 thf(fact_6617_of__int__round__le,axiom,
% 5.64/5.95 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_le
% 5.64/5.95 thf(fact_6618_of__int__round__le,axiom,
% 5.64/5.95 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % of_int_round_le
% 5.64/5.95 thf(fact_6619_arctan__double,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.95 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.64/5.95 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % arctan_double
% 5.64/5.95 thf(fact_6620_Sum__Icc__int,axiom,
% 5.64/5.95 ! [M: int,N: int] :
% 5.64/5.95 ( ( ord_less_eq_int @ M @ N )
% 5.64/5.95 => ( ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [X: int] : X
% 5.64/5.95 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.64/5.95 = ( 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 ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % Sum_Icc_int
% 5.64/5.95 thf(fact_6621_even__set__encode__iff,axiom,
% 5.64/5.95 ! [A4: set_nat] :
% 5.64/5.95 ( ( finite_finite_nat @ A4 )
% 5.64/5.95 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 5.64/5.95 = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_set_encode_iff
% 5.64/5.95 thf(fact_6622_mask__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.64/5.95 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % mask_numeral
% 5.64/5.95 thf(fact_6623_mask__numeral,axiom,
% 5.64/5.95 ! [N: num] :
% 5.64/5.95 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.64/5.95 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % mask_numeral
% 5.64/5.95 thf(fact_6624_num_Osize__gen_I3_J,axiom,
% 5.64/5.95 ! [X32: num] :
% 5.64/5.95 ( ( size_num @ ( bit1 @ X32 ) )
% 5.64/5.95 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % num.size_gen(3)
% 5.64/5.95 thf(fact_6625_take__bit__rec,axiom,
% 5.64/5.95 ( bit_se1745604003318907178nteger
% 5.64/5.95 = ( ^ [N2: nat,A3: 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 @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_rec
% 5.64/5.95 thf(fact_6626_take__bit__rec,axiom,
% 5.64/5.95 ( bit_se2925701944663578781it_nat
% 5.64/5.95 = ( ^ [N2: nat,A3: 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 @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_rec
% 5.64/5.95 thf(fact_6627_take__bit__rec,axiom,
% 5.64/5.95 ( bit_se2923211474154528505it_int
% 5.64/5.95 = ( ^ [N2: nat,A3: 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 @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_rec
% 5.64/5.95 thf(fact_6628_mask__nat__positive__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.64/5.95 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % mask_nat_positive_iff
% 5.64/5.95 thf(fact_6629_take__bit__Suc__1,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.64/5.95 = one_one_nat ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_Suc_1
% 5.64/5.95 thf(fact_6630_take__bit__Suc__1,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_Suc_1
% 5.64/5.95 thf(fact_6631_take__bit__numeral__1,axiom,
% 5.64/5.95 ! [L: num] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.64/5.95 = one_one_nat ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_numeral_1
% 5.64/5.95 thf(fact_6632_take__bit__numeral__1,axiom,
% 5.64/5.95 ! [L: num] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_numeral_1
% 5.64/5.95 thf(fact_6633_zabs__less__one__iff,axiom,
% 5.64/5.95 ! [Z: int] :
% 5.64/5.95 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.64/5.95 = ( Z = zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % zabs_less_one_iff
% 5.64/5.95 thf(fact_6634_arctan__less__zero__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ ( arctan @ X2 ) @ zero_zero_real )
% 5.64/5.95 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.95
% 5.64/5.95 % arctan_less_zero_iff
% 5.64/5.95 thf(fact_6635_zero__less__arctan__iff,axiom,
% 5.64/5.95 ! [X2: real] :
% 5.64/5.95 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X2 ) )
% 5.64/5.95 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.95
% 5.64/5.95 % zero_less_arctan_iff
% 5.64/5.95 thf(fact_6636_sum__abs,axiom,
% 5.64/5.95 ! [F: int > int,A4: set_int] :
% 5.64/5.95 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A4 ) )
% 5.64/5.95 @ ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_abs
% 5.64/5.95 thf(fact_6637_sum__abs,axiom,
% 5.64/5.95 ! [F: nat > real,A4: set_nat] :
% 5.64/5.95 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A4 ) )
% 5.64/5.95 @ ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_abs
% 5.64/5.95 thf(fact_6638_take__bit__of__1__eq__0__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.64/5.95 = zero_zero_nat )
% 5.64/5.95 = ( N = zero_zero_nat ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_1_eq_0_iff
% 5.64/5.95 thf(fact_6639_take__bit__of__1__eq__0__iff,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.64/5.95 = zero_zero_int )
% 5.64/5.95 = ( N = zero_zero_nat ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_1_eq_0_iff
% 5.64/5.95 thf(fact_6640_mask__Suc__0,axiom,
% 5.64/5.95 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.64/5.95 = one_one_nat ) ).
% 5.64/5.95
% 5.64/5.95 % mask_Suc_0
% 5.64/5.95 thf(fact_6641_mask__Suc__0,axiom,
% 5.64/5.95 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.64/5.95 = one_one_int ) ).
% 5.64/5.95
% 5.64/5.95 % mask_Suc_0
% 5.64/5.95 thf(fact_6642_take__bit__minus__one__eq__mask,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.95 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_minus_one_eq_mask
% 5.64/5.95 thf(fact_6643_take__bit__minus__one__eq__mask,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.95 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_minus_one_eq_mask
% 5.64/5.95 thf(fact_6644_take__bit__of__Suc__0,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/5.95 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_Suc_0
% 5.64/5.95 thf(fact_6645_sum__abs__ge__zero,axiom,
% 5.64/5.95 ! [F: int > int,A4: set_int] :
% 5.64/5.95 ( ord_less_eq_int @ zero_zero_int
% 5.64/5.95 @ ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_abs_ge_zero
% 5.64/5.95 thf(fact_6646_sum__abs__ge__zero,axiom,
% 5.64/5.95 ! [F: nat > real,A4: set_nat] :
% 5.64/5.95 ( ord_less_eq_real @ zero_zero_real
% 5.64/5.95 @ ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [I4: nat] : ( abs_abs_real @ ( F @ I4 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_abs_ge_zero
% 5.64/5.95 thf(fact_6647_take__bit__of__1,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.64/5.95 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_1
% 5.64/5.95 thf(fact_6648_take__bit__of__1,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.64/5.95 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_1
% 5.64/5.95 thf(fact_6649_take__bit__of__1,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.64/5.95 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_1
% 5.64/5.95 thf(fact_6650_even__take__bit__eq,axiom,
% 5.64/5.95 ! [N: nat,A: code_integer] :
% 5.64/5.95 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.64/5.95 = ( ( N = zero_zero_nat )
% 5.64/5.95 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_take_bit_eq
% 5.64/5.95 thf(fact_6651_even__take__bit__eq,axiom,
% 5.64/5.95 ! [N: nat,A: nat] :
% 5.64/5.95 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.64/5.95 = ( ( N = zero_zero_nat )
% 5.64/5.95 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_take_bit_eq
% 5.64/5.95 thf(fact_6652_even__take__bit__eq,axiom,
% 5.64/5.95 ! [N: nat,A: int] :
% 5.64/5.95 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.64/5.95 = ( ( N = zero_zero_nat )
% 5.64/5.95 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % even_take_bit_eq
% 5.64/5.95 thf(fact_6653_take__bit__Suc__0,axiom,
% 5.64/5.95 ! [A: code_integer] :
% 5.64/5.95 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.64/5.95 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_Suc_0
% 5.64/5.95 thf(fact_6654_take__bit__Suc__0,axiom,
% 5.64/5.95 ! [A: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.64/5.95 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_Suc_0
% 5.64/5.95 thf(fact_6655_take__bit__Suc__0,axiom,
% 5.64/5.95 ! [A: int] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.64/5.95 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_Suc_0
% 5.64/5.95 thf(fact_6656_take__bit__of__exp,axiom,
% 5.64/5.95 ! [M: nat,N: nat] :
% 5.64/5.95 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.95 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_exp
% 5.64/5.95 thf(fact_6657_take__bit__of__exp,axiom,
% 5.64/5.95 ! [M: nat,N: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.95 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_exp
% 5.64/5.95 thf(fact_6658_take__bit__of__exp,axiom,
% 5.64/5.95 ! [M: nat,N: nat] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.95 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_exp
% 5.64/5.95 thf(fact_6659_take__bit__of__2,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_2
% 5.64/5.95 thf(fact_6660_take__bit__of__2,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_2
% 5.64/5.95 thf(fact_6661_take__bit__of__2,axiom,
% 5.64/5.95 ! [N: nat] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.95 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_of_2
% 5.64/5.95 thf(fact_6662_take__bit__add,axiom,
% 5.64/5.95 ! [N: nat,A: nat,B: nat] :
% 5.64/5.95 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.64/5.95 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_add
% 5.64/5.95 thf(fact_6663_take__bit__add,axiom,
% 5.64/5.95 ! [N: nat,A: int,B: int] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.64/5.95 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_add
% 5.64/5.95 thf(fact_6664_take__bit__tightened,axiom,
% 5.64/5.95 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.64/5.95 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.64/5.95 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.64/5.95 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.95 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.64/5.95 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_tightened
% 5.64/5.95 thf(fact_6665_take__bit__tightened,axiom,
% 5.64/5.95 ! [N: nat,A: int,B: int,M: nat] :
% 5.64/5.95 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.64/5.95 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.64/5.95 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.95 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.64/5.95 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_tightened
% 5.64/5.95 thf(fact_6666_take__bit__nat__less__eq__self,axiom,
% 5.64/5.95 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_nat_less_eq_self
% 5.64/5.95 thf(fact_6667_take__bit__tightened__less__eq__nat,axiom,
% 5.64/5.95 ! [M: nat,N: nat,Q3: nat] :
% 5.64/5.95 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.95 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N @ Q3 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_tightened_less_eq_nat
% 5.64/5.95 thf(fact_6668_take__bit__mult,axiom,
% 5.64/5.95 ! [N: nat,K: int,L: int] :
% 5.64/5.95 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 5.64/5.95 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % take_bit_mult
% 5.64/5.95 thf(fact_6669_arctan__monotone,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.95 => ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % arctan_monotone
% 5.64/5.95 thf(fact_6670_arctan__less__iff,axiom,
% 5.64/5.95 ! [X2: real,Y4: real] :
% 5.64/5.95 ( ( ord_less_real @ ( arctan @ X2 ) @ ( arctan @ Y4 ) )
% 5.64/5.95 = ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % arctan_less_iff
% 5.64/5.95 thf(fact_6671_less__eq__mask,axiom,
% 5.64/5.95 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.64/5.95
% 5.64/5.95 % less_eq_mask
% 5.64/5.95 thf(fact_6672_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.64/5.95 ( ! [I3: complex] :
% 5.64/5.95 ( ( member_complex @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6673_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.64/5.95 ( ! [I3: real] :
% 5.64/5.95 ( ( member_real @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6674_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.64/5.95 ( ! [I3: nat] :
% 5.64/5.95 ( ( member_nat @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6675_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.64/5.95 ( ! [I3: int] :
% 5.64/5.95 ( ( member_int @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6676_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.64/5.95 ( ! [I3: complex] :
% 5.64/5.95 ( ( member_complex @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6677_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.64/5.95 ( ! [I3: real] :
% 5.64/5.95 ( ( member_real @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6678_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.64/5.95 ( ! [I3: int] :
% 5.64/5.95 ( ( member_int @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6679_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.64/5.95 ( ! [I3: complex] :
% 5.64/5.95 ( ( member_complex @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6680_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_real,F: real > int,G: real > int] :
% 5.64/5.95 ( ! [I3: real] :
% 5.64/5.95 ( ( member_real @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6681_sum__mono,axiom,
% 5.64/5.95 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.64/5.95 ( ! [I3: nat] :
% 5.64/5.95 ( ( member_nat @ I3 @ K5 )
% 5.64/5.95 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_mono
% 5.64/5.95 thf(fact_6682_sum__distrib__left,axiom,
% 5.64/5.95 ! [R2: int,F: int > int,A4: set_int] :
% 5.64/5.95 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A4 ) )
% 5.64/5.95 = ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [N2: int] : ( times_times_int @ R2 @ ( F @ N2 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_left
% 5.64/5.95 thf(fact_6683_sum__distrib__left,axiom,
% 5.64/5.95 ! [R2: complex,F: complex > complex,A4: set_complex] :
% 5.64/5.95 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A4 ) )
% 5.64/5.95 = ( groups7754918857620584856omplex
% 5.64/5.95 @ ^ [N2: complex] : ( times_times_complex @ R2 @ ( F @ N2 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_left
% 5.64/5.95 thf(fact_6684_sum__distrib__left,axiom,
% 5.64/5.95 ! [R2: nat,F: nat > nat,A4: set_nat] :
% 5.64/5.95 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 5.64/5.95 = ( groups3542108847815614940at_nat
% 5.64/5.95 @ ^ [N2: nat] : ( times_times_nat @ R2 @ ( F @ N2 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_left
% 5.64/5.95 thf(fact_6685_sum__distrib__left,axiom,
% 5.64/5.95 ! [R2: real,F: nat > real,A4: set_nat] :
% 5.64/5.95 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A4 ) )
% 5.64/5.95 = ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( F @ N2 ) )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_left
% 5.64/5.95 thf(fact_6686_sum__distrib__right,axiom,
% 5.64/5.95 ! [F: int > int,A4: set_int,R2: int] :
% 5.64/5.95 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ R2 )
% 5.64/5.95 = ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R2 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_right
% 5.64/5.95 thf(fact_6687_sum__distrib__right,axiom,
% 5.64/5.95 ! [F: complex > complex,A4: set_complex,R2: complex] :
% 5.64/5.95 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A4 ) @ R2 )
% 5.64/5.95 = ( groups7754918857620584856omplex
% 5.64/5.95 @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R2 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_right
% 5.64/5.95 thf(fact_6688_sum__distrib__right,axiom,
% 5.64/5.95 ! [F: nat > nat,A4: set_nat,R2: nat] :
% 5.64/5.95 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ R2 )
% 5.64/5.95 = ( groups3542108847815614940at_nat
% 5.64/5.95 @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R2 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_right
% 5.64/5.95 thf(fact_6689_sum__distrib__right,axiom,
% 5.64/5.95 ! [F: nat > real,A4: set_nat,R2: real] :
% 5.64/5.95 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A4 ) @ R2 )
% 5.64/5.95 = ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R2 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_distrib_right
% 5.64/5.95 thf(fact_6690_sum__product,axiom,
% 5.64/5.95 ! [F: int > int,A4: set_int,G: int > int,B4: set_int] :
% 5.64/5.95 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ G @ B4 ) )
% 5.64/5.95 = ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [I4: int] :
% 5.64/5.95 ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [J3: int] : ( times_times_int @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.64/5.95 @ B4 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_product
% 5.64/5.95 thf(fact_6691_sum__product,axiom,
% 5.64/5.95 ! [F: complex > complex,A4: set_complex,G: complex > complex,B4: set_complex] :
% 5.64/5.95 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A4 ) @ ( groups7754918857620584856omplex @ G @ B4 ) )
% 5.64/5.95 = ( groups7754918857620584856omplex
% 5.64/5.95 @ ^ [I4: complex] :
% 5.64/5.95 ( groups7754918857620584856omplex
% 5.64/5.95 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.64/5.95 @ B4 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_product
% 5.64/5.95 thf(fact_6692_sum__product,axiom,
% 5.64/5.95 ! [F: nat > nat,A4: set_nat,G: nat > nat,B4: set_nat] :
% 5.64/5.95 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ B4 ) )
% 5.64/5.95 = ( groups3542108847815614940at_nat
% 5.64/5.95 @ ^ [I4: nat] :
% 5.64/5.95 ( groups3542108847815614940at_nat
% 5.64/5.95 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.64/5.95 @ B4 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_product
% 5.64/5.95 thf(fact_6693_sum__product,axiom,
% 5.64/5.95 ! [F: nat > real,A4: set_nat,G: nat > real,B4: set_nat] :
% 5.64/5.95 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A4 ) @ ( groups6591440286371151544t_real @ G @ B4 ) )
% 5.64/5.95 = ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [I4: nat] :
% 5.64/5.95 ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [J3: nat] : ( times_times_real @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.64/5.95 @ B4 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_product
% 5.64/5.95 thf(fact_6694_sum_Odistrib,axiom,
% 5.64/5.95 ! [G: int > int,H2: int > int,A4: set_int] :
% 5.64/5.95 ( ( groups4538972089207619220nt_int
% 5.64/5.95 @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.95 @ A4 )
% 5.64/5.95 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A4 ) @ ( groups4538972089207619220nt_int @ H2 @ A4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum.distrib
% 5.64/5.95 thf(fact_6695_sum_Odistrib,axiom,
% 5.64/5.95 ! [G: complex > complex,H2: complex > complex,A4: set_complex] :
% 5.64/5.95 ( ( groups7754918857620584856omplex
% 5.64/5.95 @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.95 @ A4 )
% 5.64/5.95 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A4 ) @ ( groups7754918857620584856omplex @ H2 @ A4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum.distrib
% 5.64/5.95 thf(fact_6696_sum_Odistrib,axiom,
% 5.64/5.95 ! [G: nat > nat,H2: nat > nat,A4: set_nat] :
% 5.64/5.95 ( ( groups3542108847815614940at_nat
% 5.64/5.95 @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.95 @ A4 )
% 5.64/5.95 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A4 ) @ ( groups3542108847815614940at_nat @ H2 @ A4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum.distrib
% 5.64/5.95 thf(fact_6697_sum_Odistrib,axiom,
% 5.64/5.95 ! [G: nat > real,H2: nat > real,A4: set_nat] :
% 5.64/5.95 ( ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.95 @ A4 )
% 5.64/5.95 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A4 ) @ ( groups6591440286371151544t_real @ H2 @ A4 ) ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum.distrib
% 5.64/5.95 thf(fact_6698_sum__divide__distrib,axiom,
% 5.64/5.95 ! [F: complex > complex,A4: set_complex,R2: complex] :
% 5.64/5.95 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A4 ) @ R2 )
% 5.64/5.95 = ( groups7754918857620584856omplex
% 5.64/5.95 @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R2 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_divide_distrib
% 5.64/5.95 thf(fact_6699_sum__divide__distrib,axiom,
% 5.64/5.95 ! [F: nat > real,A4: set_nat,R2: real] :
% 5.64/5.95 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A4 ) @ R2 )
% 5.64/5.95 = ( groups6591440286371151544t_real
% 5.64/5.95 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R2 )
% 5.64/5.95 @ A4 ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_divide_distrib
% 5.64/5.95 thf(fact_6700_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_complex,F: complex > rat] :
% 5.64/5.95 ( ! [X4: complex] :
% 5.64/5.95 ( ( member_complex @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6701_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_real,F: real > rat] :
% 5.64/5.95 ( ! [X4: real] :
% 5.64/5.95 ( ( member_real @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6702_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_nat,F: nat > rat] :
% 5.64/5.95 ( ! [X4: nat] :
% 5.64/5.95 ( ( member_nat @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6703_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_int,F: int > rat] :
% 5.64/5.95 ( ! [X4: int] :
% 5.64/5.95 ( ( member_int @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_rat @ ( F @ X4 ) @ zero_zero_rat ) )
% 5.64/5.95 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ zero_zero_rat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6704_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.95 ( ! [X4: complex] :
% 5.64/5.95 ( ( member_complex @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.64/5.95 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6705_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_real,F: real > nat] :
% 5.64/5.95 ( ! [X4: real] :
% 5.64/5.95 ( ( member_real @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.64/5.95 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6706_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_int,F: int > nat] :
% 5.64/5.95 ( ! [X4: int] :
% 5.64/5.95 ( ( member_int @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_nat @ ( F @ X4 ) @ zero_zero_nat ) )
% 5.64/5.95 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ zero_zero_nat ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6707_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_complex,F: complex > int] :
% 5.64/5.95 ( ! [X4: complex] :
% 5.64/5.95 ( ( member_complex @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6708_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_real,F: real > int] :
% 5.64/5.95 ( ! [X4: real] :
% 5.64/5.95 ( ( member_real @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A4 ) @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6709_sum__nonpos,axiom,
% 5.64/5.95 ! [A4: set_nat,F: nat > int] :
% 5.64/5.95 ( ! [X4: nat] :
% 5.64/5.95 ( ( member_nat @ X4 @ A4 )
% 5.64/5.95 => ( ord_less_eq_int @ ( F @ X4 ) @ zero_zero_int ) )
% 5.64/5.95 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ zero_zero_int ) ) ).
% 5.64/5.95
% 5.64/5.95 % sum_nonpos
% 5.64/5.95 thf(fact_6710_sum__nonneg,axiom,
% 5.64/5.95 ! [A4: set_complex,F: complex > rat] :
% 5.64/5.96 ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6711_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > rat] :
% 5.64/5.96 ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6712_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > rat] :
% 5.64/5.96 ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6713_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > rat] :
% 5.64/5.96 ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6714_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.96 ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6715_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > nat] :
% 5.64/5.96 ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6716_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > nat] :
% 5.64/5.96 ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6717_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > int] :
% 5.64/5.96 ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( groups5690904116761175830ex_int @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6718_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > int] :
% 5.64/5.96 ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( groups1932886352136224148al_int @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6719_sum__nonneg,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > int] :
% 5.64/5.96 ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg
% 5.64/5.96 thf(fact_6720_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: real > rat,I5: set_real,G: real > rat,I: real] :
% 5.64/5.96 ( ( ( groups1300246762558778688al_rat @ F @ I5 )
% 5.64/5.96 = ( groups1300246762558778688al_rat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_real @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6721_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: nat > rat,I5: set_nat,G: nat > rat,I: nat] :
% 5.64/5.96 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.64/5.96 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_nat @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_nat @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6722_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: int > rat,I5: set_int,G: int > rat,I: int] :
% 5.64/5.96 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.64/5.96 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_int @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6723_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: complex > rat,I5: set_complex,G: complex > rat,I: complex] :
% 5.64/5.96 ( ( ( groups5058264527183730370ex_rat @ F @ I5 )
% 5.64/5.96 = ( groups5058264527183730370ex_rat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_complex @ I @ I5 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6724_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: real > nat,I5: set_real,G: real > nat,I: real] :
% 5.64/5.96 ( ( ( groups1935376822645274424al_nat @ F @ I5 )
% 5.64/5.96 = ( groups1935376822645274424al_nat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_real @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6725_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: int > nat,I5: set_int,G: int > nat,I: int] :
% 5.64/5.96 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.64/5.96 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_int @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6726_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: complex > nat,I5: set_complex,G: complex > nat,I: complex] :
% 5.64/5.96 ( ( ( groups5693394587270226106ex_nat @ F @ I5 )
% 5.64/5.96 = ( groups5693394587270226106ex_nat @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_complex @ I @ I5 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6727_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: real > int,I5: set_real,G: real > int,I: real] :
% 5.64/5.96 ( ( ( groups1932886352136224148al_int @ F @ I5 )
% 5.64/5.96 = ( groups1932886352136224148al_int @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_real @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6728_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: nat > int,I5: set_nat,G: nat > int,I: nat] :
% 5.64/5.96 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 5.64/5.96 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_nat @ I @ I5 )
% 5.64/5.96 => ( ( finite_finite_nat @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6729_sum__mono__inv,axiom,
% 5.64/5.96 ! [F: complex > int,I5: set_complex,G: complex > int,I: complex] :
% 5.64/5.96 ( ( ( groups5690904116761175830ex_int @ F @ I5 )
% 5.64/5.96 = ( groups5690904116761175830ex_int @ G @ I5 ) )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.64/5.96 => ( ( member_complex @ I @ I5 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = ( G @ I ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono_inv
% 5.64/5.96 thf(fact_6730_take__bit__tightened__less__eq__int,axiom,
% 5.64/5.96 ! [M: nat,N: nat,K: int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_tightened_less_eq_int
% 5.64/5.96 thf(fact_6731_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,A: int,B: int] :
% 5.64/5.96 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.64/5.96 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.64/5.96 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.64/5.96 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % signed_take_bit_eq_iff_take_bit_eq
% 5.64/5.96 thf(fact_6732_not__take__bit__negative,axiom,
% 5.64/5.96 ! [N: nat,K: int] :
% 5.64/5.96 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % not_take_bit_negative
% 5.64/5.96 thf(fact_6733_take__bit__int__greater__self__iff,axiom,
% 5.64/5.96 ! [K: int,N: nat] :
% 5.64/5.96 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.64/5.96 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_greater_self_iff
% 5.64/5.96 thf(fact_6734_signed__take__bit__take__bit,axiom,
% 5.64/5.96 ! [M: nat,N: nat,A: int] :
% 5.64/5.96 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.64/5.96 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.64/5.96
% 5.64/5.96 % signed_take_bit_take_bit
% 5.64/5.96 thf(fact_6735_take__bit__unset__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,M: nat,A: nat] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.64/5.96 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.64/5.96 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_unset_bit_eq
% 5.64/5.96 thf(fact_6736_take__bit__unset__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,M: nat,A: int] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.64/5.96 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.64/5.96 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_unset_bit_eq
% 5.64/5.96 thf(fact_6737_take__bit__set__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,M: nat,A: nat] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.64/5.96 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.64/5.96 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_set_bit_eq
% 5.64/5.96 thf(fact_6738_take__bit__set__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,M: nat,A: int] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.64/5.96 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.64/5.96 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_set_bit_eq
% 5.64/5.96 thf(fact_6739_take__bit__flip__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,M: nat,A: nat] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.64/5.96 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.64/5.96 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_flip_bit_eq
% 5.64/5.96 thf(fact_6740_take__bit__flip__bit__eq,axiom,
% 5.64/5.96 ! [N: nat,M: nat,A: int] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.64/5.96 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.64/5.96 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_flip_bit_eq
% 5.64/5.96 thf(fact_6741_abs__zmult__eq__1,axiom,
% 5.64/5.96 ! [M: int,N: int] :
% 5.64/5.96 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.64/5.96 = one_one_int )
% 5.64/5.96 => ( ( abs_abs_int @ M )
% 5.64/5.96 = one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_zmult_eq_1
% 5.64/5.96 thf(fact_6742_abs__div,axiom,
% 5.64/5.96 ! [Y4: int,X2: int] :
% 5.64/5.96 ( ( dvd_dvd_int @ Y4 @ X2 )
% 5.64/5.96 => ( ( abs_abs_int @ ( divide_divide_int @ X2 @ Y4 ) )
% 5.64/5.96 = ( divide_divide_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_div
% 5.64/5.96 thf(fact_6743_not__mask__negative__int,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % not_mask_negative_int
% 5.64/5.96 thf(fact_6744_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups1300246762558778688al_rat @ F @ A4 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 = ( ! [X: real] :
% 5.64/5.96 ( ( member_real @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6745_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups2906978787729119204at_rat @ F @ A4 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 = ( ! [X: nat] :
% 5.64/5.96 ( ( member_nat @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6746_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups3906332499630173760nt_rat @ F @ A4 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 = ( ! [X: int] :
% 5.64/5.96 ( ( member_int @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6747_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups5058264527183730370ex_rat @ F @ A4 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 = ( ! [X: complex] :
% 5.64/5.96 ( ( member_complex @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6748_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > nat] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups1935376822645274424al_nat @ F @ A4 )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 = ( ! [X: real] :
% 5.64/5.96 ( ( member_real @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6749_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 = ( ! [X: int] :
% 5.64/5.96 ( ( member_int @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6750_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 = ( ! [X: complex] :
% 5.64/5.96 ( ( member_complex @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6751_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > int] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups1932886352136224148al_int @ F @ A4 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 = ( ! [X: real] :
% 5.64/5.96 ( ( member_real @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_int ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6752_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > int] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups3539618377306564664at_int @ F @ A4 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 = ( ! [X: nat] :
% 5.64/5.96 ( ( member_nat @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_int ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6753_sum__nonneg__eq__0__iff,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > int] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( ( groups5690904116761175830ex_int @ F @ A4 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 = ( ! [X: complex] :
% 5.64/5.96 ( ( member_complex @ X @ A4 )
% 5.64/5.96 => ( ( F @ X )
% 5.64/5.96 = zero_zero_int ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_eq_0_iff
% 5.64/5.96 thf(fact_6754_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ( finite_finite_nat @ T )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: nat] :
% 5.64/5.96 ( ( member_nat @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6755_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ( finite_finite_int @ T )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: int] :
% 5.64/5.96 ( ( member_int @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6756_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ T )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: complex] :
% 5.64/5.96 ( ( member_complex @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6757_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ( finite_finite_nat @ T )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: nat] :
% 5.64/5.96 ( ( member_nat @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6758_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ( finite_finite_int @ T )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: int] :
% 5.64/5.96 ( ( member_int @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6759_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ T )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: complex] :
% 5.64/5.96 ( ( member_complex @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6760_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_complex,T: set_nat,G: nat > rat,I: nat > complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ( finite_finite_nat @ T )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: nat] :
% 5.64/5.96 ( ( member_nat @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6761_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_complex,T: set_int,G: int > rat,I: int > complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ( finite_finite_int @ T )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: int] :
% 5.64/5.96 ( ( member_int @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6762_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_complex,T: set_complex,G: complex > rat,I: complex > complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ T )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: complex] :
% 5.64/5.96 ( ( member_complex @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6763_sum__le__included,axiom,
% 5.64/5.96 ! [S2: set_int,T: set_int,G: int > nat,I: int > int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ( finite_finite_int @ T )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ T )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S2 )
% 5.64/5.96 => ? [Xa: int] :
% 5.64/5.96 ( ( member_int @ Xa @ T )
% 5.64/5.96 & ( ( I @ Xa )
% 5.64/5.96 = X4 )
% 5.64/5.96 & ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ Xa ) ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ T ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_le_included
% 5.64/5.96 thf(fact_6764_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: nat] :
% 5.64/5.96 ( ( member_nat @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6765_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > rat,G: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: int] :
% 5.64/5.96 ( ( member_int @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6766_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: complex] :
% 5.64/5.96 ( ( member_complex @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6767_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > nat,G: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: int] :
% 5.64/5.96 ( ( member_int @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6768_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > nat,G: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: complex] :
% 5.64/5.96 ( ( member_complex @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6769_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > int,G: nat > int] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: nat] :
% 5.64/5.96 ( ( member_nat @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A4 ) @ ( groups3539618377306564664at_int @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6770_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > int,G: complex > int] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: complex] :
% 5.64/5.96 ( ( member_complex @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( groups5690904116761175830ex_int @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6771_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > real,G: int > real] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: int] :
% 5.64/5.96 ( ( member_int @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6772_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: complex] :
% 5.64/5.96 ( ( member_complex @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_real @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6773_sum__strict__mono__ex1,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > int,G: int > int] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ? [X3: int] :
% 5.64/5.96 ( ( member_int @ X3 @ A4 )
% 5.64/5.96 & ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.64/5.96 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A4 ) @ ( groups4538972089207619220nt_int @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono_ex1
% 5.64/5.96 thf(fact_6774_sum_Orelated,axiom,
% 5.64/5.96 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.64/5.96 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.64/5.96 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_complex @ X16 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_nat @ S3 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups2073611262835488442omplex @ H2 @ S3 ) @ ( groups2073611262835488442omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6775_sum_Orelated,axiom,
% 5.64/5.96 ! [R: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.64/5.96 ( ( R @ zero_zero_complex @ zero_zero_complex )
% 5.64/5.96 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_complex @ X16 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_int @ S3 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups3049146728041665814omplex @ H2 @ S3 ) @ ( groups3049146728041665814omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6776_sum_Orelated,axiom,
% 5.64/5.96 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.64/5.96 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.64/5.96 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_real @ X16 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_int @ S3 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups8778361861064173332t_real @ H2 @ S3 ) @ ( groups8778361861064173332t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6777_sum_Orelated,axiom,
% 5.64/5.96 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.64/5.96 ( ( R @ zero_zero_real @ zero_zero_real )
% 5.64/5.96 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_real @ X16 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups5808333547571424918x_real @ H2 @ S3 ) @ ( groups5808333547571424918x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6778_sum_Orelated,axiom,
% 5.64/5.96 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.64/5.96 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.64/5.96 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_nat @ S3 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups2906978787729119204at_rat @ H2 @ S3 ) @ ( groups2906978787729119204at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6779_sum_Orelated,axiom,
% 5.64/5.96 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.64/5.96 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.64/5.96 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_int @ S3 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups3906332499630173760nt_rat @ H2 @ S3 ) @ ( groups3906332499630173760nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6780_sum_Orelated,axiom,
% 5.64/5.96 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.64/5.96 ( ( R @ zero_zero_rat @ zero_zero_rat )
% 5.64/5.96 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_rat @ X16 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups5058264527183730370ex_rat @ H2 @ S3 ) @ ( groups5058264527183730370ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6781_sum_Orelated,axiom,
% 5.64/5.96 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.64/5.96 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.64/5.96 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_nat @ X16 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_int @ S3 )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups4541462559716669496nt_nat @ H2 @ S3 ) @ ( groups4541462559716669496nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6782_sum_Orelated,axiom,
% 5.64/5.96 ! [R: nat > nat > $o,S3: set_complex,H2: complex > nat,G: complex > nat] :
% 5.64/5.96 ( ( R @ zero_zero_nat @ zero_zero_nat )
% 5.64/5.96 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_nat @ X16 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups5693394587270226106ex_nat @ H2 @ S3 ) @ ( groups5693394587270226106ex_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6783_sum_Orelated,axiom,
% 5.64/5.96 ! [R: int > int > $o,S3: set_nat,H2: nat > int,G: nat > int] :
% 5.64/5.96 ( ( R @ zero_zero_int @ zero_zero_int )
% 5.64/5.96 => ( ! [X16: int,Y15: int,X23: int,Y23: int] :
% 5.64/5.96 ( ( ( R @ X16 @ X23 )
% 5.64/5.96 & ( R @ Y15 @ Y23 ) )
% 5.64/5.96 => ( R @ ( plus_plus_int @ X16 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.64/5.96 => ( ( finite_finite_nat @ S3 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ S3 )
% 5.64/5.96 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( R @ ( groups3539618377306564664at_int @ H2 @ S3 ) @ ( groups3539618377306564664at_int @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.related
% 5.64/5.96 thf(fact_6784_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_complex )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A4 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6785_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > real,G: int > real] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_int )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6786_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > real,G: real > real] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_real )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6787_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_complex )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6788_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_nat )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A4 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6789_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > rat,G: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_int )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6790_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > rat,G: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_real )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6791_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > nat,G: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_complex )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6792_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > nat,G: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_int )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6793_sum__strict__mono,axiom,
% 5.64/5.96 ! [A4: set_real,F: real > nat,G: real > nat] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ( A4 != bot_bot_set_real )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( groups1935376822645274424al_nat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono
% 5.64/5.96 thf(fact_6794_take__bit__signed__take__bit,axiom,
% 5.64/5.96 ! [M: nat,N: nat,A: int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.64/5.96 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_signed_take_bit
% 5.64/5.96 thf(fact_6795_zabs__def,axiom,
% 5.64/5.96 ( abs_abs_int
% 5.64/5.96 = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % zabs_def
% 5.64/5.96 thf(fact_6796_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_real,F: real > rat,I: real] :
% 5.64/5.96 ( ( finite_finite_real @ S2 )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 => ( ( member_real @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6797_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_nat,F: nat > rat,I: nat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 => ( ( member_nat @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6798_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_int,F: int > rat,I: int] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 => ( ( member_int @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6799_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_complex,F: complex > rat,I: complex] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 => ( ( member_complex @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_rat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6800_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_real,F: real > nat,I: real] :
% 5.64/5.96 ( ( finite_finite_real @ S2 )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 => ( ( member_real @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6801_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_int,F: int > nat,I: int] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 => ( ( member_int @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6802_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_complex,F: complex > nat,I: complex] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 => ( ( member_complex @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6803_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_real,F: real > int,I: real] :
% 5.64/5.96 ( ( finite_finite_real @ S2 )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1932886352136224148al_int @ F @ S2 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 => ( ( member_real @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_int ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6804_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_nat,F: nat > int,I: nat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups3539618377306564664at_int @ F @ S2 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 => ( ( member_nat @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_int ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6805_sum__nonneg__0,axiom,
% 5.64/5.96 ! [S2: set_complex,F: complex > int,I: complex] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5690904116761175830ex_int @ F @ S2 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 => ( ( member_complex @ I @ S2 )
% 5.64/5.96 => ( ( F @ I )
% 5.64/5.96 = zero_zero_int ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_0
% 5.64/5.96 thf(fact_6806_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_real,F: real > rat,B4: rat,I: real] :
% 5.64/5.96 ( ( finite_finite_real @ S2 )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1300246762558778688al_rat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_real @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6807_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_nat,F: nat > rat,B4: rat,I: nat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_nat @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6808_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_int,F: int > rat,B4: rat,I: int] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_int @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6809_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_complex,F: complex > rat,B4: rat,I: complex] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5058264527183730370ex_rat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_complex @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6810_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_real,F: real > nat,B4: nat,I: real] :
% 5.64/5.96 ( ( finite_finite_real @ S2 )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1935376822645274424al_nat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_real @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6811_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_int,F: int > nat,B4: nat,I: int] :
% 5.64/5.96 ( ( finite_finite_int @ S2 )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_int @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6812_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_complex,F: complex > nat,B4: nat,I: complex] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5693394587270226106ex_nat @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_complex @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6813_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_real,F: real > int,B4: int,I: real] :
% 5.64/5.96 ( ( finite_finite_real @ S2 )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1932886352136224148al_int @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_real @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6814_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_nat,F: nat > int,B4: int,I: nat] :
% 5.64/5.96 ( ( finite_finite_nat @ S2 )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups3539618377306564664at_int @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_nat @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6815_sum__nonneg__leq__bound,axiom,
% 5.64/5.96 ! [S2: set_complex,F: complex > int,B4: int,I: complex] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ S2 )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5690904116761175830ex_int @ F @ S2 )
% 5.64/5.96 = B4 )
% 5.64/5.96 => ( ( member_complex @ I @ S2 )
% 5.64/5.96 => ( ord_less_eq_int @ ( F @ I ) @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nonneg_leq_bound
% 5.64/5.96 thf(fact_6816_abs__mod__less,axiom,
% 5.64/5.96 ! [L: int,K: int] :
% 5.64/5.96 ( ( L != zero_zero_int )
% 5.64/5.96 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_mod_less
% 5.64/5.96 thf(fact_6817_less__mask,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.96 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % less_mask
% 5.64/5.96 thf(fact_6818_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.64/5.96 ! [N: nat,K: int] :
% 5.64/5.96 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.64/5.96 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.64/5.96 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_mask_iff_exp_dvd
% 5.64/5.96 thf(fact_6819_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_real,I: real,F: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( member_real @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6820_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ I5 )
% 5.64/5.96 => ( ( member_nat @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6821_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_int,I: int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( member_int @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6822_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( member_complex @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6823_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_real,I: real,F: real > nat] :
% 5.64/5.96 ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( member_real @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6824_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_int,I: int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( member_int @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6825_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_complex,I: complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( member_complex @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6826_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_real,I: real,F: real > int] :
% 5.64/5.96 ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( member_real @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_int @ zero_zero_int @ ( groups1932886352136224148al_int @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6827_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_nat,I: nat,F: nat > int] :
% 5.64/5.96 ( ( finite_finite_nat @ I5 )
% 5.64/5.96 => ( ( member_nat @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6828_sum__pos2,axiom,
% 5.64/5.96 ! [I5: set_complex,I: complex,F: complex > int] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( member_complex @ I @ I5 )
% 5.64/5.96 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_int @ zero_zero_int @ ( groups5690904116761175830ex_int @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos2
% 5.64/5.96 thf(fact_6829_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_complex,F: complex > real] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_complex )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6830_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_int,F: int > real] :
% 5.64/5.96 ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_int )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6831_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_real,F: real > real] :
% 5.64/5.96 ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_real )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6832_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_complex )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6833_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_nat,F: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_nat )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6834_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_int )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6835_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_real,F: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_real )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6836_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_complex )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6837_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_int )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6838_sum__pos,axiom,
% 5.64/5.96 ! [I5: set_real,F: real > nat] :
% 5.64/5.96 ( ( finite_finite_real @ I5 )
% 5.64/5.96 => ( ( I5 != bot_bot_set_real )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.64/5.96 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_pos
% 5.64/5.96 thf(fact_6839_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,G: int > real] :
% 5.64/5.96 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.96 => ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( groups8778361861064173332t_real @ G @ A4 )
% 5.64/5.96 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups8778361861064173332t_real @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6840_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,G: complex > real] :
% 5.64/5.96 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 5.64/5.96 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5808333547571424918x_real @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6841_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,G: int > rat] :
% 5.64/5.96 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.96 => ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 5.64/5.96 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups3906332499630173760nt_rat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6842_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,G: complex > rat] :
% 5.64/5.96 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 5.64/5.96 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5058264527183730370ex_rat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6843_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,G: int > nat] :
% 5.64/5.96 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.96 => ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( groups4541462559716669496nt_nat @ G @ A4 )
% 5.64/5.96 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups4541462559716669496nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6844_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,G: complex > nat] :
% 5.64/5.96 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( groups5693394587270226106ex_nat @ G @ A4 )
% 5.64/5.96 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5693394587270226106ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6845_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,G: complex > int] :
% 5.64/5.96 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.96 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( groups5690904116761175830ex_int @ G @ A4 )
% 5.64/5.96 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups5690904116761175830ex_int @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6846_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_nat,A4: set_nat,G: nat > rat] :
% 5.64/5.96 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.64/5.96 => ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ A4 )
% 5.64/5.96 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups2906978787729119204at_rat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6847_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_nat,A4: set_nat,G: nat > int] :
% 5.64/5.96 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.64/5.96 => ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ G @ A4 )
% 5.64/5.96 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups3539618377306564664at_int @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6848_sum_Osubset__diff,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,G: int > int] :
% 5.64/5.96 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.96 => ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( groups4538972089207619220nt_int @ G @ A4 )
% 5.64/5.96 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups4538972089207619220nt_int @ G @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.subset_diff
% 5.64/5.96 thf(fact_6849_zdvd__mult__cancel1,axiom,
% 5.64/5.96 ! [M: int,N: int] :
% 5.64/5.96 ( ( M != zero_zero_int )
% 5.64/5.96 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.64/5.96 = ( ( abs_abs_int @ N )
% 5.64/5.96 = one_one_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % zdvd_mult_cancel1
% 5.64/5.96 thf(fact_6850_take__bit__Suc__bit0,axiom,
% 5.64/5.96 ! [N: nat,K: num] :
% 5.64/5.96 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.96 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_bit0
% 5.64/5.96 thf(fact_6851_take__bit__Suc__bit0,axiom,
% 5.64/5.96 ! [N: nat,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.64/5.96 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_bit0
% 5.64/5.96 thf(fact_6852_take__bit__eq__mod,axiom,
% 5.64/5.96 ( bit_se1745604003318907178nteger
% 5.64/5.96 = ( ^ [N2: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_mod
% 5.64/5.96 thf(fact_6853_take__bit__eq__mod,axiom,
% 5.64/5.96 ( bit_se2925701944663578781it_nat
% 5.64/5.96 = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_mod
% 5.64/5.96 thf(fact_6854_take__bit__eq__mod,axiom,
% 5.64/5.96 ( bit_se2923211474154528505it_int
% 5.64/5.96 = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_mod
% 5.64/5.96 thf(fact_6855_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,F: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: real] :
% 5.64/5.96 ( ( member_real @ B5 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6856_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: int] :
% 5.64/5.96 ( ( member_int @ B5 @ ( minus_minus_set_int @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6857_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ B4 )
% 5.64/5.96 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: complex] :
% 5.64/5.96 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6858_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,F: real > nat] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: real] :
% 5.64/5.96 ( ( member_real @ B5 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( groups1935376822645274424al_nat @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6859_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: int] :
% 5.64/5.96 ( ( member_int @ B5 @ ( minus_minus_set_int @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6860_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ B4 )
% 5.64/5.96 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: complex] :
% 5.64/5.96 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6861_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,F: real > int] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: real] :
% 5.64/5.96 ( ( member_real @ B5 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A4 ) @ ( groups1932886352136224148al_int @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6862_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,F: complex > int] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ B4 )
% 5.64/5.96 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: complex] :
% 5.64/5.96 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6863_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,F: real > real] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: real] :
% 5.64/5.96 ( ( member_real @ B5 @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6864_sum__mono2,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,F: int > real] :
% 5.64/5.96 ( ( finite_finite_int @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.64/5.96 => ( ! [B5: int] :
% 5.64/5.96 ( ( member_int @ B5 @ ( minus_minus_set_int @ B4 @ A4 ) )
% 5.64/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.64/5.96 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_mono2
% 5.64/5.96 thf(fact_6865_take__bit__nat__eq__self__iff,axiom,
% 5.64/5.96 ! [N: nat,M: nat] :
% 5.64/5.96 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.64/5.96 = M )
% 5.64/5.96 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_nat_eq_self_iff
% 5.64/5.96 thf(fact_6866_take__bit__nat__less__exp,axiom,
% 5.64/5.96 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_nat_less_exp
% 5.64/5.96 thf(fact_6867_take__bit__nat__eq__self,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.64/5.96 = M ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_nat_eq_self
% 5.64/5.96 thf(fact_6868_take__bit__nat__def,axiom,
% 5.64/5.96 ( bit_se2925701944663578781it_nat
% 5.64/5.96 = ( ^ [N2: nat,M2: nat] : ( modulo_modulo_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_nat_def
% 5.64/5.96 thf(fact_6869_take__bit__int__less__exp,axiom,
% 5.64/5.96 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_less_exp
% 5.64/5.96 thf(fact_6870_take__bit__int__def,axiom,
% 5.64/5.96 ( bit_se2923211474154528505it_int
% 5.64/5.96 = ( ^ [N2: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_def
% 5.64/5.96 thf(fact_6871_even__add__abs__iff,axiom,
% 5.64/5.96 ! [K: int,L: int] :
% 5.64/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.64/5.96 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_add_abs_iff
% 5.64/5.96 thf(fact_6872_even__abs__add__iff,axiom,
% 5.64/5.96 ! [K: int,L: int] :
% 5.64/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.64/5.96 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_abs_add_iff
% 5.64/5.96 thf(fact_6873_num_Osize__gen_I1_J,axiom,
% 5.64/5.96 ( ( size_num @ one )
% 5.64/5.96 = zero_zero_nat ) ).
% 5.64/5.96
% 5.64/5.96 % num.size_gen(1)
% 5.64/5.96 thf(fact_6874_take__bit__eq__0__iff,axiom,
% 5.64/5.96 ! [N: nat,A: code_integer] :
% 5.64/5.96 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.64/5.96 = zero_z3403309356797280102nteger )
% 5.64/5.96 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_0_iff
% 5.64/5.96 thf(fact_6875_take__bit__eq__0__iff,axiom,
% 5.64/5.96 ! [N: nat,A: nat] :
% 5.64/5.96 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_0_iff
% 5.64/5.96 thf(fact_6876_take__bit__eq__0__iff,axiom,
% 5.64/5.96 ! [N: nat,A: int] :
% 5.64/5.96 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_eq_0_iff
% 5.64/5.96 thf(fact_6877_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,B: real,F: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A4 ) @ ( groups1300246762558778688al_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6878_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,B: int,F: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.64/5.96 => ( ( member_int @ B @ ( minus_minus_set_int @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A4 ) @ ( groups3906332499630173760nt_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6879_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ B4 )
% 5.64/5.96 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 5.64/5.96 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A4 ) @ ( groups5058264527183730370ex_rat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6880_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,B: real,F: real > nat] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( groups1935376822645274424al_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6881_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,B: int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.64/5.96 => ( ( member_int @ B @ ( minus_minus_set_int @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6882_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ B4 )
% 5.64/5.96 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 5.64/5.96 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6883_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,B: real,F: real > int] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A4 ) @ ( groups1932886352136224148al_int @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6884_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_complex,A4: set_complex,B: complex,F: complex > int] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ B4 )
% 5.64/5.96 => ( ( ord_le211207098394363844omplex @ A4 @ B4 )
% 5.64/5.96 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A4 ) @ ( groups5690904116761175830ex_int @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6885_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_real,A4: set_real,B: real,F: real > real] :
% 5.64/5.96 ( ( finite_finite_real @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_real @ A4 @ B4 )
% 5.64/5.96 => ( ( member_real @ B @ ( minus_minus_set_real @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A4 ) @ ( groups8097168146408367636l_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6886_sum__strict__mono2,axiom,
% 5.64/5.96 ! [B4: set_int,A4: set_int,B: int,F: int > real] :
% 5.64/5.96 ( ( finite_finite_int @ B4 )
% 5.64/5.96 => ( ( ord_less_eq_set_int @ A4 @ B4 )
% 5.64/5.96 => ( ( member_int @ B @ ( minus_minus_set_int @ B4 @ A4 ) )
% 5.64/5.96 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.64/5.96 => ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ B4 )
% 5.64/5.96 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A4 ) @ ( groups8778361861064173332t_real @ F @ B4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_strict_mono2
% 5.64/5.96 thf(fact_6887_take__bit__numeral__bit0,axiom,
% 5.64/5.96 ! [L: num,K: num] :
% 5.64/5.96 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.64/5.96 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_bit0
% 5.64/5.96 thf(fact_6888_take__bit__numeral__bit0,axiom,
% 5.64/5.96 ! [L: num,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.64/5.96 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_bit0
% 5.64/5.96 thf(fact_6889_take__bit__nat__less__self__iff,axiom,
% 5.64/5.96 ! [N: nat,M: nat] :
% 5.64/5.96 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.64/5.96 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_nat_less_self_iff
% 5.64/5.96 thf(fact_6890_Suc__mask__eq__exp,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % Suc_mask_eq_exp
% 5.64/5.96 thf(fact_6891_mask__nat__less__exp,axiom,
% 5.64/5.96 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_nat_less_exp
% 5.64/5.96 thf(fact_6892_take__bit__Suc__minus__bit0,axiom,
% 5.64/5.96 ! [N: nat,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.64/5.96 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_minus_bit0
% 5.64/5.96 thf(fact_6893_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_complex,X2: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.64/5.96 ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups6621422865394947399nteger @ X2 @ I5 )
% 5.64/5.96 = one_one_Code_integer )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_le3102999989581377725nteger
% 5.64/5.96 @ ( abs_abs_Code_integer
% 5.64/5.96 @ ( minus_8373710615458151222nteger
% 5.64/5.96 @ ( groups6621422865394947399nteger
% 5.64/5.96 @ ^ [I4: complex] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6894_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_real,X2: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.64/5.96 ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups7713935264441627589nteger @ X2 @ I5 )
% 5.64/5.96 = one_one_Code_integer )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_le3102999989581377725nteger
% 5.64/5.96 @ ( abs_abs_Code_integer
% 5.64/5.96 @ ( minus_8373710615458151222nteger
% 5.64/5.96 @ ( groups7713935264441627589nteger
% 5.64/5.96 @ ^ [I4: real] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6895_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_nat,X2: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.64/5.96 ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups7501900531339628137nteger @ X2 @ I5 )
% 5.64/5.96 = one_one_Code_integer )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_le3102999989581377725nteger
% 5.64/5.96 @ ( abs_abs_Code_integer
% 5.64/5.96 @ ( minus_8373710615458151222nteger
% 5.64/5.96 @ ( groups7501900531339628137nteger
% 5.64/5.96 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6896_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_int,X2: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.64/5.96 ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups7873554091576472773nteger @ X2 @ I5 )
% 5.64/5.96 = one_one_Code_integer )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_le3102999989581377725nteger
% 5.64/5.96 @ ( abs_abs_Code_integer
% 5.64/5.96 @ ( minus_8373710615458151222nteger
% 5.64/5.96 @ ( groups7873554091576472773nteger
% 5.64/5.96 @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6897_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_complex,X2: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.64/5.96 ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5058264527183730370ex_rat @ X2 @ I5 )
% 5.64/5.96 = one_one_rat )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_less_eq_rat
% 5.64/5.96 @ ( abs_abs_rat
% 5.64/5.96 @ ( minus_minus_rat
% 5.64/5.96 @ ( groups5058264527183730370ex_rat
% 5.64/5.96 @ ^ [I4: complex] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6898_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_real,X2: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.64/5.96 ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1300246762558778688al_rat @ X2 @ I5 )
% 5.64/5.96 = one_one_rat )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_less_eq_rat
% 5.64/5.96 @ ( abs_abs_rat
% 5.64/5.96 @ ( minus_minus_rat
% 5.64/5.96 @ ( groups1300246762558778688al_rat
% 5.64/5.96 @ ^ [I4: real] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6899_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_nat,X2: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.64/5.96 ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups2906978787729119204at_rat @ X2 @ I5 )
% 5.64/5.96 = one_one_rat )
% 5.64/5.96 => ( ! [I3: nat] :
% 5.64/5.96 ( ( member_nat @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_less_eq_rat
% 5.64/5.96 @ ( abs_abs_rat
% 5.64/5.96 @ ( minus_minus_rat
% 5.64/5.96 @ ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6900_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_int,X2: int > rat,A: int > rat,B: rat,Delta: rat] :
% 5.64/5.96 ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups3906332499630173760nt_rat @ X2 @ I5 )
% 5.64/5.96 = one_one_rat )
% 5.64/5.96 => ( ! [I3: int] :
% 5.64/5.96 ( ( member_int @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_less_eq_rat
% 5.64/5.96 @ ( abs_abs_rat
% 5.64/5.96 @ ( minus_minus_rat
% 5.64/5.96 @ ( groups3906332499630173760nt_rat
% 5.64/5.96 @ ^ [I4: int] : ( times_times_rat @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6901_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_complex,X2: complex > int,A: complex > int,B: int,Delta: int] :
% 5.64/5.96 ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups5690904116761175830ex_int @ X2 @ I5 )
% 5.64/5.96 = one_one_int )
% 5.64/5.96 => ( ! [I3: complex] :
% 5.64/5.96 ( ( member_complex @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_less_eq_int
% 5.64/5.96 @ ( abs_abs_int
% 5.64/5.96 @ ( minus_minus_int
% 5.64/5.96 @ ( groups5690904116761175830ex_int
% 5.64/5.96 @ ^ [I4: complex] : ( times_times_int @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6902_convex__sum__bound__le,axiom,
% 5.64/5.96 ! [I5: set_real,X2: real > int,A: real > int,B: int,Delta: int] :
% 5.64/5.96 ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ zero_zero_int @ ( X2 @ I3 ) ) )
% 5.64/5.96 => ( ( ( groups1932886352136224148al_int @ X2 @ I5 )
% 5.64/5.96 = one_one_int )
% 5.64/5.96 => ( ! [I3: real] :
% 5.64/5.96 ( ( member_real @ I3 @ I5 )
% 5.64/5.96 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.64/5.96 => ( ord_less_eq_int
% 5.64/5.96 @ ( abs_abs_int
% 5.64/5.96 @ ( minus_minus_int
% 5.64/5.96 @ ( groups1932886352136224148al_int
% 5.64/5.96 @ ^ [I4: real] : ( times_times_int @ ( A @ I4 ) @ ( X2 @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 @ B ) )
% 5.64/5.96 @ Delta ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % convex_sum_bound_le
% 5.64/5.96 thf(fact_6903_take__bit__int__less__self__iff,axiom,
% 5.64/5.96 ! [N: nat,K: int] :
% 5.64/5.96 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.64/5.96 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_less_self_iff
% 5.64/5.96 thf(fact_6904_take__bit__int__greater__eq__self__iff,axiom,
% 5.64/5.96 ! [K: int,N: nat] :
% 5.64/5.96 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.64/5.96 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_greater_eq_self_iff
% 5.64/5.96 thf(fact_6905_nat__intermed__int__val,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.64/5.96 ( ! [I3: nat] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.64/5.96 & ( ord_less_nat @ I3 @ N ) )
% 5.64/5.96 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.64/5.96 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.64/5.96 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.64/5.96 => ? [I3: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ I3 )
% 5.64/5.96 & ( ord_less_eq_nat @ I3 @ N )
% 5.64/5.96 & ( ( F @ I3 )
% 5.64/5.96 = K ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % nat_intermed_int_val
% 5.64/5.96 thf(fact_6906_incr__lemma,axiom,
% 5.64/5.96 ! [D: int,Z: int,X2: int] :
% 5.64/5.96 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.96 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % incr_lemma
% 5.64/5.96 thf(fact_6907_decr__lemma,axiom,
% 5.64/5.96 ! [D: int,X2: int,Z: int] :
% 5.64/5.96 ( ( ord_less_int @ zero_zero_int @ D )
% 5.64/5.96 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.64/5.96
% 5.64/5.96 % decr_lemma
% 5.64/5.96 thf(fact_6908_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.64/5.96 = ( N = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % semiring_bit_operations_class.even_mask_iff
% 5.64/5.96 thf(fact_6909_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.64/5.96 = ( N = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % semiring_bit_operations_class.even_mask_iff
% 5.64/5.96 thf(fact_6910_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.64/5.96 = ( N = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % semiring_bit_operations_class.even_mask_iff
% 5.64/5.96 thf(fact_6911_take__bit__int__eq__self,axiom,
% 5.64/5.96 ! [K: int,N: nat] :
% 5.64/5.96 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.96 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.64/5.96 = K ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_eq_self
% 5.64/5.96 thf(fact_6912_take__bit__int__eq__self__iff,axiom,
% 5.64/5.96 ! [N: nat,K: int] :
% 5.64/5.96 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.64/5.96 = K )
% 5.64/5.96 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.96 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_eq_self_iff
% 5.64/5.96 thf(fact_6913_mask__nat__def,axiom,
% 5.64/5.96 ( bit_se2002935070580805687sk_nat
% 5.64/5.96 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_nat_def
% 5.64/5.96 thf(fact_6914_take__bit__numeral__minus__bit0,axiom,
% 5.64/5.96 ! [L: num,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.64/5.96 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_minus_bit0
% 5.64/5.96 thf(fact_6915_mask__half__int,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.96 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_half_int
% 5.64/5.96 thf(fact_6916_take__bit__incr__eq,axiom,
% 5.64/5.96 ! [N: nat,K: int] :
% 5.64/5.96 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.64/5.96 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.64/5.96 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_incr_eq
% 5.64/5.96 thf(fact_6917_mask__int__def,axiom,
% 5.64/5.96 ( bit_se2000444600071755411sk_int
% 5.64/5.96 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_int_def
% 5.64/5.96 thf(fact_6918_nat__ivt__aux,axiom,
% 5.64/5.96 ! [N: nat,F: nat > int,K: int] :
% 5.64/5.96 ( ! [I3: nat] :
% 5.64/5.96 ( ( ord_less_nat @ I3 @ N )
% 5.64/5.96 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.64/5.96 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.64/5.96 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.64/5.96 => ? [I3: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ I3 @ N )
% 5.64/5.96 & ( ( F @ I3 )
% 5.64/5.96 = K ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % nat_ivt_aux
% 5.64/5.96 thf(fact_6919_take__bit__Suc__minus__1__eq,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_minus_1_eq
% 5.64/5.96 thf(fact_6920_take__bit__Suc__minus__1__eq,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_minus_1_eq
% 5.64/5.96 thf(fact_6921_take__bit__Suc__bit1,axiom,
% 5.64/5.96 ! [N: nat,K: num] :
% 5.64/5.96 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_bit1
% 5.64/5.96 thf(fact_6922_take__bit__Suc__bit1,axiom,
% 5.64/5.96 ! [N: nat,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_bit1
% 5.64/5.96 thf(fact_6923_take__bit__numeral__minus__1__eq,axiom,
% 5.64/5.96 ! [K: num] :
% 5.64/5.96 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_minus_1_eq
% 5.64/5.96 thf(fact_6924_take__bit__numeral__minus__1__eq,axiom,
% 5.64/5.96 ! [K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_minus_1_eq
% 5.64/5.96 thf(fact_6925_take__bit__Suc,axiom,
% 5.64/5.96 ! [N: nat,A: code_integer] :
% 5.64/5.96 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.64/5.96 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc
% 5.64/5.96 thf(fact_6926_take__bit__Suc,axiom,
% 5.64/5.96 ! [N: nat,A: nat] :
% 5.64/5.96 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.64/5.96 = ( 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 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc
% 5.64/5.96 thf(fact_6927_take__bit__Suc,axiom,
% 5.64/5.96 ! [N: nat,A: int] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.64/5.96 = ( 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 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc
% 5.64/5.96 thf(fact_6928_mask__eq__exp__minus__1,axiom,
% 5.64/5.96 ( bit_se2002935070580805687sk_nat
% 5.64/5.96 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_eq_exp_minus_1
% 5.64/5.96 thf(fact_6929_mask__eq__exp__minus__1,axiom,
% 5.64/5.96 ( bit_se2000444600071755411sk_int
% 5.64/5.96 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_eq_exp_minus_1
% 5.64/5.96 thf(fact_6930_take__bit__int__less__eq,axiom,
% 5.64/5.96 ! [N: nat,K: int] :
% 5.64/5.96 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.64/5.96 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.96 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_less_eq
% 5.64/5.96 thf(fact_6931_take__bit__int__greater__eq,axiom,
% 5.64/5.96 ! [K: int,N: nat] :
% 5.64/5.96 ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.96 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_int_greater_eq
% 5.64/5.96 thf(fact_6932_signed__take__bit__eq__take__bit__shift,axiom,
% 5.64/5.96 ( bit_ri631733984087533419it_int
% 5.64/5.96 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % signed_take_bit_eq_take_bit_shift
% 5.64/5.96 thf(fact_6933_nat0__intermed__int__val,axiom,
% 5.64/5.96 ! [N: nat,F: nat > int,K: int] :
% 5.64/5.96 ( ! [I3: nat] :
% 5.64/5.96 ( ( ord_less_nat @ I3 @ N )
% 5.64/5.96 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.64/5.96 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.64/5.96 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.64/5.96 => ? [I3: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ I3 @ N )
% 5.64/5.96 & ( ( F @ I3 )
% 5.64/5.96 = K ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % nat0_intermed_int_val
% 5.64/5.96 thf(fact_6934_stable__imp__take__bit__eq,axiom,
% 5.64/5.96 ! [A: code_integer,N: nat] :
% 5.64/5.96 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/5.96 = A )
% 5.64/5.96 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.64/5.96 = zero_z3403309356797280102nteger ) )
% 5.64/5.96 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.64/5.96 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % stable_imp_take_bit_eq
% 5.64/5.96 thf(fact_6935_stable__imp__take__bit__eq,axiom,
% 5.64/5.96 ! [A: nat,N: nat] :
% 5.64/5.96 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.96 = A )
% 5.64/5.96 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.64/5.96 = zero_zero_nat ) )
% 5.64/5.96 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.64/5.96 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % stable_imp_take_bit_eq
% 5.64/5.96 thf(fact_6936_stable__imp__take__bit__eq,axiom,
% 5.64/5.96 ! [A: int,N: nat] :
% 5.64/5.96 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.96 = A )
% 5.64/5.96 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.64/5.96 = zero_zero_int ) )
% 5.64/5.96 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.64/5.96 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % stable_imp_take_bit_eq
% 5.64/5.96 thf(fact_6937_take__bit__numeral__bit1,axiom,
% 5.64/5.96 ! [L: num,K: num] :
% 5.64/5.96 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_bit1
% 5.64/5.96 thf(fact_6938_take__bit__numeral__bit1,axiom,
% 5.64/5.96 ! [L: num,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_bit1
% 5.64/5.96 thf(fact_6939_arctan__add,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.96 => ( ( ord_less_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.64/5.96 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y4 ) )
% 5.64/5.96 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % arctan_add
% 5.64/5.96 thf(fact_6940_take__bit__minus__small__eq,axiom,
% 5.64/5.96 ! [K: int,N: nat] :
% 5.64/5.96 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.96 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.96 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.64/5.96 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_minus_small_eq
% 5.64/5.96 thf(fact_6941_num_Osize__gen_I2_J,axiom,
% 5.64/5.96 ! [X22: num] :
% 5.64/5.96 ( ( size_num @ ( bit0 @ X22 ) )
% 5.64/5.96 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % num.size_gen(2)
% 5.64/5.96 thf(fact_6942_take__bit__numeral__minus__bit1,axiom,
% 5.64/5.96 ! [L: num,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_numeral_minus_bit1
% 5.64/5.96 thf(fact_6943_take__bit__Suc__minus__bit1,axiom,
% 5.64/5.96 ! [N: nat,K: num] :
% 5.64/5.96 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.64/5.96 = ( 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 ) ) ).
% 5.64/5.96
% 5.64/5.96 % take_bit_Suc_minus_bit1
% 5.64/5.96 thf(fact_6944_tanh__real__altdef,axiom,
% 5.64/5.96 ( tanh_real
% 5.64/5.96 = ( ^ [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 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % tanh_real_altdef
% 5.64/5.96 thf(fact_6945_and__int__unfold,axiom,
% 5.64/5.96 ( bit_se725231765392027082nd_int
% 5.64/5.96 = ( ^ [K2: int,L2: int] :
% 5.64/5.96 ( if_int
% 5.64/5.96 @ ( ( K2 = zero_zero_int )
% 5.64/5.96 | ( L2 = zero_zero_int ) )
% 5.64/5.96 @ zero_zero_int
% 5.64/5.96 @ ( if_int
% 5.64/5.96 @ ( K2
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 @ L2
% 5.64/5.96 @ ( if_int
% 5.64/5.96 @ ( L2
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 @ K2
% 5.64/5.96 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_int_unfold
% 5.64/5.96 thf(fact_6946_power__numeral,axiom,
% 5.64/5.96 ! [K: num,L: num] :
% 5.64/5.96 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.64/5.96 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % power_numeral
% 5.64/5.96 thf(fact_6947_power__numeral,axiom,
% 5.64/5.96 ! [K: num,L: num] :
% 5.64/5.96 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.64/5.96 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % power_numeral
% 5.64/5.96 thf(fact_6948_power__numeral,axiom,
% 5.64/5.96 ! [K: num,L: num] :
% 5.64/5.96 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.64/5.96 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % power_numeral
% 5.64/5.96 thf(fact_6949_power__numeral,axiom,
% 5.64/5.96 ! [K: num,L: num] :
% 5.64/5.96 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % power_numeral
% 5.64/5.96 thf(fact_6950_power__numeral,axiom,
% 5.64/5.96 ! [K: num,L: num] :
% 5.64/5.96 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.64/5.96 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % power_numeral
% 5.64/5.96 thf(fact_6951_or__int__unfold,axiom,
% 5.64/5.96 ( bit_se1409905431419307370or_int
% 5.64/5.96 = ( ^ [K2: int,L2: int] :
% 5.64/5.96 ( if_int
% 5.64/5.96 @ ( ( K2
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 | ( L2
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.64/5.96 @ ( uminus_uminus_int @ one_one_int )
% 5.64/5.96 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_int_unfold
% 5.64/5.96 thf(fact_6952_exp__less__mono,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.96 => ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_less_mono
% 5.64/5.96 thf(fact_6953_exp__less__cancel__iff,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y4 ) )
% 5.64/5.96 = ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_less_cancel_iff
% 5.64/5.96 thf(fact_6954_exp__zero,axiom,
% 5.64/5.96 ( ( exp_complex @ zero_zero_complex )
% 5.64/5.96 = one_one_complex ) ).
% 5.64/5.96
% 5.64/5.96 % exp_zero
% 5.64/5.96 thf(fact_6955_exp__zero,axiom,
% 5.64/5.96 ( ( exp_real @ zero_zero_real )
% 5.64/5.96 = one_one_real ) ).
% 5.64/5.96
% 5.64/5.96 % exp_zero
% 5.64/5.96 thf(fact_6956_and_Oleft__neutral,axiom,
% 5.64/5.96 ! [A: code_integer] :
% 5.64/5.96 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.64/5.96 = A ) ).
% 5.64/5.96
% 5.64/5.96 % and.left_neutral
% 5.64/5.96 thf(fact_6957_and_Oleft__neutral,axiom,
% 5.64/5.96 ! [A: int] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.64/5.96 = A ) ).
% 5.64/5.96
% 5.64/5.96 % and.left_neutral
% 5.64/5.96 thf(fact_6958_and_Oright__neutral,axiom,
% 5.64/5.96 ! [A: code_integer] :
% 5.64/5.96 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = A ) ).
% 5.64/5.96
% 5.64/5.96 % and.right_neutral
% 5.64/5.96 thf(fact_6959_and_Oright__neutral,axiom,
% 5.64/5.96 ! [A: int] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = A ) ).
% 5.64/5.96
% 5.64/5.96 % and.right_neutral
% 5.64/5.96 thf(fact_6960_bit_Oconj__one__right,axiom,
% 5.64/5.96 ! [X2: code_integer] :
% 5.64/5.96 ( ( bit_se3949692690581998587nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = X2 ) ).
% 5.64/5.96
% 5.64/5.96 % bit.conj_one_right
% 5.64/5.96 thf(fact_6961_bit_Oconj__one__right,axiom,
% 5.64/5.96 ! [X2: int] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = X2 ) ).
% 5.64/5.96
% 5.64/5.96 % bit.conj_one_right
% 5.64/5.96 thf(fact_6962_bit_Odisj__one__left,axiom,
% 5.64/5.96 ! [X2: code_integer] :
% 5.64/5.96 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.96
% 5.64/5.96 % bit.disj_one_left
% 5.64/5.96 thf(fact_6963_bit_Odisj__one__left,axiom,
% 5.64/5.96 ! [X2: int] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % bit.disj_one_left
% 5.64/5.96 thf(fact_6964_bit_Odisj__one__right,axiom,
% 5.64/5.96 ! [X2: code_integer] :
% 5.64/5.96 ( ( bit_se1080825931792720795nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.64/5.96
% 5.64/5.96 % bit.disj_one_right
% 5.64/5.96 thf(fact_6965_bit_Odisj__one__right,axiom,
% 5.64/5.96 ! [X2: int] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % bit.disj_one_right
% 5.64/5.96 thf(fact_6966_and__negative__int__iff,axiom,
% 5.64/5.96 ! [K: int,L: int] :
% 5.64/5.96 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.64/5.96 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.96 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_negative_int_iff
% 5.64/5.96 thf(fact_6967_or__negative__int__iff,axiom,
% 5.64/5.96 ! [K: int,L: int] :
% 5.64/5.96 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.64/5.96 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.96 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_negative_int_iff
% 5.64/5.96 thf(fact_6968_pred__numeral__inc,axiom,
% 5.64/5.96 ! [K: num] :
% 5.64/5.96 ( ( pred_numeral @ ( inc @ K ) )
% 5.64/5.96 = ( numeral_numeral_nat @ K ) ) ).
% 5.64/5.96
% 5.64/5.96 % pred_numeral_inc
% 5.64/5.96 thf(fact_6969_and__numerals_I8_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.64/5.96 = one_one_int ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(8)
% 5.64/5.96 thf(fact_6970_and__numerals_I8_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.64/5.96 = one_one_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(8)
% 5.64/5.96 thf(fact_6971_and__numerals_I2_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = one_one_int ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(2)
% 5.64/5.96 thf(fact_6972_and__numerals_I2_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = one_one_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(2)
% 5.64/5.96 thf(fact_6973_or__numerals_I8_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.64/5.96 = ( numeral_numeral_int @ ( bit1 @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(8)
% 5.64/5.96 thf(fact_6974_or__numerals_I8_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(8)
% 5.64/5.96 thf(fact_6975_or__numerals_I2_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( numeral_numeral_int @ ( bit1 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(2)
% 5.64/5.96 thf(fact_6976_or__numerals_I2_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(2)
% 5.64/5.96 thf(fact_6977_one__less__exp__iff,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.64/5.96 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_less_exp_iff
% 5.64/5.96 thf(fact_6978_exp__less__one__iff,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.64/5.96 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_less_one_iff
% 5.64/5.96 thf(fact_6979_exp__ln,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.96 => ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.96 = X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_ln
% 5.64/5.96 thf(fact_6980_exp__ln__iff,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ( exp_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.96 = X2 )
% 5.64/5.96 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_ln_iff
% 5.64/5.96 thf(fact_6981_and__numerals_I5_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.64/5.96 = zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(5)
% 5.64/5.96 thf(fact_6982_and__numerals_I5_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.64/5.96 = zero_zero_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(5)
% 5.64/5.96 thf(fact_6983_and__numerals_I1_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(1)
% 5.64/5.96 thf(fact_6984_and__numerals_I1_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = zero_zero_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(1)
% 5.64/5.96 thf(fact_6985_and__numerals_I3_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(3)
% 5.64/5.96 thf(fact_6986_and__numerals_I3_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(3)
% 5.64/5.96 thf(fact_6987_or__numerals_I3_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(3)
% 5.64/5.96 thf(fact_6988_or__numerals_I3_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(3)
% 5.64/5.96 thf(fact_6989_sum_Ocl__ivl__Suc,axiom,
% 5.64/5.96 ! [N: nat,M: nat,G: nat > complex] :
% 5.64/5.96 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = zero_zero_complex ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.cl_ivl_Suc
% 5.64/5.96 thf(fact_6990_sum_Ocl__ivl__Suc,axiom,
% 5.64/5.96 ! [N: nat,M: nat,G: nat > rat] :
% 5.64/5.96 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = zero_zero_rat ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.cl_ivl_Suc
% 5.64/5.96 thf(fact_6991_sum_Ocl__ivl__Suc,axiom,
% 5.64/5.96 ! [N: nat,M: nat,G: nat > int] :
% 5.64/5.96 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = zero_zero_int ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.cl_ivl_Suc
% 5.64/5.96 thf(fact_6992_sum_Ocl__ivl__Suc,axiom,
% 5.64/5.96 ! [N: nat,M: nat,G: nat > nat] :
% 5.64/5.96 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = zero_zero_nat ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.cl_ivl_Suc
% 5.64/5.96 thf(fact_6993_sum_Ocl__ivl__Suc,axiom,
% 5.64/5.96 ! [N: nat,M: nat,G: nat > real] :
% 5.64/5.96 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = zero_zero_real ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.cl_ivl_Suc
% 5.64/5.96 thf(fact_6994_or__numerals_I5_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.64/5.96 = ( numeral_numeral_int @ ( bit1 @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(5)
% 5.64/5.96 thf(fact_6995_or__numerals_I5_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(5)
% 5.64/5.96 thf(fact_6996_or__numerals_I1_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( numeral_numeral_int @ ( bit1 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(1)
% 5.64/5.96 thf(fact_6997_or__numerals_I1_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(1)
% 5.64/5.96 thf(fact_6998_add__neg__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/5.96 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(5)
% 5.64/5.96 thf(fact_6999_add__neg__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.96 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(5)
% 5.64/5.96 thf(fact_7000_add__neg__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.64/5.96 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(5)
% 5.64/5.96 thf(fact_7001_add__neg__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.64/5.96 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(5)
% 5.64/5.96 thf(fact_7002_add__neg__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(5)
% 5.64/5.96 thf(fact_7003_add__neg__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(6)
% 5.64/5.96 thf(fact_7004_add__neg__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.96 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(6)
% 5.64/5.96 thf(fact_7005_add__neg__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.96 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(6)
% 5.64/5.96 thf(fact_7006_add__neg__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.96 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(6)
% 5.64/5.96 thf(fact_7007_add__neg__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_neg_numeral_special(6)
% 5.64/5.96 thf(fact_7008_diff__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(6)
% 5.64/5.96 thf(fact_7009_diff__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.96 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(6)
% 5.64/5.96 thf(fact_7010_diff__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.64/5.96 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(6)
% 5.64/5.96 thf(fact_7011_diff__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.64/5.96 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(6)
% 5.64/5.96 thf(fact_7012_diff__numeral__special_I6_J,axiom,
% 5.64/5.96 ! [M: num] :
% 5.64/5.96 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(6)
% 5.64/5.96 thf(fact_7013_diff__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.64/5.96 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(5)
% 5.64/5.96 thf(fact_7014_diff__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.96 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(5)
% 5.64/5.96 thf(fact_7015_diff__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.64/5.96 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(5)
% 5.64/5.96 thf(fact_7016_diff__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.64/5.96 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(5)
% 5.64/5.96 thf(fact_7017_diff__numeral__special_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % diff_numeral_special(5)
% 5.64/5.96 thf(fact_7018_sum__zero__power,axiom,
% 5.64/5.96 ! [A4: set_nat,C: nat > complex] :
% 5.64/5.96 ( ( ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( C @ zero_zero_nat ) ) )
% 5.64/5.96 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = zero_zero_complex ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_zero_power
% 5.64/5.96 thf(fact_7019_sum__zero__power,axiom,
% 5.64/5.96 ! [A4: set_nat,C: nat > rat] :
% 5.64/5.96 ( ( ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( C @ zero_zero_nat ) ) )
% 5.64/5.96 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = zero_zero_rat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_zero_power
% 5.64/5.96 thf(fact_7020_sum__zero__power,axiom,
% 5.64/5.96 ! [A4: set_nat,C: nat > real] :
% 5.64/5.96 ( ( ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( C @ zero_zero_nat ) ) )
% 5.64/5.96 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = zero_zero_real ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_zero_power
% 5.64/5.96 thf(fact_7021_and__numerals_I6_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(6)
% 5.64/5.96 thf(fact_7022_and__numerals_I6_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(6)
% 5.64/5.96 thf(fact_7023_and__numerals_I4_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(4)
% 5.64/5.96 thf(fact_7024_and__numerals_I4_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(4)
% 5.64/5.96 thf(fact_7025_and__minus__numerals_I1_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/5.96 = zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % and_minus_numerals(1)
% 5.64/5.96 thf(fact_7026_and__minus__numerals_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.64/5.96 = zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % and_minus_numerals(5)
% 5.64/5.96 thf(fact_7027_sum__zero__power_H,axiom,
% 5.64/5.96 ! [A4: set_nat,C: nat > complex,D: nat > complex] :
% 5.64/5.96 ( ( ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.64/5.96 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [I4: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I4 ) @ ( power_power_complex @ zero_zero_complex @ I4 ) ) @ ( D @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = zero_zero_complex ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_zero_power'
% 5.64/5.96 thf(fact_7028_sum__zero__power_H,axiom,
% 5.64/5.96 ! [A4: set_nat,C: nat > rat,D: nat > rat] :
% 5.64/5.96 ( ( ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.64/5.96 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = zero_zero_rat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_zero_power'
% 5.64/5.96 thf(fact_7029_sum__zero__power_H,axiom,
% 5.64/5.96 ! [A4: set_nat,C: nat > real,D: nat > real] :
% 5.64/5.96 ( ( ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.64/5.96 & ( ~ ( ( finite_finite_nat @ A4 )
% 5.64/5.96 & ( member_nat @ zero_zero_nat @ A4 ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I4 ) @ ( power_power_real @ zero_zero_real @ I4 ) ) @ ( D @ I4 ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = zero_zero_real ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_zero_power'
% 5.64/5.96 thf(fact_7030_and__numerals_I7_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(7)
% 5.64/5.96 thf(fact_7031_and__numerals_I7_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_numerals(7)
% 5.64/5.96 thf(fact_7032_or__numerals_I7_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(7)
% 5.64/5.96 thf(fact_7033_or__numerals_I7_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(7)
% 5.64/5.96 thf(fact_7034_or__numerals_I6_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(6)
% 5.64/5.96 thf(fact_7035_or__numerals_I6_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(6)
% 5.64/5.96 thf(fact_7036_or__numerals_I4_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(4)
% 5.64/5.96 thf(fact_7037_or__numerals_I4_J,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_numerals(4)
% 5.64/5.96 thf(fact_7038_exp__less__cancel,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ord_less_real @ ( exp_real @ X2 ) @ ( exp_real @ Y4 ) )
% 5.64/5.96 => ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_less_cancel
% 5.64/5.96 thf(fact_7039_exp__times__arg__commute,axiom,
% 5.64/5.96 ! [A4: complex] :
% 5.64/5.96 ( ( times_times_complex @ ( exp_complex @ A4 ) @ A4 )
% 5.64/5.96 = ( times_times_complex @ A4 @ ( exp_complex @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_times_arg_commute
% 5.64/5.96 thf(fact_7040_exp__times__arg__commute,axiom,
% 5.64/5.96 ! [A4: real] :
% 5.64/5.96 ( ( times_times_real @ ( exp_real @ A4 ) @ A4 )
% 5.64/5.96 = ( times_times_real @ A4 @ ( exp_real @ A4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_times_arg_commute
% 5.64/5.96 thf(fact_7041_bit_Ocomplement__unique,axiom,
% 5.64/5.96 ! [A: code_integer,X2: code_integer,Y4: code_integer] :
% 5.64/5.96 ( ( ( bit_se3949692690581998587nteger @ A @ X2 )
% 5.64/5.96 = zero_z3403309356797280102nteger )
% 5.64/5.96 => ( ( ( bit_se1080825931792720795nteger @ A @ X2 )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 => ( ( ( bit_se3949692690581998587nteger @ A @ Y4 )
% 5.64/5.96 = zero_z3403309356797280102nteger )
% 5.64/5.96 => ( ( ( bit_se1080825931792720795nteger @ A @ Y4 )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 => ( X2 = Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % bit.complement_unique
% 5.64/5.96 thf(fact_7042_bit_Ocomplement__unique,axiom,
% 5.64/5.96 ! [A: int,X2: int,Y4: int] :
% 5.64/5.96 ( ( ( bit_se725231765392027082nd_int @ A @ X2 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 => ( ( ( bit_se1409905431419307370or_int @ A @ X2 )
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 => ( ( ( bit_se725231765392027082nd_int @ A @ Y4 )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 => ( ( ( bit_se1409905431419307370or_int @ A @ Y4 )
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 => ( X2 = Y4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % bit.complement_unique
% 5.64/5.96 thf(fact_7043_num__induct,axiom,
% 5.64/5.96 ! [P: num > $o,X2: num] :
% 5.64/5.96 ( ( P @ one )
% 5.64/5.96 => ( ! [X4: num] :
% 5.64/5.96 ( ( P @ X4 )
% 5.64/5.96 => ( P @ ( inc @ X4 ) ) )
% 5.64/5.96 => ( P @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % num_induct
% 5.64/5.96 thf(fact_7044_add__inc,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( plus_plus_num @ X2 @ ( inc @ Y4 ) )
% 5.64/5.96 = ( inc @ ( plus_plus_num @ X2 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_inc
% 5.64/5.96 thf(fact_7045_and__eq__minus__1__iff,axiom,
% 5.64/5.96 ! [A: code_integer,B: code_integer] :
% 5.64/5.96 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 = ( ( A
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.64/5.96 & ( B
% 5.64/5.96 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_eq_minus_1_iff
% 5.64/5.96 thf(fact_7046_and__eq__minus__1__iff,axiom,
% 5.64/5.96 ! [A: int,B: int] :
% 5.64/5.96 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 = ( ( A
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/5.96 & ( B
% 5.64/5.96 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_eq_minus_1_iff
% 5.64/5.96 thf(fact_7047_exp__total,axiom,
% 5.64/5.96 ! [Y4: real] :
% 5.64/5.96 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.96 => ? [X4: real] :
% 5.64/5.96 ( ( exp_real @ X4 )
% 5.64/5.96 = Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_total
% 5.64/5.96 thf(fact_7048_exp__gt__zero,axiom,
% 5.64/5.96 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_gt_zero
% 5.64/5.96 thf(fact_7049_not__exp__less__zero,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ~ ( ord_less_real @ ( exp_real @ X2 ) @ zero_zero_real ) ).
% 5.64/5.96
% 5.64/5.96 % not_exp_less_zero
% 5.64/5.96 thf(fact_7050_sum__cong__Suc,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > nat,G: nat > nat] :
% 5.64/5.96 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ ( suc @ X4 ) @ A4 )
% 5.64/5.96 => ( ( F @ ( suc @ X4 ) )
% 5.64/5.96 = ( G @ ( suc @ X4 ) ) ) )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ F @ A4 )
% 5.64/5.96 = ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_cong_Suc
% 5.64/5.96 thf(fact_7051_sum__cong__Suc,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > real,G: nat > real] :
% 5.64/5.96 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 5.64/5.96 => ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ ( suc @ X4 ) @ A4 )
% 5.64/5.96 => ( ( F @ ( suc @ X4 ) )
% 5.64/5.96 = ( G @ ( suc @ X4 ) ) ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ F @ A4 )
% 5.64/5.96 = ( groups6591440286371151544t_real @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_cong_Suc
% 5.64/5.96 thf(fact_7052_mult__exp__exp,axiom,
% 5.64/5.96 ! [X2: complex,Y4: complex] :
% 5.64/5.96 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y4 ) )
% 5.64/5.96 = ( exp_complex @ ( plus_plus_complex @ X2 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mult_exp_exp
% 5.64/5.96 thf(fact_7053_mult__exp__exp,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y4 ) )
% 5.64/5.96 = ( exp_real @ ( plus_plus_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mult_exp_exp
% 5.64/5.96 thf(fact_7054_exp__add__commuting,axiom,
% 5.64/5.96 ! [X2: complex,Y4: complex] :
% 5.64/5.96 ( ( ( times_times_complex @ X2 @ Y4 )
% 5.64/5.96 = ( times_times_complex @ Y4 @ X2 ) )
% 5.64/5.96 => ( ( exp_complex @ ( plus_plus_complex @ X2 @ Y4 ) )
% 5.64/5.96 = ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_add_commuting
% 5.64/5.96 thf(fact_7055_exp__add__commuting,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ( times_times_real @ X2 @ Y4 )
% 5.64/5.96 = ( times_times_real @ Y4 @ X2 ) )
% 5.64/5.96 => ( ( exp_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.96 = ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_add_commuting
% 5.64/5.96 thf(fact_7056_exp__diff,axiom,
% 5.64/5.96 ! [X2: complex,Y4: complex] :
% 5.64/5.96 ( ( exp_complex @ ( minus_minus_complex @ X2 @ Y4 ) )
% 5.64/5.96 = ( divide1717551699836669952omplex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_diff
% 5.64/5.96 thf(fact_7057_exp__diff,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( exp_real @ ( minus_minus_real @ X2 @ Y4 ) )
% 5.64/5.96 = ( divide_divide_real @ ( exp_real @ X2 ) @ ( exp_real @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_diff
% 5.64/5.96 thf(fact_7058_sum__subtractf__nat,axiom,
% 5.64/5.96 ! [A4: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.64/5.96 ( ! [X4: product_prod_nat_nat] :
% 5.64/5.96 ( ( member8440522571783428010at_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( groups977919841031483927at_nat
% 5.64/5.96 @ ^ [X: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A4 ) @ ( groups977919841031483927at_nat @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_subtractf_nat
% 5.64/5.96 thf(fact_7059_sum__subtractf__nat,axiom,
% 5.64/5.96 ! [A4: set_complex,G: complex > nat,F: complex > nat] :
% 5.64/5.96 ( ! [X4: complex] :
% 5.64/5.96 ( ( member_complex @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( groups5693394587270226106ex_nat
% 5.64/5.96 @ ^ [X: complex] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A4 ) @ ( groups5693394587270226106ex_nat @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_subtractf_nat
% 5.64/5.96 thf(fact_7060_sum__subtractf__nat,axiom,
% 5.64/5.96 ! [A4: set_real,G: real > nat,F: real > nat] :
% 5.64/5.96 ( ! [X4: real] :
% 5.64/5.96 ( ( member_real @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( groups1935376822645274424al_nat
% 5.64/5.96 @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A4 ) @ ( groups1935376822645274424al_nat @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_subtractf_nat
% 5.64/5.96 thf(fact_7061_sum__subtractf__nat,axiom,
% 5.64/5.96 ! [A4: set_int,G: int > nat,F: int > nat] :
% 5.64/5.96 ( ! [X4: int] :
% 5.64/5.96 ( ( member_int @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( groups4541462559716669496nt_nat
% 5.64/5.96 @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A4 ) @ ( groups4541462559716669496nt_nat @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_subtractf_nat
% 5.64/5.96 thf(fact_7062_sum__subtractf__nat,axiom,
% 5.64/5.96 ! [A4: set_nat,G: nat > nat,F: nat > nat] :
% 5.64/5.96 ( ! [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 => ( ord_less_eq_nat @ ( G @ X4 ) @ ( F @ X4 ) ) )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.64/5.96 @ A4 )
% 5.64/5.96 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A4 ) @ ( groups3542108847815614940at_nat @ G @ A4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_subtractf_nat
% 5.64/5.96 thf(fact_7063_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.64/5.96 ! [G: nat > nat,M: nat,N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.64/5.96 = ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.shift_bounds_cl_Suc_ivl
% 5.64/5.96 thf(fact_7064_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.64/5.96 ! [G: nat > real,M: nat,N: nat] :
% 5.64/5.96 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.64/5.96 = ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.shift_bounds_cl_Suc_ivl
% 5.64/5.96 thf(fact_7065_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.64/5.96 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.64/5.96 = ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.shift_bounds_cl_nat_ivl
% 5.64/5.96 thf(fact_7066_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.64/5.96 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.64/5.96 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.64/5.96 = ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.shift_bounds_cl_nat_ivl
% 5.64/5.96 thf(fact_7067_pow_Osimps_I1_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( pow @ X2 @ one )
% 5.64/5.96 = X2 ) ).
% 5.64/5.96
% 5.64/5.96 % pow.simps(1)
% 5.64/5.96 thf(fact_7068_inc_Osimps_I1_J,axiom,
% 5.64/5.96 ( ( inc @ one )
% 5.64/5.96 = ( bit0 @ one ) ) ).
% 5.64/5.96
% 5.64/5.96 % inc.simps(1)
% 5.64/5.96 thf(fact_7069_inc_Osimps_I3_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( inc @ ( bit1 @ X2 ) )
% 5.64/5.96 = ( bit0 @ ( inc @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % inc.simps(3)
% 5.64/5.96 thf(fact_7070_inc_Osimps_I2_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( inc @ ( bit0 @ X2 ) )
% 5.64/5.96 = ( bit1 @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % inc.simps(2)
% 5.64/5.96 thf(fact_7071_sum__eq__Suc0__iff,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 5.64/5.96 = ( suc @ zero_zero_nat ) )
% 5.64/5.96 = ( ? [X: int] :
% 5.64/5.96 ( ( member_int @ X @ A4 )
% 5.64/5.96 & ( ( F @ X )
% 5.64/5.96 = ( suc @ zero_zero_nat ) )
% 5.64/5.96 & ! [Y: int] :
% 5.64/5.96 ( ( member_int @ Y @ A4 )
% 5.64/5.96 => ( ( X != Y )
% 5.64/5.96 => ( ( F @ Y )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_eq_Suc0_iff
% 5.64/5.96 thf(fact_7072_sum__eq__Suc0__iff,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 5.64/5.96 = ( suc @ zero_zero_nat ) )
% 5.64/5.96 = ( ? [X: complex] :
% 5.64/5.96 ( ( member_complex @ X @ A4 )
% 5.64/5.96 & ( ( F @ X )
% 5.64/5.96 = ( suc @ zero_zero_nat ) )
% 5.64/5.96 & ! [Y: complex] :
% 5.64/5.96 ( ( member_complex @ Y @ A4 )
% 5.64/5.96 => ( ( X != Y )
% 5.64/5.96 => ( ( F @ Y )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_eq_Suc0_iff
% 5.64/5.96 thf(fact_7073_sum__eq__Suc0__iff,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > nat] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 5.64/5.96 = ( suc @ zero_zero_nat ) )
% 5.64/5.96 = ( ? [X: nat] :
% 5.64/5.96 ( ( member_nat @ X @ A4 )
% 5.64/5.96 & ( ( F @ X )
% 5.64/5.96 = ( suc @ zero_zero_nat ) )
% 5.64/5.96 & ! [Y: nat] :
% 5.64/5.96 ( ( member_nat @ Y @ A4 )
% 5.64/5.96 => ( ( X != Y )
% 5.64/5.96 => ( ( F @ Y )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_eq_Suc0_iff
% 5.64/5.96 thf(fact_7074_sum__SucD,axiom,
% 5.64/5.96 ! [F: nat > nat,A4: set_nat,N: nat] :
% 5.64/5.96 ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 5.64/5.96 = ( suc @ N ) )
% 5.64/5.96 => ? [X4: nat] :
% 5.64/5.96 ( ( member_nat @ X4 @ A4 )
% 5.64/5.96 & ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_SucD
% 5.64/5.96 thf(fact_7075_sum__eq__1__iff,axiom,
% 5.64/5.96 ! [A4: set_int,F: int > nat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ( ( groups4541462559716669496nt_nat @ F @ A4 )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 = ( ? [X: int] :
% 5.64/5.96 ( ( member_int @ X @ A4 )
% 5.64/5.96 & ( ( F @ X )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 & ! [Y: int] :
% 5.64/5.96 ( ( member_int @ Y @ A4 )
% 5.64/5.96 => ( ( X != Y )
% 5.64/5.96 => ( ( F @ Y )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_eq_1_iff
% 5.64/5.96 thf(fact_7076_sum__eq__1__iff,axiom,
% 5.64/5.96 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ( ( groups5693394587270226106ex_nat @ F @ A4 )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 = ( ? [X: complex] :
% 5.64/5.96 ( ( member_complex @ X @ A4 )
% 5.64/5.96 & ( ( F @ X )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 & ! [Y: complex] :
% 5.64/5.96 ( ( member_complex @ Y @ A4 )
% 5.64/5.96 => ( ( X != Y )
% 5.64/5.96 => ( ( F @ Y )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_eq_1_iff
% 5.64/5.96 thf(fact_7077_sum__eq__1__iff,axiom,
% 5.64/5.96 ! [A4: set_nat,F: nat > nat] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ( ( groups3542108847815614940at_nat @ F @ A4 )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 = ( ? [X: nat] :
% 5.64/5.96 ( ( member_nat @ X @ A4 )
% 5.64/5.96 & ( ( F @ X )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 & ! [Y: nat] :
% 5.64/5.96 ( ( member_nat @ Y @ A4 )
% 5.64/5.96 => ( ( X != Y )
% 5.64/5.96 => ( ( F @ Y )
% 5.64/5.96 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_eq_1_iff
% 5.64/5.96 thf(fact_7078_exp__gt__one,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.96 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_gt_one
% 5.64/5.96 thf(fact_7079_add__One,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( plus_plus_num @ X2 @ one )
% 5.64/5.96 = ( inc @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % add_One
% 5.64/5.96 thf(fact_7080_and__less__eq,axiom,
% 5.64/5.96 ! [L: int,K: int] :
% 5.64/5.96 ( ( ord_less_int @ L @ zero_zero_int )
% 5.64/5.96 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_less_eq
% 5.64/5.96 thf(fact_7081_AND__upper1_H_H,axiom,
% 5.64/5.96 ! [Y4: int,Z: int,Ya: int] :
% 5.64/5.96 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.96 => ( ( ord_less_int @ Y4 @ Z )
% 5.64/5.96 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y4 @ Ya ) @ Z ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % AND_upper1''
% 5.64/5.96 thf(fact_7082_AND__upper2_H_H,axiom,
% 5.64/5.96 ! [Y4: int,Z: int,X2: int] :
% 5.64/5.96 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.96 => ( ( ord_less_int @ Y4 @ Z )
% 5.64/5.96 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y4 ) @ Z ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % AND_upper2''
% 5.64/5.96 thf(fact_7083_inc__BitM__eq,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( inc @ ( bitM @ N ) )
% 5.64/5.96 = ( bit0 @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % inc_BitM_eq
% 5.64/5.96 thf(fact_7084_exp__minus__inverse,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) )
% 5.64/5.96 = one_one_real ) ).
% 5.64/5.96
% 5.64/5.96 % exp_minus_inverse
% 5.64/5.96 thf(fact_7085_exp__minus__inverse,axiom,
% 5.64/5.96 ! [X2: complex] :
% 5.64/5.96 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) )
% 5.64/5.96 = one_one_complex ) ).
% 5.64/5.96
% 5.64/5.96 % exp_minus_inverse
% 5.64/5.96 thf(fact_7086_BitM__inc__eq,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( bitM @ ( inc @ N ) )
% 5.64/5.96 = ( bit1 @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % BitM_inc_eq
% 5.64/5.96 thf(fact_7087_mult__inc,axiom,
% 5.64/5.96 ! [X2: num,Y4: num] :
% 5.64/5.96 ( ( times_times_num @ X2 @ ( inc @ Y4 ) )
% 5.64/5.96 = ( plus_plus_num @ ( times_times_num @ X2 @ Y4 ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % mult_inc
% 5.64/5.96 thf(fact_7088_sum__power__add,axiom,
% 5.64/5.96 ! [X2: complex,M: nat,I5: set_nat] :
% 5.64/5.96 ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ I5 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_power_add
% 5.64/5.96 thf(fact_7089_sum__power__add,axiom,
% 5.64/5.96 ! [X2: rat,M: nat,I5: set_nat] :
% 5.64/5.96 ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ I5 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_power_add
% 5.64/5.96 thf(fact_7090_sum__power__add,axiom,
% 5.64/5.96 ! [X2: int,M: nat,I5: set_nat] :
% 5.64/5.96 ( ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ I5 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_power_add
% 5.64/5.96 thf(fact_7091_sum__power__add,axiom,
% 5.64/5.96 ! [X2: real,M: nat,I5: set_nat] :
% 5.64/5.96 ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( plus_plus_nat @ M @ I4 ) )
% 5.64/5.96 @ I5 )
% 5.64/5.96 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ I5 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_power_add
% 5.64/5.96 thf(fact_7092_sum_OatLeastAtMost__rev,axiom,
% 5.64/5.96 ! [G: nat > nat,N: nat,M: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.64/5.96 = ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeastAtMost_rev
% 5.64/5.96 thf(fact_7093_sum_OatLeastAtMost__rev,axiom,
% 5.64/5.96 ! [G: nat > real,N: nat,M: nat] :
% 5.64/5.96 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.64/5.96 = ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeastAtMost_rev
% 5.64/5.96 thf(fact_7094_sum__roots__unity,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ord_less_nat @ one_one_nat @ N )
% 5.64/5.96 => ( ( groups7754918857620584856omplex
% 5.64/5.96 @ ^ [X: complex] : X
% 5.64/5.96 @ ( collect_complex
% 5.64/5.96 @ ^ [Z4: complex] :
% 5.64/5.96 ( ( power_power_complex @ Z4 @ N )
% 5.64/5.96 = one_one_complex ) ) )
% 5.64/5.96 = zero_zero_complex ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_roots_unity
% 5.64/5.96 thf(fact_7095_sum__nth__roots,axiom,
% 5.64/5.96 ! [N: nat,C: complex] :
% 5.64/5.96 ( ( ord_less_nat @ one_one_nat @ N )
% 5.64/5.96 => ( ( groups7754918857620584856omplex
% 5.64/5.96 @ ^ [X: complex] : X
% 5.64/5.96 @ ( collect_complex
% 5.64/5.96 @ ^ [Z4: complex] :
% 5.64/5.96 ( ( power_power_complex @ Z4 @ N )
% 5.64/5.96 = C ) ) )
% 5.64/5.96 = zero_zero_complex ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_nth_roots
% 5.64/5.96 thf(fact_7096_even__and__iff,axiom,
% 5.64/5.96 ! [A: code_integer,B: code_integer] :
% 5.64/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.64/5.96 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_and_iff
% 5.64/5.96 thf(fact_7097_even__and__iff,axiom,
% 5.64/5.96 ! [A: int,B: int] :
% 5.64/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.64/5.96 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_and_iff
% 5.64/5.96 thf(fact_7098_even__and__iff,axiom,
% 5.64/5.96 ! [A: nat,B: nat] :
% 5.64/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.64/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_and_iff
% 5.64/5.96 thf(fact_7099_even__or__iff,axiom,
% 5.64/5.96 ! [A: code_integer,B: code_integer] :
% 5.64/5.96 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 5.64/5.96 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_or_iff
% 5.64/5.96 thf(fact_7100_even__or__iff,axiom,
% 5.64/5.96 ! [A: int,B: int] :
% 5.64/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.64/5.96 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_or_iff
% 5.64/5.96 thf(fact_7101_even__or__iff,axiom,
% 5.64/5.96 ! [A: nat,B: nat] :
% 5.64/5.96 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.64/5.96 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.64/5.96 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_or_iff
% 5.64/5.96 thf(fact_7102_sum__shift__lb__Suc0__0,axiom,
% 5.64/5.96 ! [F: nat > complex,K: nat] :
% 5.64/5.96 ( ( ( F @ zero_zero_nat )
% 5.64/5.96 = zero_zero_complex )
% 5.64/5.96 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.64/5.96 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_shift_lb_Suc0_0
% 5.64/5.96 thf(fact_7103_sum__shift__lb__Suc0__0,axiom,
% 5.64/5.96 ! [F: nat > rat,K: nat] :
% 5.64/5.96 ( ( ( F @ zero_zero_nat )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.64/5.96 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_shift_lb_Suc0_0
% 5.64/5.96 thf(fact_7104_sum__shift__lb__Suc0__0,axiom,
% 5.64/5.96 ! [F: nat > int,K: nat] :
% 5.64/5.96 ( ( ( F @ zero_zero_nat )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.64/5.96 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_shift_lb_Suc0_0
% 5.64/5.96 thf(fact_7105_sum__shift__lb__Suc0__0,axiom,
% 5.64/5.96 ! [F: nat > nat,K: nat] :
% 5.64/5.96 ( ( ( F @ zero_zero_nat )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.64/5.96 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_shift_lb_Suc0_0
% 5.64/5.96 thf(fact_7106_sum__shift__lb__Suc0__0,axiom,
% 5.64/5.96 ! [F: nat > real,K: nat] :
% 5.64/5.96 ( ( ( F @ zero_zero_nat )
% 5.64/5.96 = zero_zero_real )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.64/5.96 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_shift_lb_Suc0_0
% 5.64/5.96 thf(fact_7107_sum_OatLeast0__atMost__Suc,axiom,
% 5.64/5.96 ! [G: nat > rat,N: nat] :
% 5.64/5.96 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast0_atMost_Suc
% 5.64/5.96 thf(fact_7108_sum_OatLeast0__atMost__Suc,axiom,
% 5.64/5.96 ! [G: nat > int,N: nat] :
% 5.64/5.96 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast0_atMost_Suc
% 5.64/5.96 thf(fact_7109_sum_OatLeast0__atMost__Suc,axiom,
% 5.64/5.96 ! [G: nat > nat,N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast0_atMost_Suc
% 5.64/5.96 thf(fact_7110_sum_OatLeast0__atMost__Suc,axiom,
% 5.64/5.96 ! [G: nat > real,N: nat] :
% 5.64/5.96 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast0_atMost_Suc
% 5.64/5.96 thf(fact_7111_even__and__iff__int,axiom,
% 5.64/5.96 ! [K: int,L: int] :
% 5.64/5.96 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.64/5.96 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.64/5.96 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % even_and_iff_int
% 5.64/5.96 thf(fact_7112_sum_OatLeast__Suc__atMost,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > rat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast_Suc_atMost
% 5.64/5.96 thf(fact_7113_sum_OatLeast__Suc__atMost,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast_Suc_atMost
% 5.64/5.96 thf(fact_7114_sum_OatLeast__Suc__atMost,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast_Suc_atMost
% 5.64/5.96 thf(fact_7115_sum_OatLeast__Suc__atMost,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > real] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.atLeast_Suc_atMost
% 5.64/5.96 thf(fact_7116_sum_Onat__ivl__Suc_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > rat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.nat_ivl_Suc'
% 5.64/5.96 thf(fact_7117_sum_Onat__ivl__Suc_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.nat_ivl_Suc'
% 5.64/5.96 thf(fact_7118_sum_Onat__ivl__Suc_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.nat_ivl_Suc'
% 5.64/5.96 thf(fact_7119_sum_Onat__ivl__Suc_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > real] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.nat_ivl_Suc'
% 5.64/5.96 thf(fact_7120_ln__ge__iff,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.96 => ( ( ord_less_eq_real @ Y4 @ ( ln_ln_real @ X2 ) )
% 5.64/5.96 = ( ord_less_eq_real @ ( exp_real @ Y4 ) @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % ln_ge_iff
% 5.64/5.96 thf(fact_7121_numeral__inc,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( numera6690914467698888265omplex @ ( inc @ X2 ) )
% 5.64/5.96 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_inc
% 5.64/5.96 thf(fact_7122_numeral__inc,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( numeral_numeral_real @ ( inc @ X2 ) )
% 5.64/5.96 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_inc
% 5.64/5.96 thf(fact_7123_numeral__inc,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( numeral_numeral_rat @ ( inc @ X2 ) )
% 5.64/5.96 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_inc
% 5.64/5.96 thf(fact_7124_numeral__inc,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( numeral_numeral_nat @ ( inc @ X2 ) )
% 5.64/5.96 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_inc
% 5.64/5.96 thf(fact_7125_numeral__inc,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( numeral_numeral_int @ ( inc @ X2 ) )
% 5.64/5.96 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_inc
% 5.64/5.96 thf(fact_7126_ln__x__over__x__mono,axiom,
% 5.64/5.96 ! [X2: real,Y4: real] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X2 )
% 5.64/5.96 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.96 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y4 ) @ Y4 ) @ ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % ln_x_over_x_mono
% 5.64/5.96 thf(fact_7127_sum_OSuc__reindex__ivl,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > rat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ M )
% 5.64/5.96 @ ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.Suc_reindex_ivl
% 5.64/5.96 thf(fact_7128_sum_OSuc__reindex__ivl,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( G @ M )
% 5.64/5.96 @ ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.Suc_reindex_ivl
% 5.64/5.96 thf(fact_7129_sum_OSuc__reindex__ivl,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( G @ M )
% 5.64/5.96 @ ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.Suc_reindex_ivl
% 5.64/5.96 thf(fact_7130_sum_OSuc__reindex__ivl,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > real] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ M )
% 5.64/5.96 @ ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.Suc_reindex_ivl
% 5.64/5.96 thf(fact_7131_sum__Suc__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > rat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_Suc_diff
% 5.64/5.96 thf(fact_7132_sum__Suc__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_Suc_diff
% 5.64/5.96 thf(fact_7133_sum__Suc__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > real] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_Suc_diff
% 5.64/5.96 thf(fact_7134_and__one__eq,axiom,
% 5.64/5.96 ! [A: code_integer] :
% 5.64/5.96 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.64/5.96 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_one_eq
% 5.64/5.96 thf(fact_7135_and__one__eq,axiom,
% 5.64/5.96 ! [A: int] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.64/5.96 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_one_eq
% 5.64/5.96 thf(fact_7136_and__one__eq,axiom,
% 5.64/5.96 ! [A: nat] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.64/5.96 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_one_eq
% 5.64/5.96 thf(fact_7137_one__and__eq,axiom,
% 5.64/5.96 ! [A: code_integer] :
% 5.64/5.96 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.64/5.96 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_and_eq
% 5.64/5.96 thf(fact_7138_one__and__eq,axiom,
% 5.64/5.96 ! [A: int] :
% 5.64/5.96 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.64/5.96 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_and_eq
% 5.64/5.96 thf(fact_7139_one__and__eq,axiom,
% 5.64/5.96 ! [A: nat] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.64/5.96 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_and_eq
% 5.64/5.96 thf(fact_7140_exp__le,axiom,
% 5.64/5.96 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_le
% 5.64/5.96 thf(fact_7141_sum_Oub__add__nat,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > rat,P2: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.64/5.96 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.ub_add_nat
% 5.64/5.96 thf(fact_7142_sum_Oub__add__nat,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > int,P2: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.64/5.96 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.64/5.96 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.ub_add_nat
% 5.64/5.96 thf(fact_7143_sum_Oub__add__nat,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > nat,P2: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.64/5.96 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.64/5.96 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.ub_add_nat
% 5.64/5.96 thf(fact_7144_sum_Oub__add__nat,axiom,
% 5.64/5.96 ! [M: nat,N: nat,G: nat > real,P2: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P2 ) ) )
% 5.64/5.96 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P2 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.ub_add_nat
% 5.64/5.96 thf(fact_7145_set__encode__def,axiom,
% 5.64/5.96 ( nat_set_encode
% 5.64/5.96 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % set_encode_def
% 5.64/5.96 thf(fact_7146_tanh__altdef,axiom,
% 5.64/5.96 ( tanh_real
% 5.64/5.96 = ( ^ [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 ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % tanh_altdef
% 5.64/5.96 thf(fact_7147_tanh__altdef,axiom,
% 5.64/5.96 ( tanh_complex
% 5.64/5.96 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % tanh_altdef
% 5.64/5.96 thf(fact_7148_exp__half__le2,axiom,
% 5.64/5.96 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_half_le2
% 5.64/5.96 thf(fact_7149_mask__Suc__exp,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 5.64/5.96 = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_Suc_exp
% 5.64/5.96 thf(fact_7150_mask__Suc__exp,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 5.64/5.96 = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_Suc_exp
% 5.64/5.96 thf(fact_7151_exp__double,axiom,
% 5.64/5.96 ! [Z: complex] :
% 5.64/5.96 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.64/5.96 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_double
% 5.64/5.96 thf(fact_7152_exp__double,axiom,
% 5.64/5.96 ! [Z: real] :
% 5.64/5.96 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.64/5.96 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_double
% 5.64/5.96 thf(fact_7153_sum__natinterval__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > complex] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups2073611262835488442omplex
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_complex ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_natinterval_diff
% 5.64/5.96 thf(fact_7154_sum__natinterval__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > rat] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_rat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_natinterval_diff
% 5.64/5.96 thf(fact_7155_sum__natinterval__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > int] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_natinterval_diff
% 5.64/5.96 thf(fact_7156_sum__natinterval__diff,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > real] :
% 5.64/5.96 ( ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.64/5.96 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_real ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_natinterval_diff
% 5.64/5.96 thf(fact_7157_sum__telescope_H_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > rat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.64/5.96 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_telescope''
% 5.64/5.96 thf(fact_7158_sum__telescope_H_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.64/5.96 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_telescope''
% 5.64/5.96 thf(fact_7159_sum__telescope_H_H,axiom,
% 5.64/5.96 ! [M: nat,N: nat,F: nat > real] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.64/5.96 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_telescope''
% 5.64/5.96 thf(fact_7160_one__or__eq,axiom,
% 5.64/5.96 ! [A: code_integer] :
% 5.64/5.96 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 5.64/5.96 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_or_eq
% 5.64/5.96 thf(fact_7161_one__or__eq,axiom,
% 5.64/5.96 ! [A: int] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 5.64/5.96 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_or_eq
% 5.64/5.96 thf(fact_7162_one__or__eq,axiom,
% 5.64/5.96 ! [A: nat] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 5.64/5.96 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % one_or_eq
% 5.64/5.96 thf(fact_7163_or__one__eq,axiom,
% 5.64/5.96 ! [A: code_integer] :
% 5.64/5.96 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 5.64/5.96 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_one_eq
% 5.64/5.96 thf(fact_7164_or__one__eq,axiom,
% 5.64/5.96 ! [A: int] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 5.64/5.96 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_one_eq
% 5.64/5.96 thf(fact_7165_or__one__eq,axiom,
% 5.64/5.96 ! [A: nat] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 5.64/5.96 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_one_eq
% 5.64/5.96 thf(fact_7166_mask__Suc__double,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N ) )
% 5.64/5.96 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_Suc_double
% 5.64/5.96 thf(fact_7167_mask__Suc__double,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( bit_se2000444600071755411sk_int @ ( suc @ N ) )
% 5.64/5.96 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_Suc_double
% 5.64/5.96 thf(fact_7168_OR__upper,axiom,
% 5.64/5.96 ! [X2: int,N: nat,Y4: int] :
% 5.64/5.96 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.96 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.96 => ( ( ord_less_int @ Y4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.96 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y4 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % OR_upper
% 5.64/5.96 thf(fact_7169_or__int__rec,axiom,
% 5.64/5.96 ( bit_se1409905431419307370or_int
% 5.64/5.96 = ( ^ [K2: int,L2: int] :
% 5.64/5.96 ( plus_plus_int
% 5.64/5.96 @ ( zero_n2684676970156552555ol_int
% 5.64/5.96 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.64/5.96 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.64/5.96 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_int_rec
% 5.64/5.96 thf(fact_7170_and__int__rec,axiom,
% 5.64/5.96 ( bit_se725231765392027082nd_int
% 5.64/5.96 = ( ^ [K2: int,L2: int] :
% 5.64/5.96 ( plus_plus_int
% 5.64/5.96 @ ( zero_n2684676970156552555ol_int
% 5.64/5.96 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.64/5.96 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.64/5.96 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_int_rec
% 5.64/5.96 thf(fact_7171_mask__eq__sum__exp,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.64/5.96 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.96 @ ( collect_nat
% 5.64/5.96 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_eq_sum_exp
% 5.64/5.96 thf(fact_7172_mask__eq__sum__exp,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.64/5.96 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.96 @ ( collect_nat
% 5.64/5.96 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_eq_sum_exp
% 5.64/5.96 thf(fact_7173_sum__gp__multiplied,axiom,
% 5.64/5.96 ! [M: nat,N: nat,X2: complex] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.64/5.96 = ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp_multiplied
% 5.64/5.96 thf(fact_7174_sum__gp__multiplied,axiom,
% 5.64/5.96 ! [M: nat,N: nat,X2: rat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.64/5.96 = ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp_multiplied
% 5.64/5.96 thf(fact_7175_sum__gp__multiplied,axiom,
% 5.64/5.96 ! [M: nat,N: nat,X2: int] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.64/5.96 = ( minus_minus_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp_multiplied
% 5.64/5.96 thf(fact_7176_sum__gp__multiplied,axiom,
% 5.64/5.96 ! [M: nat,N: nat,X2: real] :
% 5.64/5.96 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.96 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.64/5.96 = ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp_multiplied
% 5.64/5.96 thf(fact_7177_sum_Oin__pairs,axiom,
% 5.64/5.96 ! [G: nat > rat,M: nat,N: nat] :
% 5.64/5.96 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.96 = ( groups2906978787729119204at_rat
% 5.64/5.96 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.in_pairs
% 5.64/5.96 thf(fact_7178_sum_Oin__pairs,axiom,
% 5.64/5.96 ! [G: nat > int,M: nat,N: nat] :
% 5.64/5.96 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.96 = ( groups3539618377306564664at_int
% 5.64/5.96 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.in_pairs
% 5.64/5.96 thf(fact_7179_sum_Oin__pairs,axiom,
% 5.64/5.96 ! [G: nat > nat,M: nat,N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.96 = ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.in_pairs
% 5.64/5.96 thf(fact_7180_sum_Oin__pairs,axiom,
% 5.64/5.96 ! [G: nat > real,M: nat,N: nat] :
% 5.64/5.96 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.96 = ( groups6591440286371151544t_real
% 5.64/5.96 @ ^ [I4: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.in_pairs
% 5.64/5.96 thf(fact_7181_exp__bound,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.96 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.96 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_bound
% 5.64/5.96 thf(fact_7182_mask__eq__sum__exp__nat,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.96 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.96 @ ( collect_nat
% 5.64/5.96 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % mask_eq_sum_exp_nat
% 5.64/5.96 thf(fact_7183_gauss__sum__nat,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [X: nat] : X
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.96 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % gauss_sum_nat
% 5.64/5.96 thf(fact_7184_real__exp__bound__lemma,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.96 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.96 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_exp_bound_lemma
% 5.64/5.96 thf(fact_7185_arith__series__nat,axiom,
% 5.64/5.96 ! [A: nat,D: nat,N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D ) )
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.96 = ( 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 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % arith_series_nat
% 5.64/5.96 thf(fact_7186_Sum__Icc__nat,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( groups3542108847815614940at_nat
% 5.64/5.96 @ ^ [X: nat] : X
% 5.64/5.96 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( 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 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % Sum_Icc_nat
% 5.64/5.96 thf(fact_7187_exp__lower__Taylor__quadratic,axiom,
% 5.64/5.96 ! [X2: real] :
% 5.64/5.96 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.96 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( divide_divide_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % exp_lower_Taylor_quadratic
% 5.64/5.96 thf(fact_7188_infinite__int__iff__unbounded,axiom,
% 5.64/5.96 ! [S3: set_int] :
% 5.64/5.96 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.64/5.96 = ( ! [M2: int] :
% 5.64/5.96 ? [N2: int] :
% 5.64/5.96 ( ( ord_less_int @ M2 @ ( abs_abs_int @ N2 ) )
% 5.64/5.96 & ( member_int @ N2 @ S3 ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % infinite_int_iff_unbounded
% 5.64/5.96 thf(fact_7189_and__int_Osimps,axiom,
% 5.64/5.96 ( bit_se725231765392027082nd_int
% 5.64/5.96 = ( ^ [K2: int,L2: int] :
% 5.64/5.96 ( if_int
% 5.64/5.96 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.96 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.96 @ ( uminus_uminus_int
% 5.64/5.96 @ ( zero_n2684676970156552555ol_int
% 5.64/5.96 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.64/5.96 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.64/5.96 @ ( plus_plus_int
% 5.64/5.96 @ ( zero_n2684676970156552555ol_int
% 5.64/5.96 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.64/5.96 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.64/5.96 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_int.simps
% 5.64/5.96 thf(fact_7190_and__int_Oelims,axiom,
% 5.64/5.96 ! [X2: int,Xa2: int,Y4: int] :
% 5.64/5.96 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.64/5.96 = Y4 )
% 5.64/5.96 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.96 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.96 => ( Y4
% 5.64/5.96 = ( uminus_uminus_int
% 5.64/5.96 @ ( zero_n2684676970156552555ol_int
% 5.64/5.96 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.64/5.96 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.64/5.96 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.96 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.96 => ( Y4
% 5.64/5.96 = ( plus_plus_int
% 5.64/5.96 @ ( zero_n2684676970156552555ol_int
% 5.64/5.96 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.64/5.96 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.64/5.96 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % and_int.elims
% 5.64/5.96 thf(fact_7191_or__minus__numerals_I1_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/5.96 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_minus_numerals(1)
% 5.64/5.96 thf(fact_7192_or__minus__numerals_I5_J,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.64/5.96 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_minus_numerals(5)
% 5.64/5.96 thf(fact_7193_sum__gp,axiom,
% 5.64/5.96 ! [N: nat,M: nat,X2: rat] :
% 5.64/5.96 ( ( ( ord_less_nat @ N @ M )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_rat ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ N @ M )
% 5.64/5.96 => ( ( ( X2 = one_one_rat )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.64/5.96 & ( ( X2 != one_one_rat )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp
% 5.64/5.96 thf(fact_7194_sum__gp,axiom,
% 5.64/5.96 ! [N: nat,M: nat,X2: complex] :
% 5.64/5.96 ( ( ( ord_less_nat @ N @ M )
% 5.64/5.96 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_complex ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ N @ M )
% 5.64/5.96 => ( ( ( X2 = one_one_complex )
% 5.64/5.96 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.64/5.96 & ( ( X2 != one_one_complex )
% 5.64/5.96 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp
% 5.64/5.96 thf(fact_7195_sum__gp,axiom,
% 5.64/5.96 ! [N: nat,M: nat,X2: real] :
% 5.64/5.96 ( ( ( ord_less_nat @ N @ M )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = zero_zero_real ) )
% 5.64/5.96 & ( ~ ( ord_less_nat @ N @ M )
% 5.64/5.96 => ( ( ( X2 = one_one_real )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.64/5.96 & ( ( X2 != one_one_real )
% 5.64/5.96 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.64/5.96 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum_gp
% 5.64/5.96 thf(fact_7196_of__nat__eq__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ( semiri1314217659103216013at_int @ M )
% 5.64/5.96 = ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( M = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_iff
% 5.64/5.96 thf(fact_7197_of__nat__eq__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ( semiri5074537144036343181t_real @ M )
% 5.64/5.96 = ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( M = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_iff
% 5.64/5.96 thf(fact_7198_of__nat__eq__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.64/5.96 = ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.96 = ( M = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_iff
% 5.64/5.96 thf(fact_7199_of__nat__eq__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ( semiri8010041392384452111omplex @ M )
% 5.64/5.96 = ( semiri8010041392384452111omplex @ N ) )
% 5.64/5.96 = ( M = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_iff
% 5.64/5.96 thf(fact_7200_int__eq__iff__numeral,axiom,
% 5.64/5.96 ! [M: nat,V: num] :
% 5.64/5.96 ( ( ( semiri1314217659103216013at_int @ M )
% 5.64/5.96 = ( numeral_numeral_int @ V ) )
% 5.64/5.96 = ( M
% 5.64/5.96 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % int_eq_iff_numeral
% 5.64/5.96 thf(fact_7201_abs__of__nat,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.96 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_of_nat
% 5.64/5.96 thf(fact_7202_abs__of__nat,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.64/5.96 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_of_nat
% 5.64/5.96 thf(fact_7203_abs__of__nat,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_of_nat
% 5.64/5.96 thf(fact_7204_abs__of__nat,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % abs_of_nat
% 5.64/5.96 thf(fact_7205_of__nat__0,axiom,
% 5.64/5.96 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.64/5.96 = zero_zero_rat ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0
% 5.64/5.96 thf(fact_7206_of__nat__0,axiom,
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.64/5.96 = zero_zero_int ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0
% 5.64/5.96 thf(fact_7207_of__nat__0,axiom,
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.64/5.96 = zero_zero_real ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0
% 5.64/5.96 thf(fact_7208_of__nat__0,axiom,
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.64/5.96 = zero_zero_nat ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0
% 5.64/5.96 thf(fact_7209_of__nat__0,axiom,
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.64/5.96 = zero_zero_complex ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0
% 5.64/5.96 thf(fact_7210_of__nat__0__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( zero_zero_rat
% 5.64/5.96 = ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.96 = ( zero_zero_nat = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_eq_iff
% 5.64/5.96 thf(fact_7211_of__nat__0__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( zero_zero_int
% 5.64/5.96 = ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( zero_zero_nat = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_eq_iff
% 5.64/5.96 thf(fact_7212_of__nat__0__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( zero_zero_real
% 5.64/5.96 = ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( zero_zero_nat = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_eq_iff
% 5.64/5.96 thf(fact_7213_of__nat__0__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( zero_zero_nat
% 5.64/5.96 = ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.96 = ( zero_zero_nat = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_eq_iff
% 5.64/5.96 thf(fact_7214_of__nat__0__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( zero_zero_complex
% 5.64/5.96 = ( semiri8010041392384452111omplex @ N ) )
% 5.64/5.96 = ( zero_zero_nat = N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_eq_iff
% 5.64/5.96 thf(fact_7215_of__nat__eq__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ( semiri681578069525770553at_rat @ M )
% 5.64/5.96 = zero_zero_rat )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_0_iff
% 5.64/5.96 thf(fact_7216_of__nat__eq__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ( semiri1314217659103216013at_int @ M )
% 5.64/5.96 = zero_zero_int )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_0_iff
% 5.64/5.96 thf(fact_7217_of__nat__eq__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ( semiri5074537144036343181t_real @ M )
% 5.64/5.96 = zero_zero_real )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_0_iff
% 5.64/5.96 thf(fact_7218_of__nat__eq__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.64/5.96 = zero_zero_nat )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_0_iff
% 5.64/5.96 thf(fact_7219_of__nat__eq__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ( semiri8010041392384452111omplex @ M )
% 5.64/5.96 = zero_zero_complex )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_0_iff
% 5.64/5.96 thf(fact_7220_of__nat__less__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.96 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_iff
% 5.64/5.96 thf(fact_7221_of__nat__less__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_iff
% 5.64/5.96 thf(fact_7222_of__nat__less__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_iff
% 5.64/5.96 thf(fact_7223_of__nat__less__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.96 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_iff
% 5.64/5.96 thf(fact_7224_of__nat__numeral,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.64/5.96 = ( numeral_numeral_rat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_numeral
% 5.64/5.96 thf(fact_7225_of__nat__numeral,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.64/5.96 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_numeral
% 5.64/5.96 thf(fact_7226_of__nat__numeral,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.64/5.96 = ( numeral_numeral_real @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_numeral
% 5.64/5.96 thf(fact_7227_of__nat__numeral,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.64/5.96 = ( numeral_numeral_nat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_numeral
% 5.64/5.96 thf(fact_7228_of__nat__numeral,axiom,
% 5.64/5.96 ! [N: num] :
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.64/5.96 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_numeral
% 5.64/5.96 thf(fact_7229_of__nat__le__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.96 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_iff
% 5.64/5.96 thf(fact_7230_of__nat__le__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.96 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_iff
% 5.64/5.96 thf(fact_7231_of__nat__le__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_iff
% 5.64/5.96 thf(fact_7232_of__nat__le__iff,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_iff
% 5.64/5.96 thf(fact_7233_of__nat__add,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_add
% 5.64/5.96 thf(fact_7234_of__nat__add,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_add
% 5.64/5.96 thf(fact_7235_of__nat__add,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_add
% 5.64/5.96 thf(fact_7236_of__nat__add,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_add
% 5.64/5.96 thf(fact_7237_of__nat__add,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 5.64/5.96 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_add
% 5.64/5.96 thf(fact_7238_of__nat__mult,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.64/5.96 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_mult
% 5.64/5.96 thf(fact_7239_of__nat__mult,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.64/5.96 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_mult
% 5.64/5.96 thf(fact_7240_of__nat__mult,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.64/5.96 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_mult
% 5.64/5.96 thf(fact_7241_of__nat__mult,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.64/5.96 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_mult
% 5.64/5.96 thf(fact_7242_of__nat__mult,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 5.64/5.96 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_mult
% 5.64/5.96 thf(fact_7243_of__nat__1,axiom,
% 5.64/5.96 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.64/5.96 = one_one_rat ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1
% 5.64/5.96 thf(fact_7244_of__nat__1,axiom,
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.64/5.96 = one_one_int ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1
% 5.64/5.96 thf(fact_7245_of__nat__1,axiom,
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.64/5.96 = one_one_real ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1
% 5.64/5.96 thf(fact_7246_of__nat__1,axiom,
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.64/5.96 = one_one_nat ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1
% 5.64/5.96 thf(fact_7247_of__nat__1,axiom,
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.64/5.96 = one_one_complex ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1
% 5.64/5.96 thf(fact_7248_of__nat__1__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( one_one_rat
% 5.64/5.96 = ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1_eq_iff
% 5.64/5.96 thf(fact_7249_of__nat__1__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( one_one_int
% 5.64/5.96 = ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1_eq_iff
% 5.64/5.96 thf(fact_7250_of__nat__1__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( one_one_real
% 5.64/5.96 = ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1_eq_iff
% 5.64/5.96 thf(fact_7251_of__nat__1__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( one_one_nat
% 5.64/5.96 = ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1_eq_iff
% 5.64/5.96 thf(fact_7252_of__nat__1__eq__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( one_one_complex
% 5.64/5.96 = ( semiri8010041392384452111omplex @ N ) )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_1_eq_iff
% 5.64/5.96 thf(fact_7253_of__nat__eq__1__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ( semiri681578069525770553at_rat @ N )
% 5.64/5.96 = one_one_rat )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_1_iff
% 5.64/5.96 thf(fact_7254_of__nat__eq__1__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ( semiri1314217659103216013at_int @ N )
% 5.64/5.96 = one_one_int )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_1_iff
% 5.64/5.96 thf(fact_7255_of__nat__eq__1__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ( semiri5074537144036343181t_real @ N )
% 5.64/5.96 = one_one_real )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_1_iff
% 5.64/5.96 thf(fact_7256_of__nat__eq__1__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.64/5.96 = one_one_nat )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_1_iff
% 5.64/5.96 thf(fact_7257_of__nat__eq__1__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ( semiri8010041392384452111omplex @ N )
% 5.64/5.96 = one_one_complex )
% 5.64/5.96 = ( N = one_one_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_1_iff
% 5.64/5.96 thf(fact_7258_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ( semiri1314217659103216013at_int @ X2 )
% 5.64/5.96 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.64/5.96 = ( X2
% 5.64/5.96 = ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7259_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ( semiri5074537144036343181t_real @ X2 )
% 5.64/5.96 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.64/5.96 = ( X2
% 5.64/5.96 = ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7260_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ( semiri1316708129612266289at_nat @ X2 )
% 5.64/5.96 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.64/5.96 = ( X2
% 5.64/5.96 = ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7261_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ( semiri8010041392384452111omplex @ X2 )
% 5.64/5.96 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.64/5.96 = ( X2
% 5.64/5.96 = ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7262_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.64/5.96 = ( semiri1314217659103216013at_int @ X2 ) )
% 5.64/5.96 = ( ( power_power_nat @ B @ W )
% 5.64/5.96 = X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7263_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.64/5.96 = ( semiri5074537144036343181t_real @ X2 ) )
% 5.64/5.96 = ( ( power_power_nat @ B @ W )
% 5.64/5.96 = X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7264_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.64/5.96 = ( semiri1316708129612266289at_nat @ X2 ) )
% 5.64/5.96 = ( ( power_power_nat @ B @ W )
% 5.64/5.96 = X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7265_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.64/5.96 = ( semiri8010041392384452111omplex @ X2 ) )
% 5.64/5.96 = ( ( power_power_nat @ B @ W )
% 5.64/5.96 = X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_eq_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7266_of__nat__power,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.64/5.96 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power
% 5.64/5.96 thf(fact_7267_of__nat__power,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.64/5.96 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power
% 5.64/5.96 thf(fact_7268_of__nat__power,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.64/5.96 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power
% 5.64/5.96 thf(fact_7269_of__nat__power,axiom,
% 5.64/5.96 ! [M: nat,N: nat] :
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.64/5.96 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power
% 5.64/5.96 thf(fact_7270_negative__zless,axiom,
% 5.64/5.96 ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.64/5.96
% 5.64/5.96 % negative_zless
% 5.64/5.96 thf(fact_7271_of__nat__of__bool,axiom,
% 5.64/5.96 ! [P: $o] :
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.64/5.96 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_of_bool
% 5.64/5.96 thf(fact_7272_of__nat__of__bool,axiom,
% 5.64/5.96 ! [P: $o] :
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.64/5.96 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_of_bool
% 5.64/5.96 thf(fact_7273_of__nat__of__bool,axiom,
% 5.64/5.96 ! [P: $o] :
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.64/5.96 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_of_bool
% 5.64/5.96 thf(fact_7274_of__nat__of__bool,axiom,
% 5.64/5.96 ! [P: $o] :
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.64/5.96 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_of_bool
% 5.64/5.96 thf(fact_7275_of__nat__of__bool,axiom,
% 5.64/5.96 ! [P: $o] :
% 5.64/5.96 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.64/5.96 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_of_bool
% 5.64/5.96 thf(fact_7276_of__nat__le__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_0_iff
% 5.64/5.96 thf(fact_7277_of__nat__le__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_0_iff
% 5.64/5.96 thf(fact_7278_of__nat__le__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_0_iff
% 5.64/5.96 thf(fact_7279_of__nat__le__0__iff,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.64/5.96 = ( M = zero_zero_nat ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_0_iff
% 5.64/5.96 thf(fact_7280_of__nat__Suc,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.64/5.96 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_Suc
% 5.64/5.96 thf(fact_7281_of__nat__Suc,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.64/5.96 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_Suc
% 5.64/5.96 thf(fact_7282_of__nat__Suc,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.64/5.96 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_Suc
% 5.64/5.96 thf(fact_7283_of__nat__Suc,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.64/5.96 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_Suc
% 5.64/5.96 thf(fact_7284_of__nat__Suc,axiom,
% 5.64/5.96 ! [M: nat] :
% 5.64/5.96 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.64/5.96 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_Suc
% 5.64/5.96 thf(fact_7285_and__nat__numerals_I1_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = zero_zero_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_nat_numerals(1)
% 5.64/5.96 thf(fact_7286_and__nat__numerals_I3_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.96 = zero_zero_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_nat_numerals(3)
% 5.64/5.96 thf(fact_7287_or__nat__numerals_I2_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_nat_numerals(2)
% 5.64/5.96 thf(fact_7288_or__nat__numerals_I4_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_nat_numerals(4)
% 5.64/5.96 thf(fact_7289_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.64/5.96 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.96 => ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.96 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7290_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_real,X2: real,G: real > real] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.96 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7291_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_int,X2: int,G: int > real] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.96 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7292_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_complex,X2: complex,G: complex > real] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.96 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7293_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.64/5.96 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.96 => ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.96 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7294_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_real,X2: real,G: real > rat] :
% 5.64/5.96 ( ( finite_finite_real @ A4 )
% 5.64/5.96 => ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.96 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7295_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_nat,X2: nat,G: nat > rat] :
% 5.64/5.96 ( ( finite_finite_nat @ A4 )
% 5.64/5.96 => ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.96 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7296_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_int,X2: int,G: int > rat] :
% 5.64/5.96 ( ( finite_finite_int @ A4 )
% 5.64/5.96 => ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.96 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7297_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_complex,X2: complex,G: complex > rat] :
% 5.64/5.96 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.96 => ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.96 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7298_sum_Oinsert,axiom,
% 5.64/5.96 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.64/5.96 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.96 => ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.96 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.96 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % sum.insert
% 5.64/5.96 thf(fact_7299_real__of__nat__less__numeral__iff,axiom,
% 5.64/5.96 ! [N: nat,W: num] :
% 5.64/5.96 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.64/5.96 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_of_nat_less_numeral_iff
% 5.64/5.96 thf(fact_7300_numeral__less__real__of__nat__iff,axiom,
% 5.64/5.96 ! [W: num,N: nat] :
% 5.64/5.96 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_less_real_of_nat_iff
% 5.64/5.96 thf(fact_7301_numeral__le__real__of__nat__iff,axiom,
% 5.64/5.96 ! [N: num,M: nat] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.64/5.96 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_le_real_of_nat_iff
% 5.64/5.96 thf(fact_7302_of__nat__0__less__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.96 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_less_iff
% 5.64/5.96 thf(fact_7303_of__nat__0__less__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.96 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_less_iff
% 5.64/5.96 thf(fact_7304_of__nat__0__less__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.96 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_less_iff
% 5.64/5.96 thf(fact_7305_of__nat__0__less__iff,axiom,
% 5.64/5.96 ! [N: nat] :
% 5.64/5.96 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.96 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_0_less_iff
% 5.64/5.96 thf(fact_7306_or__nat__numerals_I3_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_nat_numerals(3)
% 5.64/5.96 thf(fact_7307_or__nat__numerals_I1_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/5.96 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % or_nat_numerals(1)
% 5.64/5.96 thf(fact_7308_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_less_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7309_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_less_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7310_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_less_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7311_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_less_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7312_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.64/5.96 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7313_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.64/5.96 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7314_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.64/5.96 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7315_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.64/5.96 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_less_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7316_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.96 ! [Y4: nat,X2: num,N: nat] :
% 5.64/5.96 ( ( ( semiri681578069525770553at_rat @ Y4 )
% 5.64/5.96 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.64/5.96 = ( Y4
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_of_nat_eq_numeral_power_cancel_iff
% 5.64/5.96 thf(fact_7317_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.96 ! [Y4: nat,X2: num,N: nat] :
% 5.64/5.96 ( ( ( semiri1314217659103216013at_int @ Y4 )
% 5.64/5.96 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) )
% 5.64/5.96 = ( Y4
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_of_nat_eq_numeral_power_cancel_iff
% 5.64/5.96 thf(fact_7318_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.96 ! [Y4: nat,X2: num,N: nat] :
% 5.64/5.96 ( ( ( semiri5074537144036343181t_real @ Y4 )
% 5.64/5.96 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.64/5.96 = ( Y4
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_of_nat_eq_numeral_power_cancel_iff
% 5.64/5.96 thf(fact_7319_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.96 ! [Y4: nat,X2: num,N: nat] :
% 5.64/5.96 ( ( ( semiri1316708129612266289at_nat @ Y4 )
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.64/5.96 = ( Y4
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_of_nat_eq_numeral_power_cancel_iff
% 5.64/5.96 thf(fact_7320_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.96 ! [Y4: nat,X2: num,N: nat] :
% 5.64/5.96 ( ( ( semiri8010041392384452111omplex @ Y4 )
% 5.64/5.96 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N ) )
% 5.64/5.96 = ( Y4
% 5.64/5.96 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % real_of_nat_eq_numeral_power_cancel_iff
% 5.64/5.96 thf(fact_7321_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: num,N: nat,Y4: nat] :
% 5.64/5.96 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N )
% 5.64/5.96 = ( semiri681578069525770553at_rat @ Y4 ) )
% 5.64/5.96 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.96 = Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7322_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: num,N: nat,Y4: nat] :
% 5.64/5.96 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.96 = ( semiri1314217659103216013at_int @ Y4 ) )
% 5.64/5.96 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.96 = Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7323_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: num,N: nat,Y4: nat] :
% 5.64/5.96 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N )
% 5.64/5.96 = ( semiri5074537144036343181t_real @ Y4 ) )
% 5.64/5.96 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.96 = Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7324_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: num,N: nat,Y4: nat] :
% 5.64/5.96 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.96 = ( semiri1316708129612266289at_nat @ Y4 ) )
% 5.64/5.96 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.96 = Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7325_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: num,N: nat,Y4: nat] :
% 5.64/5.96 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N )
% 5.64/5.96 = ( semiri8010041392384452111omplex @ Y4 ) )
% 5.64/5.96 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.96 = Y4 ) ) ).
% 5.64/5.96
% 5.64/5.96 % numeral_power_eq_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7326_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.64/5.96 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7327_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.64/5.96 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7328_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.64/5.96 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7329_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.64/5.96 ! [B: nat,W: nat,X2: nat] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.64/5.96 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_le_of_nat_power_cancel_iff
% 5.64/5.96 thf(fact_7330_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_le_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7331_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_le_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7332_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_le_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7333_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.96 ! [X2: nat,B: nat,W: nat] :
% 5.64/5.96 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.64/5.96 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_power_le_of_nat_cancel_iff
% 5.64/5.96 thf(fact_7334_and__nat__numerals_I4_J,axiom,
% 5.64/5.96 ! [X2: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.64/5.96 = one_one_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_nat_numerals(4)
% 5.64/5.96 thf(fact_7335_and__nat__numerals_I2_J,axiom,
% 5.64/5.96 ! [Y4: num] :
% 5.64/5.96 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/5.96 = one_one_nat ) ).
% 5.64/5.96
% 5.64/5.96 % and_nat_numerals(2)
% 5.64/5.96 thf(fact_7336_set__replicate,axiom,
% 5.64/5.96 ! [N: nat,X2: vEBT_VEBT] :
% 5.64/5.96 ( ( N != zero_zero_nat )
% 5.64/5.96 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.64/5.96 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % set_replicate
% 5.64/5.96 thf(fact_7337_set__replicate,axiom,
% 5.64/5.96 ! [N: nat,X2: nat] :
% 5.64/5.96 ( ( N != zero_zero_nat )
% 5.64/5.96 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.64/5.96 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % set_replicate
% 5.64/5.96 thf(fact_7338_set__replicate,axiom,
% 5.64/5.96 ! [N: nat,X2: int] :
% 5.64/5.96 ( ( N != zero_zero_nat )
% 5.64/5.96 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.64/5.96 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % set_replicate
% 5.64/5.96 thf(fact_7339_set__replicate,axiom,
% 5.64/5.96 ! [N: nat,X2: real] :
% 5.64/5.96 ( ( N != zero_zero_nat )
% 5.64/5.96 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.64/5.96 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % set_replicate
% 5.64/5.96 thf(fact_7340_of__nat__zero__less__power__iff,axiom,
% 5.64/5.96 ! [X2: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N ) )
% 5.64/5.96 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.96 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.96
% 5.64/5.96 % of_nat_zero_less_power_iff
% 5.64/5.96 thf(fact_7341_of__nat__zero__less__power__iff,axiom,
% 5.64/5.96 ! [X2: nat,N: nat] :
% 5.64/5.96 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N ) )
% 5.64/5.96 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_zero_less_power_iff
% 5.64/5.97 thf(fact_7342_of__nat__zero__less__power__iff,axiom,
% 5.64/5.97 ! [X2: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N ) )
% 5.64/5.97 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_zero_less_power_iff
% 5.64/5.97 thf(fact_7343_of__nat__zero__less__power__iff,axiom,
% 5.64/5.97 ! [X2: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N ) )
% 5.64/5.97 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_zero_less_power_iff
% 5.64/5.97 thf(fact_7344_and__Suc__0__eq,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % and_Suc_0_eq
% 5.64/5.97 thf(fact_7345_Suc__0__and__eq,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.97 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % Suc_0_and_eq
% 5.64/5.97 thf(fact_7346_or__minus__numerals_I4_J,axiom,
% 5.64/5.97 ! [M: num,N: num] :
% 5.64/5.97 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_minus_numerals(4)
% 5.64/5.97 thf(fact_7347_or__minus__numerals_I8_J,axiom,
% 5.64/5.97 ! [N: num,M: num] :
% 5.64/5.97 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_minus_numerals(8)
% 5.64/5.97 thf(fact_7348_or__minus__numerals_I3_J,axiom,
% 5.64/5.97 ! [M: num,N: num] :
% 5.64/5.97 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_minus_numerals(3)
% 5.64/5.97 thf(fact_7349_or__minus__numerals_I7_J,axiom,
% 5.64/5.97 ! [N: num,M: num] :
% 5.64/5.97 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_minus_numerals(7)
% 5.64/5.97 thf(fact_7350_even__of__nat,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.64/5.97 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % even_of_nat
% 5.64/5.97 thf(fact_7351_even__of__nat,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.97 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % even_of_nat
% 5.64/5.97 thf(fact_7352_even__of__nat,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.97 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % even_of_nat
% 5.64/5.97 thf(fact_7353_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7354_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7355_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7356_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7357_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_less_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7358_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.64/5.97 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_less_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7359_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.64/5.97 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_less_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7360_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.64/5.97 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_less_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7361_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_le_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7362_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_le_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7363_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_le_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7364_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.64/5.97 ! [X2: nat,I: num,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.64/5.97 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_le_numeral_power_cancel_iff
% 5.64/5.97 thf(fact_7365_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_le_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7366_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.64/5.97 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_le_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7367_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.64/5.97 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_le_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7368_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.64/5.97 ! [I: num,N: nat,X2: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.64/5.97 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_power_le_of_nat_cancel_iff
% 5.64/5.97 thf(fact_7369_real__arch__simple,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ? [N3: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_arch_simple
% 5.64/5.97 thf(fact_7370_real__arch__simple,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ? [N3: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_arch_simple
% 5.64/5.97 thf(fact_7371_reals__Archimedean2,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ? [N3: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.64/5.97
% 5.64/5.97 % reals_Archimedean2
% 5.64/5.97 thf(fact_7372_reals__Archimedean2,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ? [N3: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.64/5.97
% 5.64/5.97 % reals_Archimedean2
% 5.64/5.97 thf(fact_7373_mult__of__nat__commute,axiom,
% 5.64/5.97 ! [X2: nat,Y4: rat] :
% 5.64/5.97 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y4 )
% 5.64/5.97 = ( times_times_rat @ Y4 @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_of_nat_commute
% 5.64/5.97 thf(fact_7374_mult__of__nat__commute,axiom,
% 5.64/5.97 ! [X2: nat,Y4: int] :
% 5.64/5.97 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y4 )
% 5.64/5.97 = ( times_times_int @ Y4 @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_of_nat_commute
% 5.64/5.97 thf(fact_7375_mult__of__nat__commute,axiom,
% 5.64/5.97 ! [X2: nat,Y4: real] :
% 5.64/5.97 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y4 )
% 5.64/5.97 = ( times_times_real @ Y4 @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_of_nat_commute
% 5.64/5.97 thf(fact_7376_mult__of__nat__commute,axiom,
% 5.64/5.97 ! [X2: nat,Y4: nat] :
% 5.64/5.97 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y4 )
% 5.64/5.97 = ( times_times_nat @ Y4 @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_of_nat_commute
% 5.64/5.97 thf(fact_7377_mult__of__nat__commute,axiom,
% 5.64/5.97 ! [X2: nat,Y4: complex] :
% 5.64/5.97 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X2 ) @ Y4 )
% 5.64/5.97 = ( times_times_complex @ Y4 @ ( semiri8010041392384452111omplex @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_of_nat_commute
% 5.64/5.97 thf(fact_7378_or__not__num__neg_Osimps_I1_J,axiom,
% 5.64/5.97 ( ( bit_or_not_num_neg @ one @ one )
% 5.64/5.97 = one ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(1)
% 5.64/5.97 thf(fact_7379_of__nat__less__of__int__iff,axiom,
% 5.64/5.97 ! [N: nat,X2: int] :
% 5.64/5.97 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_of_int_iff
% 5.64/5.97 thf(fact_7380_of__nat__less__of__int__iff,axiom,
% 5.64/5.97 ! [N: nat,X2: int] :
% 5.64/5.97 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X2 ) )
% 5.64/5.97 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_of_int_iff
% 5.64/5.97 thf(fact_7381_of__nat__less__of__int__iff,axiom,
% 5.64/5.97 ! [N: nat,X2: int] :
% 5.64/5.97 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X2 ) )
% 5.64/5.97 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_of_int_iff
% 5.64/5.97 thf(fact_7382_of__nat__0__le__iff,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_0_le_iff
% 5.64/5.97 thf(fact_7383_of__nat__0__le__iff,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_0_le_iff
% 5.64/5.97 thf(fact_7384_of__nat__0__le__iff,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_0_le_iff
% 5.64/5.97 thf(fact_7385_of__nat__0__le__iff,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_0_le_iff
% 5.64/5.97 thf(fact_7386_of__nat__less__0__iff,axiom,
% 5.64/5.97 ! [M: nat] :
% 5.64/5.97 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_0_iff
% 5.64/5.97 thf(fact_7387_of__nat__less__0__iff,axiom,
% 5.64/5.97 ! [M: nat] :
% 5.64/5.97 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_0_iff
% 5.64/5.97 thf(fact_7388_of__nat__less__0__iff,axiom,
% 5.64/5.97 ! [M: nat] :
% 5.64/5.97 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_0_iff
% 5.64/5.97 thf(fact_7389_of__nat__less__0__iff,axiom,
% 5.64/5.97 ! [M: nat] :
% 5.64/5.97 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_0_iff
% 5.64/5.97 thf(fact_7390_of__nat__neq__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.64/5.97 != zero_zero_rat ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_neq_0
% 5.64/5.97 thf(fact_7391_of__nat__neq__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.64/5.97 != zero_zero_int ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_neq_0
% 5.64/5.97 thf(fact_7392_of__nat__neq__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.64/5.97 != zero_zero_real ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_neq_0
% 5.64/5.97 thf(fact_7393_of__nat__neq__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.64/5.97 != zero_zero_nat ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_neq_0
% 5.64/5.97 thf(fact_7394_of__nat__neq__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.64/5.97 != zero_zero_complex ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_neq_0
% 5.64/5.97 thf(fact_7395_div__mult2__eq_H,axiom,
% 5.64/5.97 ! [A: int,M: nat,N: nat] :
% 5.64/5.97 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.97 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % div_mult2_eq'
% 5.64/5.97 thf(fact_7396_div__mult2__eq_H,axiom,
% 5.64/5.97 ! [A: nat,M: nat,N: nat] :
% 5.64/5.97 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.64/5.97 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % div_mult2_eq'
% 5.64/5.97 thf(fact_7397_less__imp__of__nat__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_imp_of_nat_less
% 5.64/5.97 thf(fact_7398_less__imp__of__nat__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_imp_of_nat_less
% 5.64/5.97 thf(fact_7399_less__imp__of__nat__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_imp_of_nat_less
% 5.64/5.97 thf(fact_7400_less__imp__of__nat__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_imp_of_nat_less
% 5.64/5.97 thf(fact_7401_of__nat__less__imp__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.64/5.97 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_imp_less
% 5.64/5.97 thf(fact_7402_of__nat__less__imp__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.97 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_imp_less
% 5.64/5.97 thf(fact_7403_of__nat__less__imp__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.97 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_imp_less
% 5.64/5.97 thf(fact_7404_of__nat__less__imp__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.64/5.97 => ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_imp_less
% 5.64/5.97 thf(fact_7405_of__nat__mono,axiom,
% 5.64/5.97 ! [I: nat,J: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.97 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_mono
% 5.64/5.97 thf(fact_7406_of__nat__mono,axiom,
% 5.64/5.97 ! [I: nat,J: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.97 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_mono
% 5.64/5.97 thf(fact_7407_of__nat__mono,axiom,
% 5.64/5.97 ! [I: nat,J: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.97 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_mono
% 5.64/5.97 thf(fact_7408_of__nat__mono,axiom,
% 5.64/5.97 ! [I: nat,J: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ I @ J )
% 5.64/5.97 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_mono
% 5.64/5.97 thf(fact_7409_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.97 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.64/5.97 thf(fact_7410_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.97 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.64/5.97 thf(fact_7411_int__ops_I1_J,axiom,
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.64/5.97 = zero_zero_int ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(1)
% 5.64/5.97 thf(fact_7412_int__ops_I3_J,axiom,
% 5.64/5.97 ! [N: num] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.64/5.97 = ( numeral_numeral_int @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(3)
% 5.64/5.97 thf(fact_7413_int__of__nat__induct,axiom,
% 5.64/5.97 ! [P: int > $o,Z: int] :
% 5.64/5.97 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.64/5.97 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.64/5.97 => ( P @ Z ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_of_nat_induct
% 5.64/5.97 thf(fact_7414_int__cases,axiom,
% 5.64/5.97 ! [Z: int] :
% 5.64/5.97 ( ! [N3: nat] :
% 5.64/5.97 ( Z
% 5.64/5.97 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ( Z
% 5.64/5.97 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_cases
% 5.64/5.97 thf(fact_7415_nat__int__comparison_I2_J,axiom,
% 5.64/5.97 ( ord_less_nat
% 5.64/5.97 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_int_comparison(2)
% 5.64/5.97 thf(fact_7416_zle__int,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.97 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % zle_int
% 5.64/5.97 thf(fact_7417_nat__int__comparison_I3_J,axiom,
% 5.64/5.97 ( ord_less_eq_nat
% 5.64/5.97 = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_int_comparison(3)
% 5.64/5.97 thf(fact_7418_zadd__int__left,axiom,
% 5.64/5.97 ! [M: nat,N: nat,Z: int] :
% 5.64/5.97 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.64/5.97
% 5.64/5.97 % zadd_int_left
% 5.64/5.97 thf(fact_7419_int__plus,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_plus
% 5.64/5.97 thf(fact_7420_int__ops_I5_J,axiom,
% 5.64/5.97 ! [A: nat,B: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(5)
% 5.64/5.97 thf(fact_7421_int__ops_I2_J,axiom,
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.64/5.97 = one_one_int ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(2)
% 5.64/5.97 thf(fact_7422_int__ops_I7_J,axiom,
% 5.64/5.97 ! [A: nat,B: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.64/5.97 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(7)
% 5.64/5.97 thf(fact_7423_not__int__zless__negative,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % not_int_zless_negative
% 5.64/5.97 thf(fact_7424_zdiv__int,axiom,
% 5.64/5.97 ! [A: nat,B: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.64/5.97 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zdiv_int
% 5.64/5.97 thf(fact_7425_of__nat__max,axiom,
% 5.64/5.97 ! [X2: nat,Y4: nat] :
% 5.64/5.97 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X2 @ Y4 ) )
% 5.64/5.97 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X2 ) @ ( semiri4216267220026989637d_enat @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_max
% 5.64/5.97 thf(fact_7426_of__nat__max,axiom,
% 5.64/5.97 ! [X2: nat,Y4: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X2 @ Y4 ) )
% 5.64/5.97 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_max
% 5.64/5.97 thf(fact_7427_of__nat__max,axiom,
% 5.64/5.97 ! [X2: nat,Y4: nat] :
% 5.64/5.97 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X2 @ Y4 ) )
% 5.64/5.97 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_max
% 5.64/5.97 thf(fact_7428_of__nat__max,axiom,
% 5.64/5.97 ! [X2: nat,Y4: nat] :
% 5.64/5.97 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X2 @ Y4 ) )
% 5.64/5.97 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( semiri1316708129612266289at_nat @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_max
% 5.64/5.97 thf(fact_7429_nat__less__as__int,axiom,
% 5.64/5.97 ( ord_less_nat
% 5.64/5.97 = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_less_as_int
% 5.64/5.97 thf(fact_7430_nat__leq__as__int,axiom,
% 5.64/5.97 ( ord_less_eq_nat
% 5.64/5.97 = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_leq_as_int
% 5.64/5.97 thf(fact_7431_or__not__num__neg_Osimps_I4_J,axiom,
% 5.64/5.97 ! [N: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.64/5.97 = ( bit0 @ one ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(4)
% 5.64/5.97 thf(fact_7432_or__not__num__neg_Osimps_I6_J,axiom,
% 5.64/5.97 ! [N: num,M: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.64/5.97 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(6)
% 5.64/5.97 thf(fact_7433_or__not__num__neg_Osimps_I3_J,axiom,
% 5.64/5.97 ! [M: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.64/5.97 = ( bit1 @ M ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(3)
% 5.64/5.97 thf(fact_7434_or__not__num__neg_Osimps_I7_J,axiom,
% 5.64/5.97 ! [N: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.64/5.97 = one ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(7)
% 5.64/5.97 thf(fact_7435_or__not__num__neg_Osimps_I5_J,axiom,
% 5.64/5.97 ! [N: num,M: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.64/5.97 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(5)
% 5.64/5.97 thf(fact_7436_ex__less__of__nat__mult,axiom,
% 5.64/5.97 ! [X2: rat,Y4: rat] :
% 5.64/5.97 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.64/5.97 => ? [N3: nat] : ( ord_less_rat @ Y4 @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ex_less_of_nat_mult
% 5.64/5.97 thf(fact_7437_ex__less__of__nat__mult,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ex_less_of_nat_mult
% 5.64/5.97 thf(fact_7438_of__nat__diff,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.97 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_diff
% 5.64/5.97 thf(fact_7439_of__nat__diff,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.97 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_diff
% 5.64/5.97 thf(fact_7440_of__nat__diff,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.97 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_diff
% 5.64/5.97 thf(fact_7441_of__nat__diff,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.97 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_diff
% 5.64/5.97 thf(fact_7442_of__nat__diff,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 5.64/5.97 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_diff
% 5.64/5.97 thf(fact_7443_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > rat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.64/5.97 => ( ! [X4: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S4 )
% 5.64/5.97 => ( ! [Y5: vEBT_VEBT] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_VEBT_VEBT @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7444_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_complex )
% 5.64/5.97 => ( ! [X4: complex,S4: set_complex] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S4 )
% 5.64/5.97 => ( ! [Y5: complex] :
% 5.64/5.97 ( ( member_complex @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_complex @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7445_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.64/5.97 ( ( finite_finite_nat @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_nat )
% 5.64/5.97 => ( ! [X4: nat,S4: set_nat] :
% 5.64/5.97 ( ( finite_finite_nat @ S4 )
% 5.64/5.97 => ( ! [Y5: nat] :
% 5.64/5.97 ( ( member_nat @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_nat @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7446_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_int,P: set_int > $o,F: int > rat] :
% 5.64/5.97 ( ( finite_finite_int @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_int )
% 5.64/5.97 => ( ! [X4: int,S4: set_int] :
% 5.64/5.97 ( ( finite_finite_int @ S4 )
% 5.64/5.97 => ( ! [Y5: int] :
% 5.64/5.97 ( ( member_int @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_int @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7447_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_real,P: set_real > $o,F: real > rat] :
% 5.64/5.97 ( ( finite_finite_real @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_real )
% 5.64/5.97 => ( ! [X4: real,S4: set_real] :
% 5.64/5.97 ( ( finite_finite_real @ S4 )
% 5.64/5.97 => ( ! [Y5: real] :
% 5.64/5.97 ( ( member_real @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_real @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7448_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o,F: vEBT_VEBT > num] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.64/5.97 => ( ! [X4: vEBT_VEBT,S4: set_VEBT_VEBT] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S4 )
% 5.64/5.97 => ( ! [Y5: vEBT_VEBT] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_VEBT_VEBT @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7449_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_complex,P: set_complex > $o,F: complex > num] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_complex )
% 5.64/5.97 => ( ! [X4: complex,S4: set_complex] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S4 )
% 5.64/5.97 => ( ! [Y5: complex] :
% 5.64/5.97 ( ( member_complex @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_complex @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7450_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_nat,P: set_nat > $o,F: nat > num] :
% 5.64/5.97 ( ( finite_finite_nat @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_nat )
% 5.64/5.97 => ( ! [X4: nat,S4: set_nat] :
% 5.64/5.97 ( ( finite_finite_nat @ S4 )
% 5.64/5.97 => ( ! [Y5: nat] :
% 5.64/5.97 ( ( member_nat @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_nat @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7451_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_int,P: set_int > $o,F: int > num] :
% 5.64/5.97 ( ( finite_finite_int @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_int )
% 5.64/5.97 => ( ! [X4: int,S4: set_int] :
% 5.64/5.97 ( ( finite_finite_int @ S4 )
% 5.64/5.97 => ( ! [Y5: int] :
% 5.64/5.97 ( ( member_int @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_int @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7452_finite__ranking__induct,axiom,
% 5.64/5.97 ! [S3: set_real,P: set_real > $o,F: real > num] :
% 5.64/5.97 ( ( finite_finite_real @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_real )
% 5.64/5.97 => ( ! [X4: real,S4: set_real] :
% 5.64/5.97 ( ( finite_finite_real @ S4 )
% 5.64/5.97 => ( ! [Y5: real] :
% 5.64/5.97 ( ( member_real @ Y5 @ S4 )
% 5.64/5.97 => ( ord_less_eq_num @ ( F @ Y5 ) @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( P @ S4 )
% 5.64/5.97 => ( P @ ( insert_real @ X4 @ S4 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_ranking_induct
% 5.64/5.97 thf(fact_7453_finite__linorder__max__induct,axiom,
% 5.64/5.97 ! [A4: set_real,P: set_real > $o] :
% 5.64/5.97 ( ( finite_finite_real @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_real )
% 5.64/5.97 => ( ! [B5: real,A7: set_real] :
% 5.64/5.97 ( ( finite_finite_real @ A7 )
% 5.64/5.97 => ( ! [X3: real] :
% 5.64/5.97 ( ( member_real @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_real @ X3 @ B5 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_max_induct
% 5.64/5.97 thf(fact_7454_finite__linorder__max__induct,axiom,
% 5.64/5.97 ! [A4: set_rat,P: set_rat > $o] :
% 5.64/5.97 ( ( finite_finite_rat @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_rat )
% 5.64/5.97 => ( ! [B5: rat,A7: set_rat] :
% 5.64/5.97 ( ( finite_finite_rat @ A7 )
% 5.64/5.97 => ( ! [X3: rat] :
% 5.64/5.97 ( ( member_rat @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_rat @ X3 @ B5 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_max_induct
% 5.64/5.97 thf(fact_7455_finite__linorder__max__induct,axiom,
% 5.64/5.97 ! [A4: set_num,P: set_num > $o] :
% 5.64/5.97 ( ( finite_finite_num @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_num )
% 5.64/5.97 => ( ! [B5: num,A7: set_num] :
% 5.64/5.97 ( ( finite_finite_num @ A7 )
% 5.64/5.97 => ( ! [X3: num] :
% 5.64/5.97 ( ( member_num @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_num @ X3 @ B5 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_max_induct
% 5.64/5.97 thf(fact_7456_finite__linorder__max__induct,axiom,
% 5.64/5.97 ! [A4: set_nat,P: set_nat > $o] :
% 5.64/5.97 ( ( finite_finite_nat @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_nat )
% 5.64/5.97 => ( ! [B5: nat,A7: set_nat] :
% 5.64/5.97 ( ( finite_finite_nat @ A7 )
% 5.64/5.97 => ( ! [X3: nat] :
% 5.64/5.97 ( ( member_nat @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_nat @ X3 @ B5 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_max_induct
% 5.64/5.97 thf(fact_7457_finite__linorder__max__induct,axiom,
% 5.64/5.97 ! [A4: set_int,P: set_int > $o] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_int )
% 5.64/5.97 => ( ! [B5: int,A7: set_int] :
% 5.64/5.97 ( ( finite_finite_int @ A7 )
% 5.64/5.97 => ( ! [X3: int] :
% 5.64/5.97 ( ( member_int @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_int @ X3 @ B5 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_max_induct
% 5.64/5.97 thf(fact_7458_finite__linorder__min__induct,axiom,
% 5.64/5.97 ! [A4: set_real,P: set_real > $o] :
% 5.64/5.97 ( ( finite_finite_real @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_real )
% 5.64/5.97 => ( ! [B5: real,A7: set_real] :
% 5.64/5.97 ( ( finite_finite_real @ A7 )
% 5.64/5.97 => ( ! [X3: real] :
% 5.64/5.97 ( ( member_real @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_real @ B5 @ X3 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_min_induct
% 5.64/5.97 thf(fact_7459_finite__linorder__min__induct,axiom,
% 5.64/5.97 ! [A4: set_rat,P: set_rat > $o] :
% 5.64/5.97 ( ( finite_finite_rat @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_rat )
% 5.64/5.97 => ( ! [B5: rat,A7: set_rat] :
% 5.64/5.97 ( ( finite_finite_rat @ A7 )
% 5.64/5.97 => ( ! [X3: rat] :
% 5.64/5.97 ( ( member_rat @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_rat @ B5 @ X3 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_min_induct
% 5.64/5.97 thf(fact_7460_finite__linorder__min__induct,axiom,
% 5.64/5.97 ! [A4: set_num,P: set_num > $o] :
% 5.64/5.97 ( ( finite_finite_num @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_num )
% 5.64/5.97 => ( ! [B5: num,A7: set_num] :
% 5.64/5.97 ( ( finite_finite_num @ A7 )
% 5.64/5.97 => ( ! [X3: num] :
% 5.64/5.97 ( ( member_num @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_num @ B5 @ X3 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_min_induct
% 5.64/5.97 thf(fact_7461_finite__linorder__min__induct,axiom,
% 5.64/5.97 ! [A4: set_nat,P: set_nat > $o] :
% 5.64/5.97 ( ( finite_finite_nat @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_nat )
% 5.64/5.97 => ( ! [B5: nat,A7: set_nat] :
% 5.64/5.97 ( ( finite_finite_nat @ A7 )
% 5.64/5.97 => ( ! [X3: nat] :
% 5.64/5.97 ( ( member_nat @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_nat @ B5 @ X3 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_min_induct
% 5.64/5.97 thf(fact_7462_finite__linorder__min__induct,axiom,
% 5.64/5.97 ! [A4: set_int,P: set_int > $o] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( P @ bot_bot_set_int )
% 5.64/5.97 => ( ! [B5: int,A7: set_int] :
% 5.64/5.97 ( ( finite_finite_int @ A7 )
% 5.64/5.97 => ( ! [X3: int] :
% 5.64/5.97 ( ( member_int @ X3 @ A7 )
% 5.64/5.97 => ( ord_less_int @ B5 @ X3 ) )
% 5.64/5.97 => ( ( P @ A7 )
% 5.64/5.97 => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 5.64/5.97 => ( P @ A4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_linorder_min_induct
% 5.64/5.97 thf(fact_7463_exp__of__nat__mult,axiom,
% 5.64/5.97 ! [N: nat,X2: real] :
% 5.64/5.97 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) )
% 5.64/5.97 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_of_nat_mult
% 5.64/5.97 thf(fact_7464_exp__of__nat__mult,axiom,
% 5.64/5.97 ! [N: nat,X2: complex] :
% 5.64/5.97 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X2 ) )
% 5.64/5.97 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_of_nat_mult
% 5.64/5.97 thf(fact_7465_exp__of__nat2__mult,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( exp_real @ ( times_times_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.97 = ( power_power_real @ ( exp_real @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_of_nat2_mult
% 5.64/5.97 thf(fact_7466_exp__of__nat2__mult,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( exp_complex @ ( times_times_complex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.64/5.97 = ( power_power_complex @ ( exp_complex @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_of_nat2_mult
% 5.64/5.97 thf(fact_7467_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( groups2240296850493347238T_real @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7468_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_real,X2: real,G: real > real] :
% 5.64/5.97 ( ( finite_finite_real @ A4 )
% 5.64/5.97 => ( ( ( member_real @ X2 @ A4 )
% 5.64/5.97 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.97 = ( groups8097168146408367636l_real @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.97 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8097168146408367636l_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7469_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_int,X2: int,G: int > real] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.97 = ( groups8778361861064173332t_real @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7470_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,G: complex > real] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( groups5808333547571424918x_real @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7471_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( groups136491112297645522BT_rat @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7472_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_real,X2: real,G: real > rat] :
% 5.64/5.97 ( ( finite_finite_real @ A4 )
% 5.64/5.97 => ( ( ( member_real @ X2 @ A4 )
% 5.64/5.97 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.97 = ( groups1300246762558778688al_rat @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.97 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups1300246762558778688al_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7473_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_nat,X2: nat,G: nat > rat] :
% 5.64/5.97 ( ( finite_finite_nat @ A4 )
% 5.64/5.97 => ( ( ( member_nat @ X2 @ A4 )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.97 = ( groups2906978787729119204at_rat @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups2906978787729119204at_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7474_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_int,X2: int,G: int > rat] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.97 = ( groups3906332499630173760nt_rat @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7475_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,G: complex > rat] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( groups5058264527183730370ex_rat @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7476_sum_Oinsert__if,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( groups771621172384141258BT_nat @ G @ A4 ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_if
% 5.64/5.97 thf(fact_7477_reals__Archimedean3,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ! [Y5: real] :
% 5.64/5.97 ? [N3: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % reals_Archimedean3
% 5.64/5.97 thf(fact_7478_int__cases4,axiom,
% 5.64/5.97 ! [M: int] :
% 5.64/5.97 ( ! [N3: nat] :
% 5.64/5.97 ( M
% 5.64/5.97 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.97 => ( M
% 5.64/5.97 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_cases4
% 5.64/5.97 thf(fact_7479_real__of__nat__div4,axiom,
% 5.64/5.97 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_of_nat_div4
% 5.64/5.97 thf(fact_7480_int__ops_I4_J,axiom,
% 5.64/5.97 ! [A: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(4)
% 5.64/5.97 thf(fact_7481_int__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_Suc
% 5.64/5.97 thf(fact_7482_zless__iff__Suc__zadd,axiom,
% 5.64/5.97 ( ord_less_int
% 5.64/5.97 = ( ^ [W3: int,Z4: int] :
% 5.64/5.97 ? [N2: nat] :
% 5.64/5.97 ( Z4
% 5.64/5.97 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zless_iff_Suc_zadd
% 5.64/5.97 thf(fact_7483_real__of__nat__div,axiom,
% 5.64/5.97 ! [D: nat,N: nat] :
% 5.64/5.97 ( ( dvd_dvd_nat @ D @ N )
% 5.64/5.97 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.64/5.97 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_of_nat_div
% 5.64/5.97 thf(fact_7484_set__update__subset__insert,axiom,
% 5.64/5.97 ! [Xs2: list_real,I: nat,X2: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs2 @ I @ X2 ) ) @ ( insert_real @ X2 @ ( set_real2 @ Xs2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_update_subset_insert
% 5.64/5.97 thf(fact_7485_set__update__subset__insert,axiom,
% 5.64/5.97 ! [Xs2: list_int,I: nat,X2: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs2 @ I @ X2 ) ) @ ( insert_int @ X2 @ ( set_int2 @ Xs2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_update_subset_insert
% 5.64/5.97 thf(fact_7486_set__update__subset__insert,axiom,
% 5.64/5.97 ! [Xs2: list_VEBT_VEBT,I: nat,X2: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I @ X2 ) ) @ ( insert_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_update_subset_insert
% 5.64/5.97 thf(fact_7487_set__update__subset__insert,axiom,
% 5.64/5.97 ! [Xs2: list_nat,I: nat,X2: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs2 @ I @ X2 ) ) @ ( insert_nat @ X2 @ ( set_nat2 @ Xs2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_update_subset_insert
% 5.64/5.97 thf(fact_7488_or__not__num__neg_Osimps_I2_J,axiom,
% 5.64/5.97 ! [M: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.64/5.97 = ( bit1 @ M ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(2)
% 5.64/5.97 thf(fact_7489_mod__mult2__eq_H,axiom,
% 5.64/5.97 ! [A: code_integer,M: nat,N: nat] :
% 5.64/5.97 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.64/5.97 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mod_mult2_eq'
% 5.64/5.97 thf(fact_7490_mod__mult2__eq_H,axiom,
% 5.64/5.97 ! [A: int,M: nat,N: nat] :
% 5.64/5.97 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.97 = ( 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 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mod_mult2_eq'
% 5.64/5.97 thf(fact_7491_mod__mult2__eq_H,axiom,
% 5.64/5.97 ! [A: nat,M: nat,N: nat] :
% 5.64/5.97 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.64/5.97 = ( 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 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mod_mult2_eq'
% 5.64/5.97 thf(fact_7492_or__not__num__neg_Osimps_I8_J,axiom,
% 5.64/5.97 ! [N: num,M: num] :
% 5.64/5.97 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.64/5.97 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.simps(8)
% 5.64/5.97 thf(fact_7493_field__char__0__class_Oof__nat__div,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % field_char_0_class.of_nat_div
% 5.64/5.97 thf(fact_7494_field__char__0__class_Oof__nat__div,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % field_char_0_class.of_nat_div
% 5.64/5.97 thf(fact_7495_field__char__0__class_Oof__nat__div,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.64/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % field_char_0_class.of_nat_div
% 5.64/5.97 thf(fact_7496_zero__less__imp__eq__int,axiom,
% 5.64/5.97 ! [K: int] :
% 5.64/5.97 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.97 => ? [N3: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.97 & ( K
% 5.64/5.97 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_less_imp_eq_int
% 5.64/5.97 thf(fact_7497_pos__int__cases,axiom,
% 5.64/5.97 ! [K: int] :
% 5.64/5.97 ( ( ord_less_int @ zero_zero_int @ K )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ( ( K
% 5.64/5.97 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.64/5.97 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % pos_int_cases
% 5.64/5.97 thf(fact_7498_int__cases3,axiom,
% 5.64/5.97 ! [K: int] :
% 5.64/5.97 ( ( K != zero_zero_int )
% 5.64/5.97 => ( ! [N3: nat] :
% 5.64/5.97 ( ( K
% 5.64/5.97 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.64/5.97 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ( ( K
% 5.64/5.97 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.64/5.97 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_cases3
% 5.64/5.97 thf(fact_7499_nat__less__real__le,axiom,
% 5.64/5.97 ( ord_less_nat
% 5.64/5.97 = ( ^ [N2: nat,M2: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_less_real_le
% 5.64/5.97 thf(fact_7500_nat__le__real__less,axiom,
% 5.64/5.97 ( ord_less_eq_nat
% 5.64/5.97 = ( ^ [N2: nat,M2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_le_real_less
% 5.64/5.97 thf(fact_7501_zmult__zless__mono2__lemma,axiom,
% 5.64/5.97 ! [I: int,J: int,K: nat] :
% 5.64/5.97 ( ( ord_less_int @ I @ J )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.97 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zmult_zless_mono2_lemma
% 5.64/5.97 thf(fact_7502_not__zle__0__negative,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % not_zle_0_negative
% 5.64/5.97 thf(fact_7503_negD,axiom,
% 5.64/5.97 ! [X2: int] :
% 5.64/5.97 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.64/5.97 => ? [N3: nat] :
% 5.64/5.97 ( X2
% 5.64/5.97 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % negD
% 5.64/5.97 thf(fact_7504_negative__zless__0,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.64/5.97
% 5.64/5.97 % negative_zless_0
% 5.64/5.97 thf(fact_7505_finite__induct__select,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,P: set_VEBT_VEBT > $o] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( P @ bot_bo8194388402131092736T_VEBT )
% 5.64/5.97 => ( ! [T3: set_VEBT_VEBT] :
% 5.64/5.97 ( ( ord_le3480810397992357184T_VEBT @ T3 @ S3 )
% 5.64/5.97 => ( ( P @ T3 )
% 5.64/5.97 => ? [X3: vEBT_VEBT] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ X3 @ ( minus_5127226145743854075T_VEBT @ S3 @ T3 ) )
% 5.64/5.97 & ( P @ ( insert_VEBT_VEBT @ X3 @ T3 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_induct_select
% 5.64/5.97 thf(fact_7506_finite__induct__select,axiom,
% 5.64/5.97 ! [S3: set_complex,P: set_complex > $o] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_complex )
% 5.64/5.97 => ( ! [T3: set_complex] :
% 5.64/5.97 ( ( ord_less_set_complex @ T3 @ S3 )
% 5.64/5.97 => ( ( P @ T3 )
% 5.64/5.97 => ? [X3: complex] :
% 5.64/5.97 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ S3 @ T3 ) )
% 5.64/5.97 & ( P @ ( insert_complex @ X3 @ T3 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_induct_select
% 5.64/5.97 thf(fact_7507_finite__induct__select,axiom,
% 5.64/5.97 ! [S3: set_int,P: set_int > $o] :
% 5.64/5.97 ( ( finite_finite_int @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_int )
% 5.64/5.97 => ( ! [T3: set_int] :
% 5.64/5.97 ( ( ord_less_set_int @ T3 @ S3 )
% 5.64/5.97 => ( ( P @ T3 )
% 5.64/5.97 => ? [X3: int] :
% 5.64/5.97 ( ( member_int @ X3 @ ( minus_minus_set_int @ S3 @ T3 ) )
% 5.64/5.97 & ( P @ ( insert_int @ X3 @ T3 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_induct_select
% 5.64/5.97 thf(fact_7508_finite__induct__select,axiom,
% 5.64/5.97 ! [S3: set_real,P: set_real > $o] :
% 5.64/5.97 ( ( finite_finite_real @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_real )
% 5.64/5.97 => ( ! [T3: set_real] :
% 5.64/5.97 ( ( ord_less_set_real @ T3 @ S3 )
% 5.64/5.97 => ( ( P @ T3 )
% 5.64/5.97 => ? [X3: real] :
% 5.64/5.97 ( ( member_real @ X3 @ ( minus_minus_set_real @ S3 @ T3 ) )
% 5.64/5.97 & ( P @ ( insert_real @ X3 @ T3 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_induct_select
% 5.64/5.97 thf(fact_7509_finite__induct__select,axiom,
% 5.64/5.97 ! [S3: set_nat,P: set_nat > $o] :
% 5.64/5.97 ( ( finite_finite_nat @ S3 )
% 5.64/5.97 => ( ( P @ bot_bot_set_nat )
% 5.64/5.97 => ( ! [T3: set_nat] :
% 5.64/5.97 ( ( ord_less_set_nat @ T3 @ S3 )
% 5.64/5.97 => ( ( P @ T3 )
% 5.64/5.97 => ? [X3: nat] :
% 5.64/5.97 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ S3 @ T3 ) )
% 5.64/5.97 & ( P @ ( insert_nat @ X3 @ T3 ) ) ) ) )
% 5.64/5.97 => ( P @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % finite_induct_select
% 5.64/5.97 thf(fact_7510_psubset__insert__iff,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,B4: set_VEBT_VEBT] :
% 5.64/5.97 ( ( ord_le3480810397992357184T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ B4 ) )
% 5.64/5.97 = ( ( ( member_VEBT_VEBT @ X2 @ B4 )
% 5.64/5.97 => ( ord_le3480810397992357184T_VEBT @ A4 @ B4 ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ X2 @ B4 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ord_le3480810397992357184T_VEBT @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) @ B4 ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ord_le4337996190870823476T_VEBT @ A4 @ B4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % psubset_insert_iff
% 5.64/5.97 thf(fact_7511_psubset__insert__iff,axiom,
% 5.64/5.97 ! [A4: set_Pr1261947904930325089at_nat,X2: product_prod_nat_nat,B4: set_Pr1261947904930325089at_nat] :
% 5.64/5.97 ( ( ord_le7866589430770878221at_nat @ A4 @ ( insert8211810215607154385at_nat @ X2 @ B4 ) )
% 5.64/5.97 = ( ( ( member8440522571783428010at_nat @ X2 @ B4 )
% 5.64/5.97 => ( ord_le7866589430770878221at_nat @ A4 @ B4 ) )
% 5.64/5.97 & ( ~ ( member8440522571783428010at_nat @ X2 @ B4 )
% 5.64/5.97 => ( ( ( member8440522571783428010at_nat @ X2 @ A4 )
% 5.64/5.97 => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) @ B4 ) )
% 5.64/5.97 & ( ~ ( member8440522571783428010at_nat @ X2 @ A4 )
% 5.64/5.97 => ( ord_le3146513528884898305at_nat @ A4 @ B4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % psubset_insert_iff
% 5.64/5.97 thf(fact_7512_psubset__insert__iff,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,B4: set_complex] :
% 5.64/5.97 ( ( ord_less_set_complex @ A4 @ ( insert_complex @ X2 @ B4 ) )
% 5.64/5.97 = ( ( ( member_complex @ X2 @ B4 )
% 5.64/5.97 => ( ord_less_set_complex @ A4 @ B4 ) )
% 5.64/5.97 & ( ~ ( member_complex @ X2 @ B4 )
% 5.64/5.97 => ( ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) @ B4 ) )
% 5.64/5.97 & ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ord_le211207098394363844omplex @ A4 @ B4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % psubset_insert_iff
% 5.64/5.97 thf(fact_7513_psubset__insert__iff,axiom,
% 5.64/5.97 ! [A4: set_int,X2: int,B4: set_int] :
% 5.64/5.97 ( ( ord_less_set_int @ A4 @ ( insert_int @ X2 @ B4 ) )
% 5.64/5.97 = ( ( ( member_int @ X2 @ B4 )
% 5.64/5.97 => ( ord_less_set_int @ A4 @ B4 ) )
% 5.64/5.97 & ( ~ ( member_int @ X2 @ B4 )
% 5.64/5.97 => ( ( ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_set_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B4 ) )
% 5.64/5.97 & ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_eq_set_int @ A4 @ B4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % psubset_insert_iff
% 5.64/5.97 thf(fact_7514_psubset__insert__iff,axiom,
% 5.64/5.97 ! [A4: set_real,X2: real,B4: set_real] :
% 5.64/5.97 ( ( ord_less_set_real @ A4 @ ( insert_real @ X2 @ B4 ) )
% 5.64/5.97 = ( ( ( member_real @ X2 @ B4 )
% 5.64/5.97 => ( ord_less_set_real @ A4 @ B4 ) )
% 5.64/5.97 & ( ~ ( member_real @ X2 @ B4 )
% 5.64/5.97 => ( ( ( member_real @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_set_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B4 ) )
% 5.64/5.97 & ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_eq_set_real @ A4 @ B4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % psubset_insert_iff
% 5.64/5.97 thf(fact_7515_psubset__insert__iff,axiom,
% 5.64/5.97 ! [A4: set_nat,X2: nat,B4: set_nat] :
% 5.64/5.97 ( ( ord_less_set_nat @ A4 @ ( insert_nat @ X2 @ B4 ) )
% 5.64/5.97 = ( ( ( member_nat @ X2 @ B4 )
% 5.64/5.97 => ( ord_less_set_nat @ A4 @ B4 ) )
% 5.64/5.97 & ( ~ ( member_nat @ X2 @ B4 )
% 5.64/5.97 => ( ( ( member_nat @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B4 ) )
% 5.64/5.97 & ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.97 => ( ord_less_eq_set_nat @ A4 @ B4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % psubset_insert_iff
% 5.64/5.97 thf(fact_7516_set__replicate__Suc,axiom,
% 5.64/5.97 ! [N: nat,X2: vEBT_VEBT] :
% 5.64/5.97 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X2 ) )
% 5.64/5.97 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_Suc
% 5.64/5.97 thf(fact_7517_set__replicate__Suc,axiom,
% 5.64/5.97 ! [N: nat,X2: nat] :
% 5.64/5.97 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X2 ) )
% 5.64/5.97 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_Suc
% 5.64/5.97 thf(fact_7518_set__replicate__Suc,axiom,
% 5.64/5.97 ! [N: nat,X2: int] :
% 5.64/5.97 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X2 ) )
% 5.64/5.97 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_Suc
% 5.64/5.97 thf(fact_7519_set__replicate__Suc,axiom,
% 5.64/5.97 ! [N: nat,X2: real] :
% 5.64/5.97 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X2 ) )
% 5.64/5.97 = ( insert_real @ X2 @ bot_bot_set_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_Suc
% 5.64/5.97 thf(fact_7520_set__replicate__conv__if,axiom,
% 5.64/5.97 ! [N: nat,X2: vEBT_VEBT] :
% 5.64/5.97 ( ( ( N = zero_zero_nat )
% 5.64/5.97 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.64/5.97 = bot_bo8194388402131092736T_VEBT ) )
% 5.64/5.97 & ( ( N != zero_zero_nat )
% 5.64/5.97 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X2 ) )
% 5.64/5.97 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_conv_if
% 5.64/5.97 thf(fact_7521_set__replicate__conv__if,axiom,
% 5.64/5.97 ! [N: nat,X2: nat] :
% 5.64/5.97 ( ( ( N = zero_zero_nat )
% 5.64/5.97 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.64/5.97 = bot_bot_set_nat ) )
% 5.64/5.97 & ( ( N != zero_zero_nat )
% 5.64/5.97 => ( ( set_nat2 @ ( replicate_nat @ N @ X2 ) )
% 5.64/5.97 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_conv_if
% 5.64/5.97 thf(fact_7522_set__replicate__conv__if,axiom,
% 5.64/5.97 ! [N: nat,X2: int] :
% 5.64/5.97 ( ( ( N = zero_zero_nat )
% 5.64/5.97 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.64/5.97 = bot_bot_set_int ) )
% 5.64/5.97 & ( ( N != zero_zero_nat )
% 5.64/5.97 => ( ( set_int2 @ ( replicate_int @ N @ X2 ) )
% 5.64/5.97 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_conv_if
% 5.64/5.97 thf(fact_7523_set__replicate__conv__if,axiom,
% 5.64/5.97 ! [N: nat,X2: real] :
% 5.64/5.97 ( ( ( N = zero_zero_nat )
% 5.64/5.97 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.64/5.97 = bot_bot_set_real ) )
% 5.64/5.97 & ( ( N != zero_zero_nat )
% 5.64/5.97 => ( ( set_real2 @ ( replicate_real @ N @ X2 ) )
% 5.64/5.97 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_replicate_conv_if
% 5.64/5.97 thf(fact_7524_int__ops_I6_J,axiom,
% 5.64/5.97 ! [A: nat,B: nat] :
% 5.64/5.97 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.64/5.97 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.97 = zero_zero_int ) )
% 5.64/5.97 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.64/5.97 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.64/5.97 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_ops(6)
% 5.64/5.97 thf(fact_7525_real__of__nat__div__aux,axiom,
% 5.64/5.97 ! [X2: nat,D: nat] :
% 5.64/5.97 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.64/5.97 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X2 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X2 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_of_nat_div_aux
% 5.64/5.97 thf(fact_7526_simp__from__to,axiom,
% 5.64/5.97 ( set_or1266510415728281911st_int
% 5.64/5.97 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % simp_from_to
% 5.64/5.97 thf(fact_7527_nat__approx__posE,axiom,
% 5.64/5.97 ! [E: rat] :
% 5.64/5.97 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_approx_posE
% 5.64/5.97 thf(fact_7528_nat__approx__posE,axiom,
% 5.64/5.97 ! [E: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ E )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_approx_posE
% 5.64/5.97 thf(fact_7529_of__nat__less__two__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_two_power
% 5.64/5.97 thf(fact_7530_of__nat__less__two__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_two_power
% 5.64/5.97 thf(fact_7531_of__nat__less__two__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_less_two_power
% 5.64/5.97 thf(fact_7532_inverse__of__nat__le,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( N != zero_zero_nat )
% 5.64/5.97 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % inverse_of_nat_le
% 5.64/5.97 thf(fact_7533_inverse__of__nat__le,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( ( N != zero_zero_nat )
% 5.64/5.97 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % inverse_of_nat_le
% 5.64/5.97 thf(fact_7534_exp__divide__power__eq,axiom,
% 5.64/5.97 ! [N: nat,X2: real] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.64/5.97 = ( exp_real @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_divide_power_eq
% 5.64/5.97 thf(fact_7535_exp__divide__power__eq,axiom,
% 5.64/5.97 ! [N: nat,X2: complex] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X2 @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.64/5.97 = ( exp_complex @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_divide_power_eq
% 5.64/5.97 thf(fact_7536_real__archimedian__rdiv__eq__0,axiom,
% 5.64/5.97 ! [X2: real,C: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.64/5.97 => ( ! [M4: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.64/5.97 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X2 ) @ C ) )
% 5.64/5.97 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_archimedian_rdiv_eq_0
% 5.64/5.97 thf(fact_7537_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups2240296850493347238T_real @ G @ A4 )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7538_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,G: complex > real] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5808333547571424918x_real @ G @ A4 )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7539_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups136491112297645522BT_rat @ G @ A4 )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7540_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,G: complex > rat] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5058264527183730370ex_rat @ G @ A4 )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7541_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > nat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups771621172384141258BT_nat @ G @ A4 )
% 5.64/5.97 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7542_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,G: complex > nat] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5693394587270226106ex_nat @ G @ A4 )
% 5.64/5.97 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7543_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > int] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.97 => ( ( groups769130701875090982BT_int @ G @ A4 )
% 5.64/5.97 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7544_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_complex,X2: complex,G: complex > int] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( member_complex @ X2 @ A4 )
% 5.64/5.97 => ( ( groups5690904116761175830ex_int @ G @ A4 )
% 5.64/5.97 = ( plus_plus_int @ ( G @ X2 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7545_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_int,X2: int,G: int > real] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ( groups8778361861064173332t_real @ G @ A4 )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7546_sum_Oremove,axiom,
% 5.64/5.97 ! [A4: set_int,X2: int,G: int > rat] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( member_int @ X2 @ A4 )
% 5.64/5.97 => ( ( groups3906332499630173760nt_rat @ G @ A4 )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.remove
% 5.64/5.97 thf(fact_7547_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > real,X2: vEBT_VEBT] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( groups2240296850493347238T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups2240296850493347238T_real @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7548_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_complex,G: complex > real,X2: complex] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7549_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > rat,X2: vEBT_VEBT] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( groups136491112297645522BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups136491112297645522BT_rat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7550_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_complex,G: complex > rat,X2: complex] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7551_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > nat,X2: vEBT_VEBT] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( groups771621172384141258BT_nat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups771621172384141258BT_nat @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7552_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_complex,G: complex > nat,X2: complex] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_nat @ ( G @ X2 ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7553_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_VEBT_VEBT,G: vEBT_VEBT > int,X2: vEBT_VEBT] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ( groups769130701875090982BT_int @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_int @ ( G @ X2 ) @ ( groups769130701875090982BT_int @ G @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7554_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_complex,G: complex > int,X2: complex] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_int @ ( G @ X2 ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7555_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_int,G: int > real,X2: int] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ X2 ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7556_sum_Oinsert__remove,axiom,
% 5.64/5.97 ! [A4: set_int,G: int > rat,X2: int] :
% 5.64/5.97 ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ X2 ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A4 @ ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.insert_remove
% 5.64/5.97 thf(fact_7557_neg__int__cases,axiom,
% 5.64/5.97 ! [K: int] :
% 5.64/5.97 ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/5.97 => ~ ! [N3: nat] :
% 5.64/5.97 ( ( K
% 5.64/5.97 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.64/5.97 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % neg_int_cases
% 5.64/5.97 thf(fact_7558_or__not__num__neg_Oelims,axiom,
% 5.64/5.97 ! [X2: num,Xa2: num,Y4: num] :
% 5.64/5.97 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.64/5.97 = Y4 )
% 5.64/5.97 => ( ( ( X2 = one )
% 5.64/5.97 => ( ( Xa2 = one )
% 5.64/5.97 => ( Y4 != one ) ) )
% 5.64/5.97 => ( ( ( X2 = one )
% 5.64/5.97 => ! [M4: num] :
% 5.64/5.97 ( ( Xa2
% 5.64/5.97 = ( bit0 @ M4 ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bit1 @ M4 ) ) ) )
% 5.64/5.97 => ( ( ( X2 = one )
% 5.64/5.97 => ! [M4: num] :
% 5.64/5.97 ( ( Xa2
% 5.64/5.97 = ( bit1 @ M4 ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bit1 @ M4 ) ) ) )
% 5.64/5.97 => ( ( ? [N3: num] :
% 5.64/5.97 ( X2
% 5.64/5.97 = ( bit0 @ N3 ) )
% 5.64/5.97 => ( ( Xa2 = one )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bit0 @ one ) ) ) )
% 5.64/5.97 => ( ! [N3: num] :
% 5.64/5.97 ( ( X2
% 5.64/5.97 = ( bit0 @ N3 ) )
% 5.64/5.97 => ! [M4: num] :
% 5.64/5.97 ( ( Xa2
% 5.64/5.97 = ( bit0 @ M4 ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.64/5.97 => ( ! [N3: num] :
% 5.64/5.97 ( ( X2
% 5.64/5.97 = ( bit0 @ N3 ) )
% 5.64/5.97 => ! [M4: num] :
% 5.64/5.97 ( ( Xa2
% 5.64/5.97 = ( bit1 @ M4 ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.64/5.97 => ( ( ? [N3: num] :
% 5.64/5.97 ( X2
% 5.64/5.97 = ( bit1 @ N3 ) )
% 5.64/5.97 => ( ( Xa2 = one )
% 5.64/5.97 => ( Y4 != one ) ) )
% 5.64/5.97 => ( ! [N3: num] :
% 5.64/5.97 ( ( X2
% 5.64/5.97 = ( bit1 @ N3 ) )
% 5.64/5.97 => ! [M4: num] :
% 5.64/5.97 ( ( Xa2
% 5.64/5.97 = ( bit0 @ M4 ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.64/5.97 => ~ ! [N3: num] :
% 5.64/5.97 ( ( X2
% 5.64/5.97 = ( bit1 @ N3 ) )
% 5.64/5.97 => ! [M4: num] :
% 5.64/5.97 ( ( Xa2
% 5.64/5.97 = ( bit1 @ M4 ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_not_num_neg.elims
% 5.64/5.97 thf(fact_7559_zdiff__int__split,axiom,
% 5.64/5.97 ! [P: int > $o,X2: nat,Y4: nat] :
% 5.64/5.97 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y4 ) ) )
% 5.64/5.97 = ( ( ( ord_less_eq_nat @ Y4 @ X2 )
% 5.64/5.97 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) )
% 5.64/5.97 & ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/5.97 => ( P @ zero_zero_int ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zdiff_int_split
% 5.64/5.97 thf(fact_7560_real__of__nat__div2,axiom,
% 5.64/5.97 ! [N: nat,X2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_of_nat_div2
% 5.64/5.97 thf(fact_7561_real__of__nat__div3,axiom,
% 5.64/5.97 ! [N: nat,X2: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X2 ) ) ) @ one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % real_of_nat_div3
% 5.64/5.97 thf(fact_7562_ln__realpow,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ln_ln_real @ ( power_power_real @ X2 @ N ) )
% 5.64/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ln_realpow
% 5.64/5.97 thf(fact_7563_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > real,C: vEBT_VEBT > real] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups2240296850493347238T_real
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_real @ ( B @ A ) @ ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups2240296850493347238T_real
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups2240296850493347238T_real @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7564_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5808333547571424918x_real
% 5.64/5.97 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5808333547571424918x_real
% 5.64/5.97 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7565_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > rat,C: vEBT_VEBT > rat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups136491112297645522BT_rat
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_rat @ ( B @ A ) @ ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups136491112297645522BT_rat
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups136491112297645522BT_rat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7566_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5058264527183730370ex_rat
% 5.64/5.97 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5058264527183730370ex_rat
% 5.64/5.97 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7567_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > nat,C: vEBT_VEBT > nat] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups771621172384141258BT_nat
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_nat @ ( B @ A ) @ ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups771621172384141258BT_nat
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups771621172384141258BT_nat @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7568_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5693394587270226106ex_nat
% 5.64/5.97 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5693394587270226106ex_nat
% 5.64/5.97 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7569_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_VEBT_VEBT,A: vEBT_VEBT,B: vEBT_VEBT > int,C: vEBT_VEBT > int] :
% 5.64/5.97 ( ( finite5795047828879050333T_VEBT @ S3 )
% 5.64/5.97 => ( ( ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups769130701875090982BT_int
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_int @ ( B @ A ) @ ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_VEBT_VEBT @ A @ S3 )
% 5.64/5.97 => ( ( groups769130701875090982BT_int
% 5.64/5.97 @ ^ [K2: vEBT_VEBT] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups769130701875090982BT_int @ C @ ( minus_5127226145743854075T_VEBT @ S3 @ ( insert_VEBT_VEBT @ A @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7570_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_complex,A: complex,B: complex > int,C: complex > int] :
% 5.64/5.97 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.97 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5690904116761175830ex_int
% 5.64/5.97 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.97 => ( ( groups5690904116761175830ex_int
% 5.64/5.97 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7571_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_int,A: int,B: int > real,C: int > real] :
% 5.64/5.97 ( ( finite_finite_int @ S3 )
% 5.64/5.97 => ( ( ( member_int @ A @ S3 )
% 5.64/5.97 => ( ( groups8778361861064173332t_real
% 5.64/5.97 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_int @ A @ S3 )
% 5.64/5.97 => ( ( groups8778361861064173332t_real
% 5.64/5.97 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7572_sum_Odelta__remove,axiom,
% 5.64/5.97 ! [S3: set_int,A: int,B: int > rat,C: int > rat] :
% 5.64/5.97 ( ( finite_finite_int @ S3 )
% 5.64/5.97 => ( ( ( member_int @ A @ S3 )
% 5.64/5.97 => ( ( groups3906332499630173760nt_rat
% 5.64/5.97 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( member_int @ A @ S3 )
% 5.64/5.97 => ( ( groups3906332499630173760nt_rat
% 5.64/5.97 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.64/5.97 @ S3 )
% 5.64/5.97 = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.delta_remove
% 5.64/5.97 thf(fact_7573_member__le__sum,axiom,
% 5.64/5.97 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > rat] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ I @ A4 )
% 5.64/5.97 => ( ! [X4: vEBT_VEBT] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.64/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups136491112297645522BT_rat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7574_member__le__sum,axiom,
% 5.64/5.97 ! [I: complex,A4: set_complex,F: complex > rat] :
% 5.64/5.97 ( ( member_complex @ I @ A4 )
% 5.64/5.97 => ( ! [X4: complex] :
% 5.64/5.97 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.64/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7575_member__le__sum,axiom,
% 5.64/5.97 ! [I: int,A4: set_int,F: int > rat] :
% 5.64/5.97 ( ( member_int @ I @ A4 )
% 5.64/5.97 => ( ! [X4: int] :
% 5.64/5.97 ( ( member_int @ X4 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.64/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7576_member__le__sum,axiom,
% 5.64/5.97 ! [I: real,A4: set_real,F: real > rat] :
% 5.64/5.97 ( ( member_real @ I @ A4 )
% 5.64/5.97 => ( ! [X4: real] :
% 5.64/5.97 ( ( member_real @ X4 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.64/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite_finite_real @ A4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7577_member__le__sum,axiom,
% 5.64/5.97 ! [I: nat,A4: set_nat,F: nat > rat] :
% 5.64/5.97 ( ( member_nat @ I @ A4 )
% 5.64/5.97 => ( ! [X4: nat] :
% 5.64/5.97 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 5.64/5.97 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite_finite_nat @ A4 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7578_member__le__sum,axiom,
% 5.64/5.97 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > nat] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ I @ A4 )
% 5.64/5.97 => ( ! [X4: vEBT_VEBT] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.64/5.97 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups771621172384141258BT_nat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7579_member__le__sum,axiom,
% 5.64/5.97 ! [I: complex,A4: set_complex,F: complex > nat] :
% 5.64/5.97 ( ( member_complex @ I @ A4 )
% 5.64/5.97 => ( ! [X4: complex] :
% 5.64/5.97 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.64/5.97 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.97 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7580_member__le__sum,axiom,
% 5.64/5.97 ! [I: int,A4: set_int,F: int > nat] :
% 5.64/5.97 ( ( member_int @ I @ A4 )
% 5.64/5.97 => ( ! [X4: int] :
% 5.64/5.97 ( ( member_int @ X4 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.64/5.97 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite_finite_int @ A4 )
% 5.64/5.97 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups4541462559716669496nt_nat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7581_member__le__sum,axiom,
% 5.64/5.97 ! [I: real,A4: set_real,F: real > nat] :
% 5.64/5.97 ( ( member_real @ I @ A4 )
% 5.64/5.97 => ( ! [X4: real] :
% 5.64/5.97 ( ( member_real @ X4 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.64/5.97 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite_finite_real @ A4 )
% 5.64/5.97 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups1935376822645274424al_nat @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7582_member__le__sum,axiom,
% 5.64/5.97 ! [I: vEBT_VEBT,A4: set_VEBT_VEBT,F: vEBT_VEBT > int] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ I @ A4 )
% 5.64/5.97 => ( ! [X4: vEBT_VEBT] :
% 5.64/5.97 ( ( member_VEBT_VEBT @ X4 @ ( minus_5127226145743854075T_VEBT @ A4 @ ( insert_VEBT_VEBT @ I @ bot_bo8194388402131092736T_VEBT ) ) )
% 5.64/5.97 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.97 => ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.97 => ( ord_less_eq_int @ ( F @ I ) @ ( groups769130701875090982BT_int @ F @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % member_le_sum
% 5.64/5.97 thf(fact_7583_linear__plus__1__le__power,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X2 @ one_one_real ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % linear_plus_1_le_power
% 5.64/5.97 thf(fact_7584_Bernoulli__inequality,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.97 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % Bernoulli_inequality
% 5.64/5.97 thf(fact_7585_unbounded__k__infinite,axiom,
% 5.64/5.97 ! [K: nat,S3: set_nat] :
% 5.64/5.97 ( ! [M4: nat] :
% 5.64/5.97 ( ( ord_less_nat @ K @ M4 )
% 5.64/5.97 => ? [N7: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M4 @ N7 )
% 5.64/5.97 & ( member_nat @ N7 @ S3 ) ) )
% 5.64/5.97 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.64/5.97
% 5.64/5.97 % unbounded_k_infinite
% 5.64/5.97 thf(fact_7586_infinite__nat__iff__unbounded,axiom,
% 5.64/5.97 ! [S3: set_nat] :
% 5.64/5.97 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.64/5.97 = ( ! [M2: nat] :
% 5.64/5.97 ? [N2: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M2 @ N2 )
% 5.64/5.97 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % infinite_nat_iff_unbounded
% 5.64/5.97 thf(fact_7587_and__nat__unfold,axiom,
% 5.64/5.97 ( bit_se727722235901077358nd_nat
% 5.64/5.97 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.97 ( if_nat
% 5.64/5.97 @ ( ( M2 = zero_zero_nat )
% 5.64/5.97 | ( N2 = zero_zero_nat ) )
% 5.64/5.97 @ zero_zero_nat
% 5.64/5.97 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % and_nat_unfold
% 5.64/5.97 thf(fact_7588_infinite__nat__iff__unbounded__le,axiom,
% 5.64/5.97 ! [S3: set_nat] :
% 5.64/5.97 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.64/5.97 = ( ! [M2: nat] :
% 5.64/5.97 ? [N2: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.97 & ( member_nat @ N2 @ S3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % infinite_nat_iff_unbounded_le
% 5.64/5.97 thf(fact_7589_or__Suc__0__eq,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_Suc_0_eq
% 5.64/5.97 thf(fact_7590_Suc__0__or__eq,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.97 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % Suc_0_or_eq
% 5.64/5.97 thf(fact_7591_or__nat__rec,axiom,
% 5.64/5.97 ( bit_se1412395901928357646or_nat
% 5.64/5.97 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.97 ( plus_plus_nat
% 5.64/5.97 @ ( zero_n2687167440665602831ol_nat
% 5.64/5.97 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.64/5.97 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.64/5.97 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_nat_rec
% 5.64/5.97 thf(fact_7592_and__nat__rec,axiom,
% 5.64/5.97 ( bit_se727722235901077358nd_nat
% 5.64/5.97 = ( ^ [M2: nat,N2: nat] :
% 5.64/5.97 ( plus_plus_nat
% 5.64/5.97 @ ( zero_n2687167440665602831ol_nat
% 5.64/5.97 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 5.64/5.97 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.64/5.97 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % and_nat_rec
% 5.64/5.97 thf(fact_7593_double__gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum
% 5.64/5.97 thf(fact_7594_double__gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum
% 5.64/5.97 thf(fact_7595_double__gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum
% 5.64/5.97 thf(fact_7596_double__gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum
% 5.64/5.97 thf(fact_7597_double__gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum
% 5.64/5.97 thf(fact_7598_double__arith__series,axiom,
% 5.64/5.97 ! [A: rat,D: rat,N: nat] :
% 5.64/5.97 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.64/5.97 @ ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_arith_series
% 5.64/5.97 thf(fact_7599_double__arith__series,axiom,
% 5.64/5.97 ! [A: int,D: int,N: nat] :
% 5.64/5.97 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.64/5.97 @ ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_arith_series
% 5.64/5.97 thf(fact_7600_double__arith__series,axiom,
% 5.64/5.97 ! [A: complex,D: complex,N: nat] :
% 5.64/5.97 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.64/5.97 @ ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_arith_series
% 5.64/5.97 thf(fact_7601_double__arith__series,axiom,
% 5.64/5.97 ! [A: nat,D: nat,N: nat] :
% 5.64/5.97 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.64/5.97 @ ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_arith_series
% 5.64/5.97 thf(fact_7602_double__arith__series,axiom,
% 5.64/5.97 ! [A: real,D: real,N: nat] :
% 5.64/5.97 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.64/5.97 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_arith_series
% 5.64/5.97 thf(fact_7603_or__nat__unfold,axiom,
% 5.64/5.97 ( bit_se1412395901928357646or_nat
% 5.64/5.97 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % or_nat_unfold
% 5.64/5.97 thf(fact_7604_gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.97 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % gauss_sum
% 5.64/5.97 thf(fact_7605_gauss__sum,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.97 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % gauss_sum
% 5.64/5.97 thf(fact_7606_arith__series,axiom,
% 5.64/5.97 ! [A: int,D: int,N: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.97 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % arith_series
% 5.64/5.97 thf(fact_7607_arith__series,axiom,
% 5.64/5.97 ! [A: nat,D: nat,N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D ) )
% 5.64/5.97 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.97 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % arith_series
% 5.64/5.97 thf(fact_7608_double__gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.64/5.97 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7609_double__gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.64/5.97 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7610_double__gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.64/5.97 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7611_double__gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.64/5.97 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7612_double__gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.64/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % double_gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7613_Bernoulli__inequality__even,axiom,
% 5.64/5.97 ! [N: nat,X2: real] :
% 5.64/5.97 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.97 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % Bernoulli_inequality_even
% 5.64/5.97 thf(fact_7614_sum__gp__offset,axiom,
% 5.64/5.97 ! [X2: rat,M: nat,N: nat] :
% 5.64/5.97 ( ( ( X2 = one_one_rat )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.64/5.97 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.64/5.97 & ( ( X2 != one_one_rat )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.64/5.97 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_gp_offset
% 5.64/5.97 thf(fact_7615_sum__gp__offset,axiom,
% 5.64/5.97 ! [X2: complex,M: nat,N: nat] :
% 5.64/5.97 ( ( ( X2 = one_one_complex )
% 5.64/5.97 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.64/5.97 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.64/5.97 & ( ( X2 != one_one_complex )
% 5.64/5.97 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.64/5.97 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_gp_offset
% 5.64/5.97 thf(fact_7616_sum__gp__offset,axiom,
% 5.64/5.97 ! [X2: real,M: nat,N: nat] :
% 5.64/5.97 ( ( ( X2 = one_one_real )
% 5.64/5.97 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.64/5.97 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.64/5.97 & ( ( X2 != one_one_real )
% 5.64/5.97 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.64/5.97 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_gp_offset
% 5.64/5.97 thf(fact_7617_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.64/5.97 ! [N: nat,X2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_ge_one_plus_x_over_n_power_n
% 5.64/5.97 thf(fact_7618_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_ge_one_minus_x_over_n_power_n
% 5.64/5.97 thf(fact_7619_gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.64/5.97 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7620_gauss__sum__from__Suc__0,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.64/5.97 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % gauss_sum_from_Suc_0
% 5.64/5.97 thf(fact_7621_of__nat__code__if,axiom,
% 5.64/5.97 ( semiri681578069525770553at_rat
% 5.64/5.97 = ( ^ [N2: nat] :
% 5.64/5.97 ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 5.64/5.97 @ ( produc6207742614233964070at_rat
% 5.64/5.97 @ ^ [M2: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) )
% 5.64/5.97 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_code_if
% 5.64/5.97 thf(fact_7622_of__nat__code__if,axiom,
% 5.64/5.97 ( semiri1314217659103216013at_int
% 5.64/5.97 = ( ^ [N2: nat] :
% 5.64/5.97 ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 5.64/5.97 @ ( produc6840382203811409530at_int
% 5.64/5.97 @ ^ [M2: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ one_one_int ) )
% 5.64/5.97 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_code_if
% 5.64/5.97 thf(fact_7623_of__nat__code__if,axiom,
% 5.64/5.97 ( semiri5074537144036343181t_real
% 5.64/5.97 = ( ^ [N2: nat] :
% 5.64/5.97 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.64/5.97 @ ( produc1703576794950452218t_real
% 5.64/5.97 @ ^ [M2: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ one_one_real ) )
% 5.64/5.97 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_code_if
% 5.64/5.97 thf(fact_7624_of__nat__code__if,axiom,
% 5.64/5.97 ( semiri1316708129612266289at_nat
% 5.64/5.97 = ( ^ [N2: nat] :
% 5.64/5.97 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.64/5.97 @ ( produc6842872674320459806at_nat
% 5.64/5.97 @ ^ [M2: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M2 ) ) @ one_one_nat ) )
% 5.64/5.97 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_code_if
% 5.64/5.97 thf(fact_7625_of__nat__code__if,axiom,
% 5.64/5.97 ( semiri8010041392384452111omplex
% 5.64/5.97 = ( ^ [N2: nat] :
% 5.64/5.97 ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 5.64/5.97 @ ( produc1917071388513777916omplex
% 5.64/5.97 @ ^ [M2: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ one_one_complex ) )
% 5.64/5.97 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_nat_code_if
% 5.64/5.97 thf(fact_7626_height__double__log__univ__size,axiom,
% 5.64/5.97 ! [U: real,Deg: nat,T: vEBT_VEBT] :
% 5.64/5.97 ( ( U
% 5.64/5.97 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Deg ) )
% 5.64/5.97 => ( ( vEBT_invar_vebt @ T @ Deg )
% 5.64/5.97 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( vEBT_VEBT_height @ T ) ) @ ( plus_plus_real @ one_one_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ U ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % height_double_log_univ_size
% 5.64/5.97 thf(fact_7627_monoseq__arctan__series,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.97 => ( topolo6980174941875973593q_real
% 5.64/5.97 @ ^ [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 @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % monoseq_arctan_series
% 5.64/5.97 thf(fact_7628_lemma__termdiff3,axiom,
% 5.64/5.97 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.64/5.97 ( ( H2 != zero_zero_real )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.64/5.97 => ( 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 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff3
% 5.64/5.97 thf(fact_7629_lemma__termdiff3,axiom,
% 5.64/5.97 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.64/5.97 ( ( H2 != zero_zero_complex )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.64/5.97 => ( 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 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff3
% 5.64/5.97 thf(fact_7630_ln__series,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.97 => ( ( ln_ln_real @ X2 )
% 5.64/5.97 = ( suminf_real
% 5.64/5.97 @ ^ [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 @ X2 @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ln_series
% 5.64/5.97 thf(fact_7631_lemma__termdiff2,axiom,
% 5.64/5.97 ! [H2: rat,Z: rat,N: nat] :
% 5.64/5.97 ( ( H2 != zero_zero_rat )
% 5.64/5.97 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.97 = ( times_times_rat @ H2
% 5.64/5.97 @ ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [P5: nat] :
% 5.64/5.97 ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff2
% 5.64/5.97 thf(fact_7632_lemma__termdiff2,axiom,
% 5.64/5.97 ! [H2: complex,Z: complex,N: nat] :
% 5.64/5.97 ( ( H2 != zero_zero_complex )
% 5.64/5.97 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.97 = ( times_times_complex @ H2
% 5.64/5.97 @ ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [P5: nat] :
% 5.64/5.97 ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff2
% 5.64/5.97 thf(fact_7633_lemma__termdiff2,axiom,
% 5.64/5.97 ! [H2: real,Z: real,N: nat] :
% 5.64/5.97 ( ( H2 != zero_zero_real )
% 5.64/5.97 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.97 = ( times_times_real @ H2
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [P5: nat] :
% 5.64/5.97 ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff2
% 5.64/5.97 thf(fact_7634_lessThan__iff,axiom,
% 5.64/5.97 ! [I: rat,K: rat] :
% 5.64/5.97 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.64/5.97 = ( ord_less_rat @ I @ K ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_iff
% 5.64/5.97 thf(fact_7635_lessThan__iff,axiom,
% 5.64/5.97 ! [I: num,K: num] :
% 5.64/5.97 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.64/5.97 = ( ord_less_num @ I @ K ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_iff
% 5.64/5.97 thf(fact_7636_lessThan__iff,axiom,
% 5.64/5.97 ! [I: int,K: int] :
% 5.64/5.97 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.64/5.97 = ( ord_less_int @ I @ K ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_iff
% 5.64/5.97 thf(fact_7637_lessThan__iff,axiom,
% 5.64/5.97 ! [I: nat,K: nat] :
% 5.64/5.97 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.64/5.97 = ( ord_less_nat @ I @ K ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_iff
% 5.64/5.97 thf(fact_7638_lessThan__iff,axiom,
% 5.64/5.97 ! [I: real,K: real] :
% 5.64/5.97 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.64/5.97 = ( ord_less_real @ I @ K ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_iff
% 5.64/5.97 thf(fact_7639_lessThan__subset__iff,axiom,
% 5.64/5.97 ! [X2: rat,Y4: rat] :
% 5.64/5.97 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X2 ) @ ( set_ord_lessThan_rat @ Y4 ) )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_subset_iff
% 5.64/5.97 thf(fact_7640_lessThan__subset__iff,axiom,
% 5.64/5.97 ! [X2: num,Y4: num] :
% 5.64/5.97 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X2 ) @ ( set_ord_lessThan_num @ Y4 ) )
% 5.64/5.97 = ( ord_less_eq_num @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_subset_iff
% 5.64/5.97 thf(fact_7641_lessThan__subset__iff,axiom,
% 5.64/5.97 ! [X2: int,Y4: int] :
% 5.64/5.97 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X2 ) @ ( set_ord_lessThan_int @ Y4 ) )
% 5.64/5.97 = ( ord_less_eq_int @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_subset_iff
% 5.64/5.97 thf(fact_7642_lessThan__subset__iff,axiom,
% 5.64/5.97 ! [X2: nat,Y4: nat] :
% 5.64/5.97 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X2 ) @ ( set_ord_lessThan_nat @ Y4 ) )
% 5.64/5.97 = ( ord_less_eq_nat @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_subset_iff
% 5.64/5.97 thf(fact_7643_lessThan__subset__iff,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X2 ) @ ( set_or5984915006950818249n_real @ Y4 ) )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_subset_iff
% 5.64/5.97 thf(fact_7644_sum_OlessThan__Suc,axiom,
% 5.64/5.97 ! [G: nat > rat,N: nat] :
% 5.64/5.97 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc
% 5.64/5.97 thf(fact_7645_sum_OlessThan__Suc,axiom,
% 5.64/5.97 ! [G: nat > int,N: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc
% 5.64/5.97 thf(fact_7646_sum_OlessThan__Suc,axiom,
% 5.64/5.97 ! [G: nat > nat,N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc
% 5.64/5.97 thf(fact_7647_sum_OlessThan__Suc,axiom,
% 5.64/5.97 ! [G: nat > real,N: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc
% 5.64/5.97 thf(fact_7648_zero__less__log__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_less_log_cancel_iff
% 5.64/5.97 thf(fact_7649_log__less__zero__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.64/5.97 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_less_zero_cancel_iff
% 5.64/5.97 thf(fact_7650_one__less__log__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ A @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_less_log_cancel_iff
% 5.64/5.97 thf(fact_7651_log__less__one__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.64/5.97 = ( ord_less_real @ X2 @ A ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_less_one_cancel_iff
% 5.64/5.97 thf(fact_7652_log__less__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.97 => ( ( ord_less_real @ ( log @ A @ X2 ) @ ( log @ A @ Y4 ) )
% 5.64/5.97 = ( ord_less_real @ X2 @ Y4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_less_cancel_iff
% 5.64/5.97 thf(fact_7653_log__eq__one,axiom,
% 5.64/5.97 ! [A: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( A != one_one_real )
% 5.64/5.97 => ( ( log @ A @ A )
% 5.64/5.97 = one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_eq_one
% 5.64/5.97 thf(fact_7654_log__le__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ ( log @ A @ Y4 ) )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_le_cancel_iff
% 5.64/5.97 thf(fact_7655_log__le__one__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ A ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_le_one_cancel_iff
% 5.64/5.97 thf(fact_7656_one__le__log__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.64/5.97 = ( ord_less_eq_real @ A @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_le_log_cancel_iff
% 5.64/5.97 thf(fact_7657_log__le__zero__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_le_zero_cancel_iff
% 5.64/5.97 thf(fact_7658_zero__le__log__cancel__iff,axiom,
% 5.64/5.97 ! [A: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.64/5.97 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_le_log_cancel_iff
% 5.64/5.97 thf(fact_7659_powser__zero,axiom,
% 5.64/5.97 ! [F: nat > complex] :
% 5.64/5.97 ( ( suminf_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.64/5.97 = ( F @ zero_zero_nat ) ) ).
% 5.64/5.97
% 5.64/5.97 % powser_zero
% 5.64/5.97 thf(fact_7660_powser__zero,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( ( suminf_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.64/5.97 = ( F @ zero_zero_nat ) ) ).
% 5.64/5.97
% 5.64/5.97 % powser_zero
% 5.64/5.97 thf(fact_7661_log__pow__cancel,axiom,
% 5.64/5.97 ! [A: real,B: nat] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( A != one_one_real )
% 5.64/5.97 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.64/5.97 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_pow_cancel
% 5.64/5.97 thf(fact_7662_set__encode__insert,axiom,
% 5.64/5.97 ! [A4: set_nat,N: nat] :
% 5.64/5.97 ( ( finite_finite_nat @ A4 )
% 5.64/5.97 => ( ~ ( member_nat @ N @ A4 )
% 5.64/5.97 => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 5.64/5.97 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_encode_insert
% 5.64/5.97 thf(fact_7663_nat__int__comparison_I1_J,axiom,
% 5.64/5.97 ( ( ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/5.97 = ( ^ [A3: nat,B3: nat] :
% 5.64/5.97 ( ( semiri1314217659103216013at_int @ A3 )
% 5.64/5.97 = ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nat_int_comparison(1)
% 5.64/5.97 thf(fact_7664_int__if,axiom,
% 5.64/5.97 ! [P: $o,A: nat,B: nat] :
% 5.64/5.97 ( ( P
% 5.64/5.97 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.64/5.97 = ( semiri1314217659103216013at_int @ A ) ) )
% 5.64/5.97 & ( ~ P
% 5.64/5.97 => ( ( semiri1314217659103216013at_int @ ( if_nat @ P @ A @ B ) )
% 5.64/5.97 = ( semiri1314217659103216013at_int @ B ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % int_if
% 5.64/5.97 thf(fact_7665_lessThan__Suc,axiom,
% 5.64/5.97 ! [K: nat] :
% 5.64/5.97 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.64/5.97 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_Suc
% 5.64/5.97 thf(fact_7666_lessThan__nat__numeral,axiom,
% 5.64/5.97 ! [K: num] :
% 5.64/5.97 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.64/5.97 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_nat_numeral
% 5.64/5.97 thf(fact_7667_lessThan__def,axiom,
% 5.64/5.97 ( set_ord_lessThan_rat
% 5.64/5.97 = ( ^ [U2: rat] :
% 5.64/5.97 ( collect_rat
% 5.64/5.97 @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_def
% 5.64/5.97 thf(fact_7668_lessThan__def,axiom,
% 5.64/5.97 ( set_ord_lessThan_num
% 5.64/5.97 = ( ^ [U2: num] :
% 5.64/5.97 ( collect_num
% 5.64/5.97 @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_def
% 5.64/5.97 thf(fact_7669_lessThan__def,axiom,
% 5.64/5.97 ( set_ord_lessThan_int
% 5.64/5.97 = ( ^ [U2: int] :
% 5.64/5.97 ( collect_int
% 5.64/5.97 @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_def
% 5.64/5.97 thf(fact_7670_lessThan__def,axiom,
% 5.64/5.97 ( set_ord_lessThan_nat
% 5.64/5.97 = ( ^ [U2: nat] :
% 5.64/5.97 ( collect_nat
% 5.64/5.97 @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_def
% 5.64/5.97 thf(fact_7671_lessThan__def,axiom,
% 5.64/5.97 ( set_or5984915006950818249n_real
% 5.64/5.97 = ( ^ [U2: real] :
% 5.64/5.97 ( collect_real
% 5.64/5.97 @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_def
% 5.64/5.97 thf(fact_7672_log__def,axiom,
% 5.64/5.97 ( log
% 5.64/5.97 = ( ^ [A3: real,X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ A3 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_def
% 5.64/5.97 thf(fact_7673_lessThan__strict__subset__iff,axiom,
% 5.64/5.97 ! [M: rat,N: rat] :
% 5.64/5.97 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.64/5.97 = ( ord_less_rat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_strict_subset_iff
% 5.64/5.97 thf(fact_7674_lessThan__strict__subset__iff,axiom,
% 5.64/5.97 ! [M: num,N: num] :
% 5.64/5.97 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.64/5.97 = ( ord_less_num @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_strict_subset_iff
% 5.64/5.97 thf(fact_7675_lessThan__strict__subset__iff,axiom,
% 5.64/5.97 ! [M: int,N: int] :
% 5.64/5.97 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.64/5.97 = ( ord_less_int @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_strict_subset_iff
% 5.64/5.97 thf(fact_7676_lessThan__strict__subset__iff,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_strict_subset_iff
% 5.64/5.97 thf(fact_7677_lessThan__strict__subset__iff,axiom,
% 5.64/5.97 ! [M: real,N: real] :
% 5.64/5.97 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.64/5.97 = ( ord_less_real @ M @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % lessThan_strict_subset_iff
% 5.64/5.97 thf(fact_7678_log__of__power__eq,axiom,
% 5.64/5.97 ! [M: nat,B: real,N: nat] :
% 5.64/5.97 ( ( ( semiri5074537144036343181t_real @ M )
% 5.64/5.97 = ( power_power_real @ B @ N ) )
% 5.64/5.97 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.97 => ( ( semiri5074537144036343181t_real @ N )
% 5.64/5.97 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_of_power_eq
% 5.64/5.97 thf(fact_7679_less__log__of__power,axiom,
% 5.64/5.97 ! [B: real,N: nat,M: real] :
% 5.64/5.97 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.64/5.97 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.97 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_log_of_power
% 5.64/5.97 thf(fact_7680_atLeast0__atMost__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.64/5.97 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % atLeast0_atMost_Suc
% 5.64/5.97 thf(fact_7681_atLeastAtMost__insertL,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.64/5.97 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % atLeastAtMost_insertL
% 5.64/5.97 thf(fact_7682_atLeastAtMostSuc__conv,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.64/5.97 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.64/5.97 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % atLeastAtMostSuc_conv
% 5.64/5.97 thf(fact_7683_Icc__eq__insert__lb__nat,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.64/5.97 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % Icc_eq_insert_lb_nat
% 5.64/5.97 thf(fact_7684_sum_Onat__diff__reindex,axiom,
% 5.64/5.97 ! [G: nat > nat,N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.nat_diff_reindex
% 5.64/5.97 thf(fact_7685_sum_Onat__diff__reindex,axiom,
% 5.64/5.97 ! [G: nat > real,N: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.nat_diff_reindex
% 5.64/5.97 thf(fact_7686_sum__diff__distrib,axiom,
% 5.64/5.97 ! [Q: real > nat,P: real > nat,N: real] :
% 5.64/5.97 ( ! [X4: real] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.64/5.97 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.64/5.97 = ( groups1935376822645274424al_nat
% 5.64/5.97 @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.64/5.97 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_diff_distrib
% 5.64/5.97 thf(fact_7687_sum__diff__distrib,axiom,
% 5.64/5.97 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.64/5.97 ( ! [X4: nat] : ( ord_less_eq_nat @ ( Q @ X4 ) @ ( P @ X4 ) )
% 5.64/5.97 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.64/5.97 = ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_diff_distrib
% 5.64/5.97 thf(fact_7688_log__base__change,axiom,
% 5.64/5.97 ! [A: real,B: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( A != one_one_real )
% 5.64/5.97 => ( ( log @ B @ X2 )
% 5.64/5.97 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_base_change
% 5.64/5.97 thf(fact_7689_le__log__of__power,axiom,
% 5.64/5.97 ! [B: real,N: nat,M: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.64/5.97 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.97 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % le_log_of_power
% 5.64/5.97 thf(fact_7690_log__base__pow,axiom,
% 5.64/5.97 ! [A: real,N: nat,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( log @ ( power_power_real @ A @ N ) @ X2 )
% 5.64/5.97 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_base_pow
% 5.64/5.97 thf(fact_7691_log__nat__power,axiom,
% 5.64/5.97 ! [X2: real,B: real,N: nat] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( log @ B @ ( power_power_real @ X2 @ N ) )
% 5.64/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_nat_power
% 5.64/5.97 thf(fact_7692_sum_OlessThan__Suc__shift,axiom,
% 5.64/5.97 ! [G: nat > rat,N: nat] :
% 5.64/5.97 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.64/5.97 @ ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc_shift
% 5.64/5.97 thf(fact_7693_sum_OlessThan__Suc__shift,axiom,
% 5.64/5.97 ! [G: nat > int,N: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.64/5.97 @ ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc_shift
% 5.64/5.97 thf(fact_7694_sum_OlessThan__Suc__shift,axiom,
% 5.64/5.97 ! [G: nat > nat,N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.64/5.97 @ ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc_shift
% 5.64/5.97 thf(fact_7695_sum_OlessThan__Suc__shift,axiom,
% 5.64/5.97 ! [G: nat > real,N: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.lessThan_Suc_shift
% 5.64/5.97 thf(fact_7696_sum__lessThan__telescope,axiom,
% 5.64/5.97 ! [F: nat > rat,M: nat] :
% 5.64/5.97 ( ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_lessThan_telescope
% 5.64/5.97 thf(fact_7697_sum__lessThan__telescope,axiom,
% 5.64/5.97 ! [F: nat > int,M: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_lessThan_telescope
% 5.64/5.97 thf(fact_7698_sum__lessThan__telescope,axiom,
% 5.64/5.97 ! [F: nat > real,M: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_lessThan_telescope
% 5.64/5.97 thf(fact_7699_sum__lessThan__telescope_H,axiom,
% 5.64/5.97 ! [F: nat > rat,M: nat] :
% 5.64/5.97 ( ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_lessThan_telescope'
% 5.64/5.97 thf(fact_7700_sum__lessThan__telescope_H,axiom,
% 5.64/5.97 ! [F: nat > int,M: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_lessThan_telescope'
% 5.64/5.97 thf(fact_7701_sum__lessThan__telescope_H,axiom,
% 5.64/5.97 ! [F: nat > real,M: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_lessThan_telescope'
% 5.64/5.97 thf(fact_7702_sumr__diff__mult__const2,axiom,
% 5.64/5.97 ! [F: nat > rat,N: nat,R2: rat] :
% 5.64/5.97 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R2 ) )
% 5.64/5.97 = ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ R2 )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sumr_diff_mult_const2
% 5.64/5.97 thf(fact_7703_sumr__diff__mult__const2,axiom,
% 5.64/5.97 ! [F: nat > int,N: nat,R2: int] :
% 5.64/5.97 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R2 ) )
% 5.64/5.97 = ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ R2 )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sumr_diff_mult_const2
% 5.64/5.97 thf(fact_7704_sumr__diff__mult__const2,axiom,
% 5.64/5.97 ! [F: nat > complex,N: nat,R2: complex] :
% 5.64/5.97 ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R2 ) )
% 5.64/5.97 = ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [I4: nat] : ( minus_minus_complex @ ( F @ I4 ) @ R2 )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sumr_diff_mult_const2
% 5.64/5.97 thf(fact_7705_sumr__diff__mult__const2,axiom,
% 5.64/5.97 ! [F: nat > real,N: nat,R2: real] :
% 5.64/5.97 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R2 ) )
% 5.64/5.97 = ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( minus_minus_real @ ( F @ I4 ) @ R2 )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sumr_diff_mult_const2
% 5.64/5.97 thf(fact_7706_sum_OatLeast1__atMost__eq,axiom,
% 5.64/5.97 ! [G: nat > nat,N: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.64/5.97 = ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.atLeast1_atMost_eq
% 5.64/5.97 thf(fact_7707_sum_OatLeast1__atMost__eq,axiom,
% 5.64/5.97 ! [G: nat > real,N: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.64/5.97 = ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum.atLeast1_atMost_eq
% 5.64/5.97 thf(fact_7708_log2__of__power__eq,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( M
% 5.64/5.97 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.97 => ( ( semiri5074537144036343181t_real @ N )
% 5.64/5.97 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log2_of_power_eq
% 5.64/5.97 thf(fact_7709_log__of__power__less,axiom,
% 5.64/5.97 ! [M: nat,B: real,N: nat] :
% 5.64/5.97 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.64/5.97 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_of_power_less
% 5.64/5.97 thf(fact_7710_log__mult,axiom,
% 5.64/5.97 ! [A: real,X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( A != one_one_real )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.97 => ( ( log @ A @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.97 = ( plus_plus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_mult
% 5.64/5.97 thf(fact_7711_log__divide,axiom,
% 5.64/5.97 ! [A: real,X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( A != one_one_real )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.97 => ( ( log @ A @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.97 = ( minus_minus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_divide
% 5.64/5.97 thf(fact_7712_power__diff__1__eq,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex )
% 5.64/5.97 = ( times_times_complex @ ( minus_minus_complex @ X2 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_1_eq
% 5.64/5.97 thf(fact_7713_power__diff__1__eq,axiom,
% 5.64/5.97 ! [X2: rat,N: nat] :
% 5.64/5.97 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat )
% 5.64/5.97 = ( times_times_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_1_eq
% 5.64/5.97 thf(fact_7714_power__diff__1__eq,axiom,
% 5.64/5.97 ! [X2: int,N: nat] :
% 5.64/5.97 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ one_one_int )
% 5.64/5.97 = ( times_times_int @ ( minus_minus_int @ X2 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_1_eq
% 5.64/5.97 thf(fact_7715_power__diff__1__eq,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real )
% 5.64/5.97 = ( times_times_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_1_eq
% 5.64/5.97 thf(fact_7716_one__diff__power__eq,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.64/5.97 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq
% 5.64/5.97 thf(fact_7717_one__diff__power__eq,axiom,
% 5.64/5.97 ! [X2: rat,N: nat] :
% 5.64/5.97 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.64/5.97 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq
% 5.64/5.97 thf(fact_7718_one__diff__power__eq,axiom,
% 5.64/5.97 ! [X2: int,N: nat] :
% 5.64/5.97 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.64/5.97 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq
% 5.64/5.97 thf(fact_7719_one__diff__power__eq,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.64/5.97 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq
% 5.64/5.97 thf(fact_7720_geometric__sum,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( X2 != one_one_complex )
% 5.64/5.97 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % geometric_sum
% 5.64/5.97 thf(fact_7721_geometric__sum,axiom,
% 5.64/5.97 ! [X2: rat,N: nat] :
% 5.64/5.97 ( ( X2 != one_one_rat )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % geometric_sum
% 5.64/5.97 thf(fact_7722_geometric__sum,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( X2 != one_one_real )
% 5.64/5.97 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % geometric_sum
% 5.64/5.97 thf(fact_7723_log__of__power__le,axiom,
% 5.64/5.97 ! [M: nat,B: real,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.64/5.97 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_of_power_le
% 5.64/5.97 thf(fact_7724_log__eq__div__ln__mult__log,axiom,
% 5.64/5.97 ! [A: real,B: real,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( A != one_one_real )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.97 => ( ( B != one_one_real )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( log @ A @ X2 )
% 5.64/5.97 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X2 ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_eq_div_ln_mult_log
% 5.64/5.97 thf(fact_7725_sum__gp__strict,axiom,
% 5.64/5.97 ! [X2: rat,N: nat] :
% 5.64/5.97 ( ( ( X2 = one_one_rat )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.64/5.97 & ( ( X2 != one_one_rat )
% 5.64/5.97 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_gp_strict
% 5.64/5.97 thf(fact_7726_sum__gp__strict,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( ( X2 = one_one_complex )
% 5.64/5.97 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.64/5.97 & ( ( X2 != one_one_complex )
% 5.64/5.97 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_gp_strict
% 5.64/5.97 thf(fact_7727_sum__gp__strict,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( ( X2 = one_one_real )
% 5.64/5.97 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.97 & ( ( X2 != one_one_real )
% 5.64/5.97 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_gp_strict
% 5.64/5.97 thf(fact_7728_lemma__termdiff1,axiom,
% 5.64/5.97 ! [Z: complex,H2: complex,M: nat] :
% 5.64/5.97 ( ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff1
% 5.64/5.97 thf(fact_7729_lemma__termdiff1,axiom,
% 5.64/5.97 ! [Z: rat,H2: rat,M: nat] :
% 5.64/5.97 ( ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff1
% 5.64/5.97 thf(fact_7730_lemma__termdiff1,axiom,
% 5.64/5.97 ! [Z: int,H2: int,M: nat] :
% 5.64/5.97 ( ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff1
% 5.64/5.97 thf(fact_7731_lemma__termdiff1,axiom,
% 5.64/5.97 ! [Z: real,H2: real,M: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) )
% 5.64/5.97 = ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % lemma_termdiff1
% 5.64/5.97 thf(fact_7732_power__diff__sumr2,axiom,
% 5.64/5.97 ! [X2: complex,N: nat,Y4: complex] :
% 5.64/5.97 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N ) @ ( power_power_complex @ Y4 @ N ) )
% 5.64/5.97 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y4 )
% 5.64/5.97 @ ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [I4: nat] : ( times_times_complex @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_complex @ X2 @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_sumr2
% 5.64/5.97 thf(fact_7733_power__diff__sumr2,axiom,
% 5.64/5.97 ! [X2: rat,N: nat,Y4: rat] :
% 5.64/5.97 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N ) @ ( power_power_rat @ Y4 @ N ) )
% 5.64/5.97 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y4 )
% 5.64/5.97 @ ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X2 @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_sumr2
% 5.64/5.97 thf(fact_7734_power__diff__sumr2,axiom,
% 5.64/5.97 ! [X2: int,N: nat,Y4: int] :
% 5.64/5.97 ( ( minus_minus_int @ ( power_power_int @ X2 @ N ) @ ( power_power_int @ Y4 @ N ) )
% 5.64/5.97 = ( times_times_int @ ( minus_minus_int @ X2 @ Y4 )
% 5.64/5.97 @ ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_int @ X2 @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_sumr2
% 5.64/5.97 thf(fact_7735_power__diff__sumr2,axiom,
% 5.64/5.97 ! [X2: real,N: nat,Y4: real] :
% 5.64/5.97 ( ( minus_minus_real @ ( power_power_real @ X2 @ N ) @ ( power_power_real @ Y4 @ N ) )
% 5.64/5.97 = ( times_times_real @ ( minus_minus_real @ X2 @ Y4 )
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ Y4 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) ) @ ( power_power_real @ X2 @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_diff_sumr2
% 5.64/5.97 thf(fact_7736_diff__power__eq__sum,axiom,
% 5.64/5.97 ! [X2: complex,N: nat,Y4: complex] :
% 5.64/5.97 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ ( suc @ N ) ) @ ( power_power_complex @ Y4 @ ( suc @ N ) ) )
% 5.64/5.97 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y4 )
% 5.64/5.97 @ ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X2 @ P5 ) @ ( power_power_complex @ Y4 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % diff_power_eq_sum
% 5.64/5.97 thf(fact_7737_diff__power__eq__sum,axiom,
% 5.64/5.97 ! [X2: rat,N: nat,Y4: rat] :
% 5.64/5.97 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ ( suc @ N ) ) @ ( power_power_rat @ Y4 @ ( suc @ N ) ) )
% 5.64/5.97 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y4 )
% 5.64/5.97 @ ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X2 @ P5 ) @ ( power_power_rat @ Y4 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % diff_power_eq_sum
% 5.64/5.97 thf(fact_7738_diff__power__eq__sum,axiom,
% 5.64/5.97 ! [X2: int,N: nat,Y4: int] :
% 5.64/5.97 ( ( minus_minus_int @ ( power_power_int @ X2 @ ( suc @ N ) ) @ ( power_power_int @ Y4 @ ( suc @ N ) ) )
% 5.64/5.97 = ( times_times_int @ ( minus_minus_int @ X2 @ Y4 )
% 5.64/5.97 @ ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X2 @ P5 ) @ ( power_power_int @ Y4 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % diff_power_eq_sum
% 5.64/5.97 thf(fact_7739_diff__power__eq__sum,axiom,
% 5.64/5.97 ! [X2: real,N: nat,Y4: real] :
% 5.64/5.97 ( ( minus_minus_real @ ( power_power_real @ X2 @ ( suc @ N ) ) @ ( power_power_real @ Y4 @ ( suc @ N ) ) )
% 5.64/5.97 = ( times_times_real @ ( minus_minus_real @ X2 @ Y4 )
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X2 @ P5 ) @ ( power_power_real @ Y4 @ ( minus_minus_nat @ N @ P5 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % diff_power_eq_sum
% 5.64/5.97 thf(fact_7740_set__decode__plus__power__2,axiom,
% 5.64/5.97 ! [N: nat,Z: nat] :
% 5.64/5.97 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.64/5.97 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.64/5.97 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % set_decode_plus_power_2
% 5.64/5.97 thf(fact_7741_less__log2__of__power,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.64/5.97 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_log2_of_power
% 5.64/5.97 thf(fact_7742_le__log2__of__power,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.64/5.97 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % le_log2_of_power
% 5.64/5.97 thf(fact_7743_real__sum__nat__ivl__bounded2,axiom,
% 5.64/5.97 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.64/5.97 ( ! [P7: nat] :
% 5.64/5.97 ( ( ord_less_nat @ P7 @ N )
% 5.64/5.97 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.64/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.64/5.97 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_sum_nat_ivl_bounded2
% 5.64/5.97 thf(fact_7744_real__sum__nat__ivl__bounded2,axiom,
% 5.64/5.97 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.64/5.97 ( ! [P7: nat] :
% 5.64/5.97 ( ( ord_less_nat @ P7 @ N )
% 5.64/5.97 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.64/5.97 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.64/5.97 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_sum_nat_ivl_bounded2
% 5.64/5.97 thf(fact_7745_real__sum__nat__ivl__bounded2,axiom,
% 5.64/5.97 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.64/5.97 ( ! [P7: nat] :
% 5.64/5.97 ( ( ord_less_nat @ P7 @ N )
% 5.64/5.97 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.64/5.97 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.64/5.97 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_sum_nat_ivl_bounded2
% 5.64/5.97 thf(fact_7746_real__sum__nat__ivl__bounded2,axiom,
% 5.64/5.97 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.64/5.97 ( ! [P7: nat] :
% 5.64/5.97 ( ( ord_less_nat @ P7 @ N )
% 5.64/5.97 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.64/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.64/5.97 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % real_sum_nat_ivl_bounded2
% 5.64/5.97 thf(fact_7747_exp__bound__half,axiom,
% 5.64/5.97 ! [Z: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_bound_half
% 5.64/5.97 thf(fact_7748_exp__bound__half,axiom,
% 5.64/5.97 ! [Z: complex] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_bound_half
% 5.64/5.97 thf(fact_7749_one__diff__power__eq_H,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N ) )
% 5.64/5.97 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 )
% 5.64/5.97 @ ( groups2073611262835488442omplex
% 5.64/5.97 @ ^ [I4: nat] : ( power_power_complex @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq'
% 5.64/5.97 thf(fact_7750_one__diff__power__eq_H,axiom,
% 5.64/5.97 ! [X2: rat,N: nat] :
% 5.64/5.97 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N ) )
% 5.64/5.97 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 )
% 5.64/5.97 @ ( groups2906978787729119204at_rat
% 5.64/5.97 @ ^ [I4: nat] : ( power_power_rat @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq'
% 5.64/5.97 thf(fact_7751_one__diff__power__eq_H,axiom,
% 5.64/5.97 ! [X2: int,N: nat] :
% 5.64/5.97 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N ) )
% 5.64/5.97 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 )
% 5.64/5.97 @ ( groups3539618377306564664at_int
% 5.64/5.97 @ ^ [I4: nat] : ( power_power_int @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq'
% 5.64/5.97 thf(fact_7752_one__diff__power__eq_H,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N ) )
% 5.64/5.97 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 )
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_diff_power_eq'
% 5.64/5.97 thf(fact_7753_log2__of__power__less,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log2_of_power_less
% 5.64/5.97 thf(fact_7754_sum__split__even__odd,axiom,
% 5.64/5.97 ! [F: nat > real,G: nat > real,N: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( F @ I4 ) @ ( G @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/5.97 = ( plus_plus_real
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ one_one_nat ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_split_even_odd
% 5.64/5.97 thf(fact_7755_log2__of__power__le,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log2_of_power_le
% 5.64/5.97 thf(fact_7756_exp__bound__lemma,axiom,
% 5.64/5.97 ! [Z: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.97 => ( 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 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_bound_lemma
% 5.64/5.97 thf(fact_7757_exp__bound__lemma,axiom,
% 5.64/5.97 ! [Z: complex] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.97 => ( 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 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % exp_bound_lemma
% 5.64/5.97 thf(fact_7758_log__base__10__eq2,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.97 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_base_10_eq2
% 5.64/5.97 thf(fact_7759_log__base__10__eq1,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.97 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.97 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_base_10_eq1
% 5.64/5.97 thf(fact_7760_arctan__series,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.97 => ( ( arctan @ X2 )
% 5.64/5.97 = ( suminf_real
% 5.64/5.97 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % arctan_series
% 5.64/5.97 thf(fact_7761_norm__divide__numeral,axiom,
% 5.64/5.97 ! [A: real,W: num] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.97 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_divide_numeral
% 5.64/5.97 thf(fact_7762_norm__divide__numeral,axiom,
% 5.64/5.97 ! [A: complex,W: num] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.97 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_divide_numeral
% 5.64/5.97 thf(fact_7763_norm__mult__numeral2,axiom,
% 5.64/5.97 ! [A: real,W: num] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.97 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_numeral2
% 5.64/5.97 thf(fact_7764_norm__mult__numeral2,axiom,
% 5.64/5.97 ! [A: complex,W: num] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.97 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_numeral2
% 5.64/5.97 thf(fact_7765_norm__mult__numeral1,axiom,
% 5.64/5.97 ! [W: num,A: real] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.64/5.97 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_numeral1
% 5.64/5.97 thf(fact_7766_norm__mult__numeral1,axiom,
% 5.64/5.97 ! [W: num,A: complex] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.64/5.97 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_numeral1
% 5.64/5.97 thf(fact_7767_norm__neg__numeral,axiom,
% 5.64/5.97 ! [W: num] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.97 = ( numeral_numeral_real @ W ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_neg_numeral
% 5.64/5.97 thf(fact_7768_norm__neg__numeral,axiom,
% 5.64/5.97 ! [W: num] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/5.97 = ( numeral_numeral_real @ W ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_neg_numeral
% 5.64/5.97 thf(fact_7769_zero__less__norm__iff,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.64/5.97 = ( X2 != zero_zero_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_less_norm_iff
% 5.64/5.97 thf(fact_7770_zero__less__norm__iff,axiom,
% 5.64/5.97 ! [X2: complex] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.64/5.97 = ( X2 != zero_zero_complex ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_less_norm_iff
% 5.64/5.97 thf(fact_7771_norm__one,axiom,
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.64/5.97 = one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % norm_one
% 5.64/5.97 thf(fact_7772_norm__one,axiom,
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.64/5.97 = one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % norm_one
% 5.64/5.97 thf(fact_7773_norm__numeral,axiom,
% 5.64/5.97 ! [W: num] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.97 = ( numeral_numeral_real @ W ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_numeral
% 5.64/5.97 thf(fact_7774_norm__numeral,axiom,
% 5.64/5.97 ! [W: num] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.64/5.97 = ( numeral_numeral_real @ W ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_numeral
% 5.64/5.97 thf(fact_7775_norm__not__less__zero,axiom,
% 5.64/5.97 ! [X2: complex] :
% 5.64/5.97 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real ) ).
% 5.64/5.97
% 5.64/5.97 % norm_not_less_zero
% 5.64/5.97 thf(fact_7776_norm__mult,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.97 = ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult
% 5.64/5.97 thf(fact_7777_norm__mult,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y4 ) )
% 5.64/5.97 = ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult
% 5.64/5.97 thf(fact_7778_norm__divide,axiom,
% 5.64/5.97 ! [A: real,B: real] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.97 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_divide
% 5.64/5.97 thf(fact_7779_norm__divide,axiom,
% 5.64/5.97 ! [A: complex,B: complex] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.97 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_divide
% 5.64/5.97 thf(fact_7780_norm__power,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) )
% 5.64/5.97 = ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_power
% 5.64/5.97 thf(fact_7781_norm__power,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) )
% 5.64/5.97 = ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_power
% 5.64/5.97 thf(fact_7782_norm__uminus__minus,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] :
% 5.64/5.97 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ Y4 ) )
% 5.64/5.97 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_uminus_minus
% 5.64/5.97 thf(fact_7783_norm__uminus__minus,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex] :
% 5.64/5.97 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y4 ) )
% 5.64/5.97 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_uminus_minus
% 5.64/5.97 thf(fact_7784_nonzero__norm__divide,axiom,
% 5.64/5.97 ! [B: real,A: real] :
% 5.64/5.97 ( ( B != zero_zero_real )
% 5.64/5.97 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.64/5.97 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nonzero_norm_divide
% 5.64/5.97 thf(fact_7785_nonzero__norm__divide,axiom,
% 5.64/5.97 ! [B: complex,A: complex] :
% 5.64/5.97 ( ( B != zero_zero_complex )
% 5.64/5.97 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/5.97 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % nonzero_norm_divide
% 5.64/5.97 thf(fact_7786_power__eq__imp__eq__norm,axiom,
% 5.64/5.97 ! [W: real,N: nat,Z: real] :
% 5.64/5.97 ( ( ( power_power_real @ W @ N )
% 5.64/5.97 = ( power_power_real @ Z @ N ) )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ( ( real_V7735802525324610683m_real @ W )
% 5.64/5.97 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_eq_imp_eq_norm
% 5.64/5.97 thf(fact_7787_power__eq__imp__eq__norm,axiom,
% 5.64/5.97 ! [W: complex,N: nat,Z: complex] :
% 5.64/5.97 ( ( ( power_power_complex @ W @ N )
% 5.64/5.97 = ( power_power_complex @ Z @ N ) )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ( ( real_V1022390504157884413omplex @ W )
% 5.64/5.97 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_eq_imp_eq_norm
% 5.64/5.97 thf(fact_7788_norm__mult__less,axiom,
% 5.64/5.97 ! [X2: real,R2: real,Y4: real,S2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y4 ) @ S2 )
% 5.64/5.97 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y4 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_less
% 5.64/5.97 thf(fact_7789_norm__mult__less,axiom,
% 5.64/5.97 ! [X2: complex,R2: real,Y4: complex,S2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y4 ) @ S2 )
% 5.64/5.97 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y4 ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_less
% 5.64/5.97 thf(fact_7790_norm__mult__ineq,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y4 ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_ineq
% 5.64/5.97 thf(fact_7791_norm__mult__ineq,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y4 ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_mult_ineq
% 5.64/5.97 thf(fact_7792_norm__add__less,axiom,
% 5.64/5.97 ! [X2: real,R2: real,Y4: real,S2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y4 ) @ S2 )
% 5.64/5.97 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_add_less
% 5.64/5.97 thf(fact_7793_norm__add__less,axiom,
% 5.64/5.97 ! [X2: complex,R2: real,Y4: complex,S2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y4 ) @ S2 )
% 5.64/5.97 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y4 ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_add_less
% 5.64/5.97 thf(fact_7794_norm__triangle__lt,axiom,
% 5.64/5.97 ! [X2: real,Y4: real,E: real] :
% 5.64/5.97 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E )
% 5.64/5.97 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ E ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_lt
% 5.64/5.97 thf(fact_7795_norm__triangle__lt,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex,E: real] :
% 5.64/5.97 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E )
% 5.64/5.97 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y4 ) ) @ E ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_lt
% 5.64/5.97 thf(fact_7796_norm__triangle__mono,axiom,
% 5.64/5.97 ! [A: real,R2: real,B: real,S2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_mono
% 5.64/5.97 thf(fact_7797_norm__triangle__mono,axiom,
% 5.64/5.97 ! [A: complex,R2: real,B: complex,S2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_mono
% 5.64/5.97 thf(fact_7798_norm__triangle__ineq,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_ineq
% 5.64/5.97 thf(fact_7799_norm__triangle__ineq,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y4 ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_ineq
% 5.64/5.97 thf(fact_7800_norm__triangle__le,axiom,
% 5.64/5.97 ! [X2: real,Y4: real,E: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y4 ) ) @ E )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ E ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_le
% 5.64/5.97 thf(fact_7801_norm__triangle__le,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex,E: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y4 ) ) @ E )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y4 ) ) @ E ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_triangle_le
% 5.64/5.97 thf(fact_7802_norm__add__leD,axiom,
% 5.64/5.97 ! [A: real,B: real,C: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_add_leD
% 5.64/5.97 thf(fact_7803_norm__add__leD,axiom,
% 5.64/5.97 ! [A: complex,B: complex,C: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_add_leD
% 5.64/5.97 thf(fact_7804_norm__power__ineq,axiom,
% 5.64/5.97 ! [X2: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_power_ineq
% 5.64/5.97 thf(fact_7805_norm__power__ineq,axiom,
% 5.64/5.97 ! [X2: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_power_ineq
% 5.64/5.97 thf(fact_7806_norm__diff__triangle__less,axiom,
% 5.64/5.97 ! [X2: real,Y4: real,E1: real,Z: real,E22: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y4 ) ) @ E1 )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y4 @ Z ) ) @ E22 )
% 5.64/5.97 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_diff_triangle_less
% 5.64/5.97 thf(fact_7807_norm__diff__triangle__less,axiom,
% 5.64/5.97 ! [X2: complex,Y4: complex,E1: real,Z: complex,E22: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y4 ) ) @ E1 )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y4 @ Z ) ) @ E22 )
% 5.64/5.97 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_diff_triangle_less
% 5.64/5.97 thf(fact_7808_norm__diff__ineq,axiom,
% 5.64/5.97 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_diff_ineq
% 5.64/5.97 thf(fact_7809_norm__diff__ineq,axiom,
% 5.64/5.97 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_diff_ineq
% 5.64/5.97 thf(fact_7810_power__eq__1__iff,axiom,
% 5.64/5.97 ! [W: real,N: nat] :
% 5.64/5.97 ( ( ( power_power_real @ W @ N )
% 5.64/5.97 = one_one_real )
% 5.64/5.97 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.64/5.97 = one_one_real )
% 5.64/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_eq_1_iff
% 5.64/5.97 thf(fact_7811_power__eq__1__iff,axiom,
% 5.64/5.97 ! [W: complex,N: nat] :
% 5.64/5.97 ( ( ( power_power_complex @ W @ N )
% 5.64/5.97 = one_one_complex )
% 5.64/5.97 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.64/5.97 = one_one_real )
% 5.64/5.97 | ( N = zero_zero_nat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % power_eq_1_iff
% 5.64/5.97 thf(fact_7812_norm__diff__triangle__ineq,axiom,
% 5.64/5.97 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_diff_triangle_ineq
% 5.64/5.97 thf(fact_7813_norm__diff__triangle__ineq,axiom,
% 5.64/5.97 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_diff_triangle_ineq
% 5.64/5.97 thf(fact_7814_square__norm__one,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = one_one_real )
% 5.64/5.97 => ( ( real_V7735802525324610683m_real @ X2 )
% 5.64/5.97 = one_one_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % square_norm_one
% 5.64/5.97 thf(fact_7815_square__norm__one,axiom,
% 5.64/5.97 ! [X2: complex] :
% 5.64/5.97 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = one_one_complex )
% 5.64/5.97 => ( ( real_V1022390504157884413omplex @ X2 )
% 5.64/5.97 = one_one_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % square_norm_one
% 5.64/5.97 thf(fact_7816_norm__power__diff,axiom,
% 5.64/5.97 ! [Z: real,W: real,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.64/5.97 => ( 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 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_power_diff
% 5.64/5.97 thf(fact_7817_norm__power__diff,axiom,
% 5.64/5.97 ! [Z: complex,W: complex,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.64/5.97 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.64/5.97 => ( 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 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % norm_power_diff
% 5.64/5.97 thf(fact_7818_suminf__geometric,axiom,
% 5.64/5.97 ! [C: real] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.64/5.97 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.64/5.97 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_geometric
% 5.64/5.97 thf(fact_7819_suminf__geometric,axiom,
% 5.64/5.97 ! [C: complex] :
% 5.64/5.97 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.64/5.97 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.64/5.97 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_geometric
% 5.64/5.97 thf(fact_7820_sum__bounds__lt__plus1,axiom,
% 5.64/5.97 ! [F: nat > nat,Mm: nat] :
% 5.64/5.97 ( ( groups3542108847815614940at_nat
% 5.64/5.97 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.64/5.97 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_bounds_lt_plus1
% 5.64/5.97 thf(fact_7821_sum__bounds__lt__plus1,axiom,
% 5.64/5.97 ! [F: nat > real,Mm: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [K2: nat] : ( F @ ( suc @ K2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.64/5.97 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % sum_bounds_lt_plus1
% 5.64/5.97 thf(fact_7822_heigt__uplog__rel,axiom,
% 5.64/5.97 ! [T: vEBT_VEBT,N: nat] :
% 5.64/5.97 ( ( vEBT_invar_vebt @ T @ N )
% 5.64/5.97 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ T ) )
% 5.64/5.97 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % heigt_uplog_rel
% 5.64/5.97 thf(fact_7823_sumr__cos__zero__one,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ zero_zero_real @ M2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.97 = one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % sumr_cos_zero_one
% 5.64/5.97 thf(fact_7824_log__ceil__idem,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.64/5.97 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.97 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % log_ceil_idem
% 5.64/5.97 thf(fact_7825_ceiling__numeral,axiom,
% 5.64/5.97 ! [V: num] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.64/5.97 = ( numeral_numeral_int @ V ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_numeral
% 5.64/5.97 thf(fact_7826_ceiling__numeral,axiom,
% 5.64/5.97 ! [V: num] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( numeral_numeral_rat @ V ) )
% 5.64/5.97 = ( numeral_numeral_int @ V ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_numeral
% 5.64/5.97 thf(fact_7827_ceiling__one,axiom,
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.64/5.97 = one_one_int ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_one
% 5.64/5.97 thf(fact_7828_ceiling__one,axiom,
% 5.64/5.97 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.64/5.97 = one_one_int ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_one
% 5.64/5.97 thf(fact_7829_ceiling__add__of__int,axiom,
% 5.64/5.97 ! [X2: rat,Z: int] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_of_int
% 5.64/5.97 thf(fact_7830_ceiling__add__of__int,axiom,
% 5.64/5.97 ! [X2: real,Z: int] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ Z ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_of_int
% 5.64/5.97 thf(fact_7831_ceiling__le__zero,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_zero
% 5.64/5.97 thf(fact_7832_ceiling__le__zero,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_zero
% 5.64/5.97 thf(fact_7833_zero__less__ceiling,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_less_ceiling
% 5.64/5.97 thf(fact_7834_zero__less__ceiling,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_less_ceiling
% 5.64/5.97 thf(fact_7835_ceiling__le__numeral,axiom,
% 5.64/5.97 ! [X2: rat,V: num] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_numeral
% 5.64/5.97 thf(fact_7836_ceiling__le__numeral,axiom,
% 5.64/5.97 ! [X2: real,V: num] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_numeral
% 5.64/5.97 thf(fact_7837_ceiling__less__one,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ zero_zero_rat ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_one
% 5.64/5.97 thf(fact_7838_ceiling__less__one,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_one
% 5.64/5.97 thf(fact_7839_one__le__ceiling,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ zero_zero_rat @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_le_ceiling
% 5.64/5.97 thf(fact_7840_one__le__ceiling,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_le_ceiling
% 5.64/5.97 thf(fact_7841_numeral__less__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: real] :
% 5.64/5.97 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_less_ceiling
% 5.64/5.97 thf(fact_7842_numeral__less__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_less_ceiling
% 5.64/5.97 thf(fact_7843_ceiling__le__one,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_one
% 5.64/5.97 thf(fact_7844_ceiling__le__one,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_one
% 5.64/5.97 thf(fact_7845_one__less__ceiling,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ one_one_rat @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_less_ceiling
% 5.64/5.97 thf(fact_7846_one__less__ceiling,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ one_one_real @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % one_less_ceiling
% 5.64/5.97 thf(fact_7847_ceiling__add__numeral,axiom,
% 5.64/5.97 ! [X2: real,V: num] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_numeral
% 5.64/5.97 thf(fact_7848_ceiling__add__numeral,axiom,
% 5.64/5.97 ! [X2: rat,V: num] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_numeral
% 5.64/5.97 thf(fact_7849_ceiling__neg__numeral,axiom,
% 5.64/5.97 ! [V: num] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_neg_numeral
% 5.64/5.97 thf(fact_7850_ceiling__neg__numeral,axiom,
% 5.64/5.97 ! [V: num] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_neg_numeral
% 5.64/5.97 thf(fact_7851_ceiling__add__one,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) )
% 5.64/5.97 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_one
% 5.64/5.97 thf(fact_7852_ceiling__add__one,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ one_one_real ) )
% 5.64/5.97 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_one
% 5.64/5.97 thf(fact_7853_ceiling__diff__numeral,axiom,
% 5.64/5.97 ! [X2: real,V: num] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.97 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_diff_numeral
% 5.64/5.97 thf(fact_7854_ceiling__diff__numeral,axiom,
% 5.64/5.97 ! [X2: rat,V: num] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.97 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_diff_numeral
% 5.64/5.97 thf(fact_7855_ceiling__diff__one,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.64/5.97 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ one_one_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_diff_one
% 5.64/5.97 thf(fact_7856_ceiling__diff__one,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.64/5.97 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X2 ) @ one_one_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_diff_one
% 5.64/5.97 thf(fact_7857_ceiling__numeral__power,axiom,
% 5.64/5.97 ! [X2: num,N: nat] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.64/5.97 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_numeral_power
% 5.64/5.97 thf(fact_7858_ceiling__numeral__power,axiom,
% 5.64/5.97 ! [X2: num,N: nat] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.64/5.97 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_numeral_power
% 5.64/5.97 thf(fact_7859_ceiling__less__zero,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ zero_zero_int )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_zero
% 5.64/5.97 thf(fact_7860_ceiling__less__zero,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ zero_zero_int )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_zero
% 5.64/5.97 thf(fact_7861_zero__le__ceiling,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_le_ceiling
% 5.64/5.97 thf(fact_7862_zero__le__ceiling,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % zero_le_ceiling
% 5.64/5.97 thf(fact_7863_ceiling__divide__eq__div__numeral,axiom,
% 5.64/5.97 ! [A: num,B: num] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_eq_div_numeral
% 5.64/5.97 thf(fact_7864_ceiling__less__numeral,axiom,
% 5.64/5.97 ! [X2: rat,V: num] :
% 5.64/5.97 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_numeral
% 5.64/5.97 thf(fact_7865_ceiling__less__numeral,axiom,
% 5.64/5.97 ! [X2: real,V: num] :
% 5.64/5.97 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_numeral
% 5.64/5.97 thf(fact_7866_numeral__le__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_le_ceiling
% 5.64/5.97 thf(fact_7867_numeral__le__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % numeral_le_ceiling
% 5.64/5.97 thf(fact_7868_ceiling__le__neg__numeral,axiom,
% 5.64/5.97 ! [X2: rat,V: num] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_neg_numeral
% 5.64/5.97 thf(fact_7869_ceiling__le__neg__numeral,axiom,
% 5.64/5.97 ! [X2: real,V: num] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_neg_numeral
% 5.64/5.97 thf(fact_7870_neg__numeral__less__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: real] :
% 5.64/5.97 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % neg_numeral_less_ceiling
% 5.64/5.97 thf(fact_7871_neg__numeral__less__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % neg_numeral_less_ceiling
% 5.64/5.97 thf(fact_7872_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.64/5.97 ! [A: num,B: num] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_minus_divide_eq_div_numeral
% 5.64/5.97 thf(fact_7873_ceiling__less__neg__numeral,axiom,
% 5.64/5.97 ! [X2: rat,V: num] :
% 5.64/5.97 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_neg_numeral
% 5.64/5.97 thf(fact_7874_ceiling__less__neg__numeral,axiom,
% 5.64/5.97 ! [X2: real,V: num] :
% 5.64/5.97 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_neg_numeral
% 5.64/5.97 thf(fact_7875_neg__numeral__le__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % neg_numeral_le_ceiling
% 5.64/5.97 thf(fact_7876_neg__numeral__le__ceiling,axiom,
% 5.64/5.97 ! [V: num,X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % neg_numeral_le_ceiling
% 5.64/5.97 thf(fact_7877_ceiling__mono,axiom,
% 5.64/5.97 ! [Y4: rat,X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_rat @ Y4 @ X2 )
% 5.64/5.97 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y4 ) @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_mono
% 5.64/5.97 thf(fact_7878_ceiling__mono,axiom,
% 5.64/5.97 ! [Y4: real,X2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.97 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y4 ) @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_mono
% 5.64/5.97 thf(fact_7879_le__of__int__ceiling,axiom,
% 5.64/5.97 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % le_of_int_ceiling
% 5.64/5.97 thf(fact_7880_le__of__int__ceiling,axiom,
% 5.64/5.97 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % le_of_int_ceiling
% 5.64/5.97 thf(fact_7881_ceiling__less__cancel,axiom,
% 5.64/5.97 ! [X2: rat,Y4: rat] :
% 5.64/5.97 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y4 ) )
% 5.64/5.97 => ( ord_less_rat @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_cancel
% 5.64/5.97 thf(fact_7882_ceiling__less__cancel,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] :
% 5.64/5.97 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y4 ) )
% 5.64/5.97 => ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_cancel
% 5.64/5.97 thf(fact_7883_ceiling__le,axiom,
% 5.64/5.97 ! [X2: rat,A: int] :
% 5.64/5.97 ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) )
% 5.64/5.97 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ A ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le
% 5.64/5.97 thf(fact_7884_ceiling__le,axiom,
% 5.64/5.97 ! [X2: real,A: int] :
% 5.64/5.97 ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) )
% 5.64/5.97 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ A ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le
% 5.64/5.97 thf(fact_7885_ceiling__le__iff,axiom,
% 5.64/5.97 ! [X2: rat,Z: int] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_iff
% 5.64/5.97 thf(fact_7886_ceiling__le__iff,axiom,
% 5.64/5.97 ! [X2: real,Z: int] :
% 5.64/5.97 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_le_iff
% 5.64/5.97 thf(fact_7887_less__ceiling__iff,axiom,
% 5.64/5.97 ! [Z: int,X2: rat] :
% 5.64/5.97 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_ceiling_iff
% 5.64/5.97 thf(fact_7888_less__ceiling__iff,axiom,
% 5.64/5.97 ! [Z: int,X2: real] :
% 5.64/5.97 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % less_ceiling_iff
% 5.64/5.97 thf(fact_7889_ceiling__add__le,axiom,
% 5.64/5.97 ! [X2: rat,Y4: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X2 @ Y4 ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X2 ) @ ( archim2889992004027027881ng_rat @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_le
% 5.64/5.97 thf(fact_7890_ceiling__add__le,axiom,
% 5.64/5.97 ! [X2: real,Y4: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X2 ) @ ( archim7802044766580827645g_real @ Y4 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_add_le
% 5.64/5.97 thf(fact_7891_of__int__ceiling__le__add__one,axiom,
% 5.64/5.97 ! [R2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ ( plus_plus_rat @ R2 @ one_one_rat ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_int_ceiling_le_add_one
% 5.64/5.97 thf(fact_7892_of__int__ceiling__le__add__one,axiom,
% 5.64/5.97 ! [R2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ ( plus_plus_real @ R2 @ one_one_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % of_int_ceiling_le_add_one
% 5.64/5.97 thf(fact_7893_of__int__ceiling__diff__one__le,axiom,
% 5.64/5.97 ! [R2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R2 ) ) @ one_one_rat ) @ R2 ) ).
% 5.64/5.97
% 5.64/5.97 % of_int_ceiling_diff_one_le
% 5.64/5.97 thf(fact_7894_of__int__ceiling__diff__one__le,axiom,
% 5.64/5.97 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R2 ) ) @ one_one_real ) @ R2 ) ).
% 5.64/5.97
% 5.64/5.97 % of_int_ceiling_diff_one_le
% 5.64/5.97 thf(fact_7895_ceiling__divide__eq__div,axiom,
% 5.64/5.97 ! [A: int,B: int] :
% 5.64/5.97 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_eq_div
% 5.64/5.97 thf(fact_7896_ceiling__divide__eq__div,axiom,
% 5.64/5.97 ! [A: int,B: int] :
% 5.64/5.97 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.64/5.97 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_eq_div
% 5.64/5.97 thf(fact_7897_ceiling__split,axiom,
% 5.64/5.97 ! [P: int > $o,T: rat] :
% 5.64/5.97 ( ( P @ ( archim2889992004027027881ng_rat @ T ) )
% 5.64/5.97 = ( ! [I4: int] :
% 5.64/5.97 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T )
% 5.64/5.97 & ( ord_less_eq_rat @ T @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.64/5.97 => ( P @ I4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_split
% 5.64/5.97 thf(fact_7898_ceiling__split,axiom,
% 5.64/5.97 ! [P: int > $o,T: real] :
% 5.64/5.97 ( ( P @ ( archim7802044766580827645g_real @ T ) )
% 5.64/5.97 = ( ! [I4: int] :
% 5.64/5.97 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) @ T )
% 5.64/5.97 & ( ord_less_eq_real @ T @ ( ring_1_of_int_real @ I4 ) ) )
% 5.64/5.97 => ( P @ I4 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_split
% 5.64/5.97 thf(fact_7899_ceiling__eq__iff,axiom,
% 5.64/5.97 ! [X2: rat,A: int] :
% 5.64/5.97 ( ( ( archim2889992004027027881ng_rat @ X2 )
% 5.64/5.97 = A )
% 5.64/5.97 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X2 )
% 5.64/5.97 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_eq_iff
% 5.64/5.97 thf(fact_7900_ceiling__eq__iff,axiom,
% 5.64/5.97 ! [X2: real,A: int] :
% 5.64/5.97 ( ( ( archim7802044766580827645g_real @ X2 )
% 5.64/5.97 = A )
% 5.64/5.97 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X2 )
% 5.64/5.97 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_eq_iff
% 5.64/5.97 thf(fact_7901_ceiling__unique,axiom,
% 5.64/5.97 ! [Z: int,X2: rat] :
% 5.64/5.97 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z ) )
% 5.64/5.97 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.64/5.97 = Z ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_unique
% 5.64/5.97 thf(fact_7902_ceiling__unique,axiom,
% 5.64/5.97 ! [Z: int,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z ) )
% 5.64/5.97 => ( ( archim7802044766580827645g_real @ X2 )
% 5.64/5.97 = Z ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_unique
% 5.64/5.97 thf(fact_7903_ceiling__correct,axiom,
% 5.64/5.97 ! [X2: rat] :
% 5.64/5.97 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) @ one_one_rat ) @ X2 )
% 5.64/5.97 & ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_correct
% 5.64/5.97 thf(fact_7904_ceiling__correct,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) @ one_one_real ) @ X2 )
% 5.64/5.97 & ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_correct
% 5.64/5.97 thf(fact_7905_mult__ceiling__le,axiom,
% 5.64/5.97 ! [A: rat,B: rat] :
% 5.64/5.97 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.97 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.97 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_ceiling_le
% 5.64/5.97 thf(fact_7906_mult__ceiling__le,axiom,
% 5.64/5.97 ! [A: real,B: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.97 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.97 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % mult_ceiling_le
% 5.64/5.97 thf(fact_7907_ceiling__less__iff,axiom,
% 5.64/5.97 ! [X2: rat,Z: int] :
% 5.64/5.97 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X2 ) @ Z )
% 5.64/5.97 = ( ord_less_eq_rat @ X2 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_iff
% 5.64/5.97 thf(fact_7908_ceiling__less__iff,axiom,
% 5.64/5.97 ! [X2: real,Z: int] :
% 5.64/5.97 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X2 ) @ Z )
% 5.64/5.97 = ( ord_less_eq_real @ X2 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_less_iff
% 5.64/5.97 thf(fact_7909_le__ceiling__iff,axiom,
% 5.64/5.97 ! [Z: int,X2: rat] :
% 5.64/5.97 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X2 ) )
% 5.64/5.97 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % le_ceiling_iff
% 5.64/5.97 thf(fact_7910_le__ceiling__iff,axiom,
% 5.64/5.97 ! [Z: int,X2: real] :
% 5.64/5.97 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X2 ) )
% 5.64/5.97 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % le_ceiling_iff
% 5.64/5.97 thf(fact_7911_ceiling__divide__upper,axiom,
% 5.64/5.97 ! [Q3: rat,P2: rat] :
% 5.64/5.97 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.64/5.97 => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_upper
% 5.64/5.97 thf(fact_7912_ceiling__divide__upper,axiom,
% 5.64/5.97 ! [Q3: real,P2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.64/5.97 => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_upper
% 5.64/5.97 thf(fact_7913_ceiling__divide__lower,axiom,
% 5.64/5.97 ! [Q3: real,P2: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.64/5.97 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_lower
% 5.64/5.97 thf(fact_7914_ceiling__divide__lower,axiom,
% 5.64/5.97 ! [Q3: rat,P2: rat] :
% 5.64/5.97 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.64/5.97 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P2 ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_divide_lower
% 5.64/5.97 thf(fact_7915_ceiling__eq,axiom,
% 5.64/5.97 ! [N: int,X2: rat] :
% 5.64/5.97 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N ) @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N ) @ one_one_rat ) )
% 5.64/5.97 => ( ( archim2889992004027027881ng_rat @ X2 )
% 5.64/5.97 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_eq
% 5.64/5.97 thf(fact_7916_ceiling__eq,axiom,
% 5.64/5.97 ! [N: int,X2: real] :
% 5.64/5.97 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.64/5.97 => ( ( ord_less_eq_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.64/5.97 => ( ( archim7802044766580827645g_real @ X2 )
% 5.64/5.97 = ( plus_plus_int @ N @ one_one_int ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_eq
% 5.64/5.97 thf(fact_7917_ceiling__log2__div2,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.97 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.97 = ( 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 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_log2_div2
% 5.64/5.97 thf(fact_7918_ceiling__log__nat__eq__if,axiom,
% 5.64/5.97 ! [B: nat,N: nat,K: nat] :
% 5.64/5.97 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.64/5.97 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.64/5.97 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.97 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_log_nat_eq_if
% 5.64/5.97 thf(fact_7919_ceiling__log__nat__eq__powr__iff,axiom,
% 5.64/5.97 ! [B: nat,K: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.97 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.64/5.97 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.64/5.97 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.64/5.97 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % ceiling_log_nat_eq_powr_iff
% 5.64/5.97 thf(fact_7920_pi__series,axiom,
% 5.64/5.97 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.97 = ( suminf_real
% 5.64/5.97 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % pi_series
% 5.64/5.97 thf(fact_7921_summable__arctan__series,axiom,
% 5.64/5.97 ! [X2: real] :
% 5.64/5.97 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_arctan_series
% 5.64/5.97 thf(fact_7922_and__int_Opsimps,axiom,
% 5.64/5.97 ! [K: int,L: int] :
% 5.64/5.97 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.64/5.97 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.97 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.97 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.64/5.97 = ( uminus_uminus_int
% 5.64/5.97 @ ( zero_n2684676970156552555ol_int
% 5.64/5.97 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.64/5.97 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.97 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.97 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.64/5.97 = ( plus_plus_int
% 5.64/5.97 @ ( zero_n2684676970156552555ol_int
% 5.64/5.97 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.64/5.97 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.64/5.97 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % and_int.psimps
% 5.64/5.97 thf(fact_7923_and__int_Opelims,axiom,
% 5.64/5.97 ! [X2: int,Xa2: int,Y4: int] :
% 5.64/5.97 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.64/5.97 = Y4 )
% 5.64/5.97 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.64/5.97 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.97 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 = ( uminus_uminus_int
% 5.64/5.97 @ ( zero_n2684676970156552555ol_int
% 5.64/5.97 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.64/5.97 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.64/5.97 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.97 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.97 => ( Y4
% 5.64/5.97 = ( plus_plus_int
% 5.64/5.97 @ ( zero_n2684676970156552555ol_int
% 5.64/5.97 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.64/5.97 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.64/5.97 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.64/5.97 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % and_int.pelims
% 5.64/5.97 thf(fact_7924_Maclaurin__exp__lt,axiom,
% 5.64/5.97 ! [X2: real,N: nat] :
% 5.64/5.97 ( ( X2 != zero_zero_real )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.97 => ? [T4: real] :
% 5.64/5.97 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.64/5.97 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/5.97 & ( ( exp_real @ X2 )
% 5.64/5.97 = ( plus_plus_real
% 5.64/5.97 @ ( groups6591440286371151544t_real
% 5.64/5.97 @ ^ [M2: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) )
% 5.64/5.97 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.97 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % Maclaurin_exp_lt
% 5.64/5.97 thf(fact_7925_summable__iff__shift,axiom,
% 5.64/5.97 ! [F: nat > real,K: nat] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.64/5.97 = ( summable_real @ F ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_iff_shift
% 5.64/5.97 thf(fact_7926_fact__0,axiom,
% 5.64/5.97 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.64/5.97 = one_one_complex ) ).
% 5.64/5.97
% 5.64/5.97 % fact_0
% 5.64/5.97 thf(fact_7927_fact__0,axiom,
% 5.64/5.97 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.64/5.97 = one_one_rat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_0
% 5.64/5.97 thf(fact_7928_fact__0,axiom,
% 5.64/5.97 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.64/5.97 = one_one_int ) ).
% 5.64/5.97
% 5.64/5.97 % fact_0
% 5.64/5.97 thf(fact_7929_fact__0,axiom,
% 5.64/5.97 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.64/5.97 = one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % fact_0
% 5.64/5.97 thf(fact_7930_fact__0,axiom,
% 5.64/5.97 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.64/5.97 = one_one_nat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_0
% 5.64/5.97 thf(fact_7931_fact__1,axiom,
% 5.64/5.97 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.64/5.97 = one_one_complex ) ).
% 5.64/5.97
% 5.64/5.97 % fact_1
% 5.64/5.97 thf(fact_7932_fact__1,axiom,
% 5.64/5.97 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.64/5.97 = one_one_rat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_1
% 5.64/5.97 thf(fact_7933_fact__1,axiom,
% 5.64/5.97 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.64/5.97 = one_one_int ) ).
% 5.64/5.97
% 5.64/5.97 % fact_1
% 5.64/5.97 thf(fact_7934_fact__1,axiom,
% 5.64/5.97 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.64/5.97 = one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % fact_1
% 5.64/5.97 thf(fact_7935_fact__1,axiom,
% 5.64/5.97 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.64/5.97 = one_one_nat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_1
% 5.64/5.97 thf(fact_7936_summable__cmult__iff,axiom,
% 5.64/5.97 ! [C: complex,F: nat > complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.64/5.97 = ( ( C = zero_zero_complex )
% 5.64/5.97 | ( summable_complex @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_cmult_iff
% 5.64/5.97 thf(fact_7937_summable__cmult__iff,axiom,
% 5.64/5.97 ! [C: real,F: nat > real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.64/5.97 = ( ( C = zero_zero_real )
% 5.64/5.97 | ( summable_real @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_cmult_iff
% 5.64/5.97 thf(fact_7938_summable__divide__iff,axiom,
% 5.64/5.97 ! [F: nat > complex,C: complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.64/5.97 = ( ( C = zero_zero_complex )
% 5.64/5.97 | ( summable_complex @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_divide_iff
% 5.64/5.97 thf(fact_7939_summable__divide__iff,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.64/5.97 = ( ( C = zero_zero_real )
% 5.64/5.97 | ( summable_real @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_divide_iff
% 5.64/5.97 thf(fact_7940_fact__Suc__0,axiom,
% 5.64/5.97 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = one_one_complex ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc_0
% 5.64/5.97 thf(fact_7941_fact__Suc__0,axiom,
% 5.64/5.97 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = one_one_rat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc_0
% 5.64/5.97 thf(fact_7942_fact__Suc__0,axiom,
% 5.64/5.97 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = one_one_int ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc_0
% 5.64/5.97 thf(fact_7943_fact__Suc__0,axiom,
% 5.64/5.97 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = one_one_real ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc_0
% 5.64/5.97 thf(fact_7944_fact__Suc__0,axiom,
% 5.64/5.97 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.64/5.97 = one_one_nat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc_0
% 5.64/5.97 thf(fact_7945_fact__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 5.64/5.97 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc
% 5.64/5.97 thf(fact_7946_fact__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 5.64/5.97 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc
% 5.64/5.97 thf(fact_7947_fact__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri5044797733671781792omplex @ ( suc @ N ) )
% 5.64/5.97 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc
% 5.64/5.97 thf(fact_7948_fact__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 5.64/5.97 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc
% 5.64/5.97 thf(fact_7949_fact__Suc,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 5.64/5.97 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_Suc
% 5.64/5.97 thf(fact_7950_fact__2,axiom,
% 5.64/5.97 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_2
% 5.64/5.97 thf(fact_7951_fact__2,axiom,
% 5.64/5.97 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_2
% 5.64/5.97 thf(fact_7952_fact__2,axiom,
% 5.64/5.97 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_2
% 5.64/5.97 thf(fact_7953_fact__2,axiom,
% 5.64/5.97 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_2
% 5.64/5.97 thf(fact_7954_fact__2,axiom,
% 5.64/5.97 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.97 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_2
% 5.64/5.97 thf(fact_7955_summable__geometric__iff,axiom,
% 5.64/5.97 ! [C: real] :
% 5.64/5.97 ( ( summable_real @ ( power_power_real @ C ) )
% 5.64/5.97 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_geometric_iff
% 5.64/5.97 thf(fact_7956_summable__geometric__iff,axiom,
% 5.64/5.97 ! [C: complex] :
% 5.64/5.97 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.64/5.97 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_geometric_iff
% 5.64/5.97 thf(fact_7957_summable__comparison__test_H,axiom,
% 5.64/5.97 ! [G: nat > real,N5: nat,F: nat > real] :
% 5.64/5.97 ( ( summable_real @ G )
% 5.64/5.97 => ( ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.64/5.97 => ( summable_real @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_comparison_test'
% 5.64/5.97 thf(fact_7958_summable__comparison__test_H,axiom,
% 5.64/5.97 ! [G: nat > real,N5: nat,F: nat > complex] :
% 5.64/5.97 ( ( summable_real @ G )
% 5.64/5.97 => ( ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.64/5.97 => ( summable_complex @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_comparison_test'
% 5.64/5.97 thf(fact_7959_summable__comparison__test,axiom,
% 5.64/5.97 ! [F: nat > real,G: nat > real] :
% 5.64/5.97 ( ? [N8: nat] :
% 5.64/5.97 ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( summable_real @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_comparison_test
% 5.64/5.97 thf(fact_7960_summable__comparison__test,axiom,
% 5.64/5.97 ! [F: nat > complex,G: nat > real] :
% 5.64/5.97 ( ? [N8: nat] :
% 5.64/5.97 ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( summable_complex @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_comparison_test
% 5.64/5.97 thf(fact_7961_summable__mult2,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_mult2
% 5.64/5.97 thf(fact_7962_summable__mult,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_mult
% 5.64/5.97 thf(fact_7963_summable__add,axiom,
% 5.64/5.97 ! [F: nat > real,G: nat > real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_add
% 5.64/5.97 thf(fact_7964_summable__add,axiom,
% 5.64/5.97 ! [F: nat > nat,G: nat > nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.97 => ( ( summable_nat @ G )
% 5.64/5.97 => ( summable_nat
% 5.64/5.97 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_add
% 5.64/5.97 thf(fact_7965_summable__add,axiom,
% 5.64/5.97 ! [F: nat > int,G: nat > int] :
% 5.64/5.97 ( ( summable_int @ F )
% 5.64/5.97 => ( ( summable_int @ G )
% 5.64/5.97 => ( summable_int
% 5.64/5.97 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_add
% 5.64/5.97 thf(fact_7966_summable__divide,axiom,
% 5.64/5.97 ! [F: nat > complex,C: complex] :
% 5.64/5.97 ( ( summable_complex @ F )
% 5.64/5.97 => ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_divide
% 5.64/5.97 thf(fact_7967_summable__divide,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_divide
% 5.64/5.97 thf(fact_7968_summable__Suc__iff,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.64/5.97 = ( summable_real @ F ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_Suc_iff
% 5.64/5.97 thf(fact_7969_summable__ignore__initial__segment,axiom,
% 5.64/5.97 ! [F: nat > real,K: nat] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_ignore_initial_segment
% 5.64/5.97 thf(fact_7970_powser__insidea,axiom,
% 5.64/5.97 ! [F: nat > real,X2: real,Z: real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % powser_insidea
% 5.64/5.97 thf(fact_7971_powser__insidea,axiom,
% 5.64/5.97 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.64/5.97 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % powser_insidea
% 5.64/5.97 thf(fact_7972_suminf__le,axiom,
% 5.64/5.97 ! [F: nat > nat,G: nat > nat] :
% 5.64/5.97 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/5.97 => ( ( summable_nat @ F )
% 5.64/5.97 => ( ( summable_nat @ G )
% 5.64/5.97 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_le
% 5.64/5.97 thf(fact_7973_suminf__le,axiom,
% 5.64/5.97 ! [F: nat > int,G: nat > int] :
% 5.64/5.97 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/5.97 => ( ( summable_int @ F )
% 5.64/5.97 => ( ( summable_int @ G )
% 5.64/5.97 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_le
% 5.64/5.97 thf(fact_7974_suminf__le,axiom,
% 5.64/5.97 ! [F: nat > real,G: nat > real] :
% 5.64/5.97 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/5.97 => ( ( summable_real @ F )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_le
% 5.64/5.97 thf(fact_7975_fact__ge__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_zero
% 5.64/5.97 thf(fact_7976_fact__ge__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_zero
% 5.64/5.97 thf(fact_7977_fact__ge__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_zero
% 5.64/5.97 thf(fact_7978_fact__ge__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_zero
% 5.64/5.97 thf(fact_7979_fact__not__neg,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_not_neg
% 5.64/5.97 thf(fact_7980_fact__not__neg,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 5.64/5.97
% 5.64/5.97 % fact_not_neg
% 5.64/5.97 thf(fact_7981_fact__not__neg,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 5.64/5.97
% 5.64/5.97 % fact_not_neg
% 5.64/5.97 thf(fact_7982_fact__not__neg,axiom,
% 5.64/5.97 ! [N: nat] :
% 5.64/5.97 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 5.64/5.97
% 5.64/5.97 % fact_not_neg
% 5.64/5.97 thf(fact_7983_fact__gt__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_gt_zero
% 5.64/5.97 thf(fact_7984_fact__gt__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_gt_zero
% 5.64/5.97 thf(fact_7985_fact__gt__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_gt_zero
% 5.64/5.97 thf(fact_7986_fact__gt__zero,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_gt_zero
% 5.64/5.97 thf(fact_7987_fact__ge__1,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_1
% 5.64/5.97 thf(fact_7988_fact__ge__1,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_1
% 5.64/5.97 thf(fact_7989_fact__ge__1,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_1
% 5.64/5.97 thf(fact_7990_fact__ge__1,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_ge_1
% 5.64/5.97 thf(fact_7991_fact__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mono
% 5.64/5.97 thf(fact_7992_fact__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mono
% 5.64/5.97 thf(fact_7993_fact__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mono
% 5.64/5.97 thf(fact_7994_fact__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mono
% 5.64/5.97 thf(fact_7995_summable__mult__D,axiom,
% 5.64/5.97 ! [C: complex,F: nat > complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) ) )
% 5.64/5.97 => ( ( C != zero_zero_complex )
% 5.64/5.97 => ( summable_complex @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_mult_D
% 5.64/5.97 thf(fact_7996_summable__mult__D,axiom,
% 5.64/5.97 ! [C: real,F: nat > real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.64/5.97 => ( ( C != zero_zero_real )
% 5.64/5.97 => ( summable_real @ F ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_mult_D
% 5.64/5.97 thf(fact_7997_fact__dvd,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_dvd
% 5.64/5.97 thf(fact_7998_fact__dvd,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_dvd
% 5.64/5.97 thf(fact_7999_fact__dvd,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_dvd
% 5.64/5.97 thf(fact_8000_fact__dvd,axiom,
% 5.64/5.97 ! [N: nat,M: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.97 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_dvd
% 5.64/5.97 thf(fact_8001_summable__zero__power,axiom,
% 5.64/5.97 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.64/5.97
% 5.64/5.97 % summable_zero_power
% 5.64/5.97 thf(fact_8002_summable__zero__power,axiom,
% 5.64/5.97 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.64/5.97
% 5.64/5.97 % summable_zero_power
% 5.64/5.97 thf(fact_8003_summable__zero__power,axiom,
% 5.64/5.97 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.64/5.97
% 5.64/5.97 % summable_zero_power
% 5.64/5.97 thf(fact_8004_pi__not__less__zero,axiom,
% 5.64/5.97 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.64/5.97
% 5.64/5.97 % pi_not_less_zero
% 5.64/5.97 thf(fact_8005_pi__gt__zero,axiom,
% 5.64/5.97 ord_less_real @ zero_zero_real @ pi ).
% 5.64/5.97
% 5.64/5.97 % pi_gt_zero
% 5.64/5.97 thf(fact_8006_suminf__mult,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ( suminf_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) ) )
% 5.64/5.97 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_mult
% 5.64/5.97 thf(fact_8007_suminf__mult2,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.64/5.97 = ( suminf_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_mult2
% 5.64/5.97 thf(fact_8008_suminf__add,axiom,
% 5.64/5.97 ! [F: nat > real,G: nat > real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.64/5.97 = ( suminf_real
% 5.64/5.97 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_add
% 5.64/5.97 thf(fact_8009_suminf__add,axiom,
% 5.64/5.97 ! [F: nat > nat,G: nat > nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.97 => ( ( summable_nat @ G )
% 5.64/5.97 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.64/5.97 = ( suminf_nat
% 5.64/5.97 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_add
% 5.64/5.97 thf(fact_8010_suminf__add,axiom,
% 5.64/5.97 ! [F: nat > int,G: nat > int] :
% 5.64/5.97 ( ( summable_int @ F )
% 5.64/5.97 => ( ( summable_int @ G )
% 5.64/5.97 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.64/5.97 = ( suminf_int
% 5.64/5.97 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_add
% 5.64/5.97 thf(fact_8011_suminf__divide,axiom,
% 5.64/5.97 ! [F: nat > complex,C: complex] :
% 5.64/5.97 ( ( summable_complex @ F )
% 5.64/5.97 => ( ( suminf_complex
% 5.64/5.97 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C ) )
% 5.64/5.97 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_divide
% 5.64/5.97 thf(fact_8012_suminf__divide,axiom,
% 5.64/5.97 ! [F: nat > real,C: real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ( suminf_real
% 5.64/5.97 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C ) )
% 5.64/5.97 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_divide
% 5.64/5.97 thf(fact_8013_suminf__eq__zero__iff,axiom,
% 5.64/5.97 ! [F: nat > nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.64/5.97 => ( ( ( suminf_nat @ F )
% 5.64/5.97 = zero_zero_nat )
% 5.64/5.97 = ( ! [N2: nat] :
% 5.64/5.97 ( ( F @ N2 )
% 5.64/5.97 = zero_zero_nat ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_eq_zero_iff
% 5.64/5.97 thf(fact_8014_suminf__eq__zero__iff,axiom,
% 5.64/5.97 ! [F: nat > int] :
% 5.64/5.97 ( ( summable_int @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.64/5.97 => ( ( ( suminf_int @ F )
% 5.64/5.97 = zero_zero_int )
% 5.64/5.97 = ( ! [N2: nat] :
% 5.64/5.97 ( ( F @ N2 )
% 5.64/5.97 = zero_zero_int ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_eq_zero_iff
% 5.64/5.97 thf(fact_8015_suminf__eq__zero__iff,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.64/5.97 => ( ( ( suminf_real @ F )
% 5.64/5.97 = zero_zero_real )
% 5.64/5.97 = ( ! [N2: nat] :
% 5.64/5.97 ( ( F @ N2 )
% 5.64/5.97 = zero_zero_real ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_eq_zero_iff
% 5.64/5.97 thf(fact_8016_suminf__nonneg,axiom,
% 5.64/5.97 ! [F: nat > nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.64/5.97 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_nonneg
% 5.64/5.97 thf(fact_8017_suminf__nonneg,axiom,
% 5.64/5.97 ! [F: nat > int] :
% 5.64/5.97 ( ( summable_int @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.64/5.97 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_nonneg
% 5.64/5.97 thf(fact_8018_suminf__nonneg,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.64/5.97 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_nonneg
% 5.64/5.97 thf(fact_8019_suminf__pos,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.64/5.97 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_pos
% 5.64/5.97 thf(fact_8020_suminf__pos,axiom,
% 5.64/5.97 ! [F: nat > nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.64/5.97 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_pos
% 5.64/5.97 thf(fact_8021_suminf__pos,axiom,
% 5.64/5.97 ! [F: nat > int] :
% 5.64/5.97 ( ( summable_int @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.64/5.97 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_pos
% 5.64/5.97 thf(fact_8022_summable__0__powser,axiom,
% 5.64/5.97 ! [F: nat > complex] :
% 5.64/5.97 ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_0_powser
% 5.64/5.97 thf(fact_8023_summable__0__powser,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_0_powser
% 5.64/5.97 thf(fact_8024_summable__zero__power_H,axiom,
% 5.64/5.97 ! [F: nat > complex] :
% 5.64/5.97 ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_zero_power'
% 5.64/5.97 thf(fact_8025_summable__zero__power_H,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_zero_power'
% 5.64/5.97 thf(fact_8026_summable__zero__power_H,axiom,
% 5.64/5.97 ! [F: nat > int] :
% 5.64/5.97 ( summable_int
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_int @ ( F @ N2 ) @ ( power_power_int @ zero_zero_int @ N2 ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_zero_power'
% 5.64/5.97 thf(fact_8027_powser__split__head_I3_J,axiom,
% 5.64/5.97 ! [F: nat > complex,Z: complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.97 => ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % powser_split_head(3)
% 5.64/5.97 thf(fact_8028_powser__split__head_I3_J,axiom,
% 5.64/5.97 ! [F: nat > real,Z: real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % powser_split_head(3)
% 5.64/5.97 thf(fact_8029_summable__powser__split__head,axiom,
% 5.64/5.97 ! [F: nat > complex,Z: complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.97 = ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_powser_split_head
% 5.64/5.97 thf(fact_8030_summable__powser__split__head,axiom,
% 5.64/5.97 ! [F: nat > real,Z: real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.97 = ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_powser_split_head
% 5.64/5.97 thf(fact_8031_summable__powser__ignore__initial__segment,axiom,
% 5.64/5.97 ! [F: nat > complex,M: nat,Z: complex] :
% 5.64/5.97 ( ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.97 = ( summable_complex
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_powser_ignore_initial_segment
% 5.64/5.97 thf(fact_8032_summable__powser__ignore__initial__segment,axiom,
% 5.64/5.97 ! [F: nat > real,M: nat,Z: real] :
% 5.64/5.97 ( ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N2 @ M ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.97 = ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_powser_ignore_initial_segment
% 5.64/5.97 thf(fact_8033_fact__less__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_less_mono
% 5.64/5.97 thf(fact_8034_fact__less__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_less_mono
% 5.64/5.97 thf(fact_8035_fact__less__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_less_mono
% 5.64/5.97 thf(fact_8036_fact__less__mono,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.97 => ( ( ord_less_nat @ M @ N )
% 5.64/5.97 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_less_mono
% 5.64/5.97 thf(fact_8037_fact__fact__dvd__fact,axiom,
% 5.64/5.97 ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_fact_dvd_fact
% 5.64/5.97 thf(fact_8038_fact__fact__dvd__fact,axiom,
% 5.64/5.97 ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_fact_dvd_fact
% 5.64/5.97 thf(fact_8039_fact__fact__dvd__fact,axiom,
% 5.64/5.97 ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_fact_dvd_fact
% 5.64/5.97 thf(fact_8040_fact__fact__dvd__fact,axiom,
% 5.64/5.97 ! [K: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_fact_dvd_fact
% 5.64/5.97 thf(fact_8041_fact__fact__dvd__fact,axiom,
% 5.64/5.97 ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_fact_dvd_fact
% 5.64/5.97 thf(fact_8042_fact__mod,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.64/5.97 = zero_zero_int ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mod
% 5.64/5.97 thf(fact_8043_fact__mod,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.64/5.97 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mod
% 5.64/5.97 thf(fact_8044_fact__mod,axiom,
% 5.64/5.97 ! [M: nat,N: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.97 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.64/5.97 = zero_zero_nat ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_mod
% 5.64/5.97 thf(fact_8045_fact__le__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_le_power
% 5.64/5.97 thf(fact_8046_fact__le__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_le_power
% 5.64/5.97 thf(fact_8047_fact__le__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_le_power
% 5.64/5.97 thf(fact_8048_fact__le__power,axiom,
% 5.64/5.97 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % fact_le_power
% 5.64/5.97 thf(fact_8049_summable__norm__comparison__test,axiom,
% 5.64/5.97 ! [F: nat > complex,G: nat > real] :
% 5.64/5.97 ( ? [N8: nat] :
% 5.64/5.97 ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.64/5.97 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( real_V1022390504157884413omplex @ ( F @ N2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_norm_comparison_test
% 5.64/5.97 thf(fact_8050_summable__rabs__comparison__test,axiom,
% 5.64/5.97 ! [F: nat > real,G: nat > real] :
% 5.64/5.97 ( ? [N8: nat] :
% 5.64/5.97 ! [N3: nat] :
% 5.64/5.97 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.64/5.97 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.64/5.97 => ( ( summable_real @ G )
% 5.64/5.97 => ( summable_real
% 5.64/5.97 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % summable_rabs_comparison_test
% 5.64/5.97 thf(fact_8051_suminf__pos__iff,axiom,
% 5.64/5.97 ! [F: nat > nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.64/5.97 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.64/5.97 = ( ? [I4: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_pos_iff
% 5.64/5.97 thf(fact_8052_suminf__pos__iff,axiom,
% 5.64/5.97 ! [F: nat > int] :
% 5.64/5.97 ( ( summable_int @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.64/5.97 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.64/5.97 = ( ? [I4: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_pos_iff
% 5.64/5.97 thf(fact_8053_suminf__pos__iff,axiom,
% 5.64/5.97 ! [F: nat > real] :
% 5.64/5.97 ( ( summable_real @ F )
% 5.64/5.97 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.64/5.97 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.64/5.97 = ( ? [I4: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) ) ) ) ) ).
% 5.64/5.97
% 5.64/5.97 % suminf_pos_iff
% 5.64/5.97 thf(fact_8054_suminf__pos2,axiom,
% 5.64/5.97 ! [F: nat > nat,I: nat] :
% 5.64/5.97 ( ( summable_nat @ F )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.64/5.98 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.64/5.98 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_pos2
% 5.64/5.98 thf(fact_8055_suminf__pos2,axiom,
% 5.64/5.98 ! [F: nat > int,I: nat] :
% 5.64/5.98 ( ( summable_int @ F )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.64/5.98 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.64/5.98 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_pos2
% 5.64/5.98 thf(fact_8056_suminf__pos2,axiom,
% 5.64/5.98 ! [F: nat > real,I: nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_pos2
% 5.64/5.98 thf(fact_8057_suminf__le__const,axiom,
% 5.64/5.98 ! [F: nat > int,X2: int] :
% 5.64/5.98 ( ( summable_int @ F )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.64/5.98 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_le_const
% 5.64/5.98 thf(fact_8058_suminf__le__const,axiom,
% 5.64/5.98 ! [F: nat > nat,X2: nat] :
% 5.64/5.98 ( ( summable_nat @ F )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.64/5.98 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_le_const
% 5.64/5.98 thf(fact_8059_suminf__le__const,axiom,
% 5.64/5.98 ! [F: nat > real,X2: real] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.64/5.98 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_le_const
% 5.64/5.98 thf(fact_8060_powser__inside,axiom,
% 5.64/5.98 ! [F: nat > real,X2: real,Z: real] :
% 5.64/5.98 ( ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.64/5.98 => ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_inside
% 5.64/5.98 thf(fact_8061_powser__inside,axiom,
% 5.64/5.98 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.64/5.98 ( ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.64/5.98 => ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_inside
% 5.64/5.98 thf(fact_8062_summableI__nonneg__bounded,axiom,
% 5.64/5.98 ! [F: nat > int,X2: int] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.64/5.98 => ( summable_int @ F ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summableI_nonneg_bounded
% 5.64/5.98 thf(fact_8063_summableI__nonneg__bounded,axiom,
% 5.64/5.98 ! [F: nat > nat,X2: nat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.64/5.98 => ( summable_nat @ F ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summableI_nonneg_bounded
% 5.64/5.98 thf(fact_8064_summableI__nonneg__bounded,axiom,
% 5.64/5.98 ! [F: nat > real,X2: real] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X2 )
% 5.64/5.98 => ( summable_real @ F ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summableI_nonneg_bounded
% 5.64/5.98 thf(fact_8065_summable__geometric,axiom,
% 5.64/5.98 ! [C: real] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.64/5.98 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_geometric
% 5.64/5.98 thf(fact_8066_summable__geometric,axiom,
% 5.64/5.98 ! [C: complex] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.64/5.98 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_geometric
% 5.64/5.98 thf(fact_8067_complete__algebra__summable__geometric,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ one_one_real )
% 5.64/5.98 => ( summable_real @ ( power_power_real @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % complete_algebra_summable_geometric
% 5.64/5.98 thf(fact_8068_complete__algebra__summable__geometric,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ one_one_real )
% 5.64/5.98 => ( summable_complex @ ( power_power_complex @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % complete_algebra_summable_geometric
% 5.64/5.98 thf(fact_8069_suminf__split__head,axiom,
% 5.64/5.98 ! [F: nat > real] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) ) )
% 5.64/5.98 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_split_head
% 5.64/5.98 thf(fact_8070_choose__dvd,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_dvd
% 5.64/5.98 thf(fact_8071_choose__dvd,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_dvd
% 5.64/5.98 thf(fact_8072_choose__dvd,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_dvd
% 5.64/5.98 thf(fact_8073_choose__dvd,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_dvd
% 5.64/5.98 thf(fact_8074_choose__dvd,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_dvd
% 5.64/5.98 thf(fact_8075_pi__less__4,axiom,
% 5.64/5.98 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pi_less_4
% 5.64/5.98 thf(fact_8076_pi__ge__two,axiom,
% 5.64/5.98 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.64/5.98
% 5.64/5.98 % pi_ge_two
% 5.64/5.98 thf(fact_8077_pi__half__neq__two,axiom,
% 5.64/5.98 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pi_half_neq_two
% 5.64/5.98 thf(fact_8078_fact__numeral,axiom,
% 5.64/5.98 ! [K: num] :
% 5.64/5.98 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.64/5.98 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_numeral
% 5.64/5.98 thf(fact_8079_fact__numeral,axiom,
% 5.64/5.98 ! [K: num] :
% 5.64/5.98 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.64/5.98 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_numeral
% 5.64/5.98 thf(fact_8080_fact__numeral,axiom,
% 5.64/5.98 ! [K: num] :
% 5.64/5.98 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.64/5.98 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_numeral
% 5.64/5.98 thf(fact_8081_fact__numeral,axiom,
% 5.64/5.98 ! [K: num] :
% 5.64/5.98 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.64/5.98 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_numeral
% 5.64/5.98 thf(fact_8082_fact__numeral,axiom,
% 5.64/5.98 ! [K: num] :
% 5.64/5.98 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.64/5.98 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_numeral
% 5.64/5.98 thf(fact_8083_sum__le__suminf,axiom,
% 5.64/5.98 ! [F: nat > int,I5: set_nat] :
% 5.64/5.98 ( ( summable_int @ F )
% 5.64/5.98 => ( ( finite_finite_nat @ I5 )
% 5.64/5.98 => ( ! [N3: nat] :
% 5.64/5.98 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.64/5.98 => ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) ) )
% 5.64/5.98 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ I5 ) @ ( suminf_int @ F ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_le_suminf
% 5.64/5.98 thf(fact_8084_sum__le__suminf,axiom,
% 5.64/5.98 ! [F: nat > nat,I5: set_nat] :
% 5.64/5.98 ( ( summable_nat @ F )
% 5.64/5.98 => ( ( finite_finite_nat @ I5 )
% 5.64/5.98 => ( ! [N3: nat] :
% 5.64/5.98 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.64/5.98 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) ) )
% 5.64/5.98 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ I5 ) @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_le_suminf
% 5.64/5.98 thf(fact_8085_sum__le__suminf,axiom,
% 5.64/5.98 ! [F: nat > real,I5: set_nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ( finite_finite_nat @ I5 )
% 5.64/5.98 => ( ! [N3: nat] :
% 5.64/5.98 ( ( member_nat @ N3 @ ( uminus5710092332889474511et_nat @ I5 ) )
% 5.64/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) ) )
% 5.64/5.98 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ I5 ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_le_suminf
% 5.64/5.98 thf(fact_8086_suminf__split__initial__segment,axiom,
% 5.64/5.98 ! [F: nat > real,K: nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ( suminf_real @ F )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.64/5.98 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_split_initial_segment
% 5.64/5.98 thf(fact_8087_suminf__minus__initial__segment,axiom,
% 5.64/5.98 ! [F: nat > real,K: nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.64/5.98 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_minus_initial_segment
% 5.64/5.98 thf(fact_8088_pi__half__neq__zero,axiom,
% 5.64/5.98 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 != zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % pi_half_neq_zero
% 5.64/5.98 thf(fact_8089_pi__half__less__two,axiom,
% 5.64/5.98 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.64/5.98
% 5.64/5.98 % pi_half_less_two
% 5.64/5.98 thf(fact_8090_pi__half__le__two,axiom,
% 5.64/5.98 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.64/5.98
% 5.64/5.98 % pi_half_le_two
% 5.64/5.98 thf(fact_8091_sum__less__suminf,axiom,
% 5.64/5.98 ! [F: nat > int,N: nat] :
% 5.64/5.98 ( ( summable_int @ F )
% 5.64/5.98 => ( ! [M4: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N @ M4 )
% 5.64/5.98 => ( ord_less_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.64/5.98 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_less_suminf
% 5.64/5.98 thf(fact_8092_sum__less__suminf,axiom,
% 5.64/5.98 ! [F: nat > nat,N: nat] :
% 5.64/5.98 ( ( summable_nat @ F )
% 5.64/5.98 => ( ! [M4: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N @ M4 )
% 5.64/5.98 => ( ord_less_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.64/5.98 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_less_suminf
% 5.64/5.98 thf(fact_8093_sum__less__suminf,axiom,
% 5.64/5.98 ! [F: nat > real,N: nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ! [M4: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N @ M4 )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.64/5.98 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_less_suminf
% 5.64/5.98 thf(fact_8094_square__fact__le__2__fact,axiom,
% 5.64/5.98 ! [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 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % square_fact_le_2_fact
% 5.64/5.98 thf(fact_8095_powser__split__head_I1_J,axiom,
% 5.64/5.98 ! [F: nat > complex,Z: complex] :
% 5.64/5.98 ( ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.98 => ( ( suminf_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.98 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.64/5.98 @ ( times_times_complex
% 5.64/5.98 @ ( suminf_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.98 @ Z ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_split_head(1)
% 5.64/5.98 thf(fact_8096_powser__split__head_I1_J,axiom,
% 5.64/5.98 ! [F: nat > real,Z: real] :
% 5.64/5.98 ( ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.98 => ( ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.98 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.64/5.98 @ ( times_times_real
% 5.64/5.98 @ ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.98 @ Z ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_split_head(1)
% 5.64/5.98 thf(fact_8097_powser__split__head_I2_J,axiom,
% 5.64/5.98 ! [F: nat > complex,Z: complex] :
% 5.64/5.98 ( ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.98 => ( ( times_times_complex
% 5.64/5.98 @ ( suminf_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.98 @ Z )
% 5.64/5.98 = ( minus_minus_complex
% 5.64/5.98 @ ( suminf_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) )
% 5.64/5.98 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_split_head(2)
% 5.64/5.98 thf(fact_8098_powser__split__head_I2_J,axiom,
% 5.64/5.98 ! [F: nat > real,Z: real] :
% 5.64/5.98 ( ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.98 => ( ( times_times_real
% 5.64/5.98 @ ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.98 @ Z )
% 5.64/5.98 = ( minus_minus_real
% 5.64/5.98 @ ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ Z @ N2 ) ) )
% 5.64/5.98 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_split_head(2)
% 5.64/5.98 thf(fact_8099_summable__partial__sum__bound,axiom,
% 5.64/5.98 ! [F: nat > complex,E: real] :
% 5.64/5.98 ( ( summable_complex @ F )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.64/5.98 => ~ ! [N9: nat] :
% 5.64/5.98 ~ ! [M5: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N9 @ M5 )
% 5.64/5.98 => ! [N7: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M5 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_partial_sum_bound
% 5.64/5.98 thf(fact_8100_summable__partial__sum__bound,axiom,
% 5.64/5.98 ! [F: nat > real,E: real] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.64/5.98 => ~ ! [N9: nat] :
% 5.64/5.98 ~ ! [M5: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N9 @ M5 )
% 5.64/5.98 => ! [N7: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M5 @ N7 ) ) ) @ E ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_partial_sum_bound
% 5.64/5.98 thf(fact_8101_suminf__exist__split,axiom,
% 5.64/5.98 ! [R2: real,F: nat > real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.64/5.98 => ( ( summable_real @ F )
% 5.64/5.98 => ? [N9: nat] :
% 5.64/5.98 ! [N7: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.64/5.98 => ( ord_less_real
% 5.64/5.98 @ ( real_V7735802525324610683m_real
% 5.64/5.98 @ ( suminf_real
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N7 ) ) ) )
% 5.64/5.98 @ R2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_exist_split
% 5.64/5.98 thf(fact_8102_suminf__exist__split,axiom,
% 5.64/5.98 ! [R2: real,F: nat > complex] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.64/5.98 => ( ( summable_complex @ F )
% 5.64/5.98 => ? [N9: nat] :
% 5.64/5.98 ! [N7: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N9 @ N7 )
% 5.64/5.98 => ( ord_less_real
% 5.64/5.98 @ ( real_V1022390504157884413omplex
% 5.64/5.98 @ ( suminf_complex
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N7 ) ) ) )
% 5.64/5.98 @ R2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % suminf_exist_split
% 5.64/5.98 thf(fact_8103_summable__power__series,axiom,
% 5.64/5.98 ! [F: nat > real,Z: real] :
% 5.64/5.98 ( ! [I3: nat] : ( ord_less_eq_real @ ( F @ I3 ) @ one_one_real )
% 5.64/5.98 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.64/5.98 => ( ( ord_less_real @ Z @ one_one_real )
% 5.64/5.98 => ( summable_real
% 5.64/5.98 @ ^ [I4: nat] : ( times_times_real @ ( F @ I4 ) @ ( power_power_real @ Z @ I4 ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_power_series
% 5.64/5.98 thf(fact_8104_Abel__lemma,axiom,
% 5.64/5.98 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.64/5.98 => ( ( ord_less_real @ R2 @ R0 )
% 5.64/5.98 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.64/5.98 => ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N2 ) ) @ ( power_power_real @ R2 @ N2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Abel_lemma
% 5.64/5.98 thf(fact_8105_fact__num__eq__if,axiom,
% 5.64/5.98 ( semiri773545260158071498ct_rat
% 5.64/5.98 = ( ^ [M2: nat] : ( if_rat @ ( M2 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_num_eq_if
% 5.64/5.98 thf(fact_8106_fact__num__eq__if,axiom,
% 5.64/5.98 ( semiri1406184849735516958ct_int
% 5.64/5.98 = ( ^ [M2: nat] : ( if_int @ ( M2 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_num_eq_if
% 5.64/5.98 thf(fact_8107_fact__num__eq__if,axiom,
% 5.64/5.98 ( semiri5044797733671781792omplex
% 5.64/5.98 = ( ^ [M2: nat] : ( if_complex @ ( M2 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_num_eq_if
% 5.64/5.98 thf(fact_8108_fact__num__eq__if,axiom,
% 5.64/5.98 ( semiri2265585572941072030t_real
% 5.64/5.98 = ( ^ [M2: nat] : ( if_real @ ( M2 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_num_eq_if
% 5.64/5.98 thf(fact_8109_fact__num__eq__if,axiom,
% 5.64/5.98 ( semiri1408675320244567234ct_nat
% 5.64/5.98 = ( ^ [M2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_num_eq_if
% 5.64/5.98 thf(fact_8110_fact__reduce,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( semiri773545260158071498ct_rat @ N )
% 5.64/5.98 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_reduce
% 5.64/5.98 thf(fact_8111_fact__reduce,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( semiri1406184849735516958ct_int @ N )
% 5.64/5.98 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_reduce
% 5.64/5.98 thf(fact_8112_fact__reduce,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( semiri5044797733671781792omplex @ N )
% 5.64/5.98 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_reduce
% 5.64/5.98 thf(fact_8113_fact__reduce,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( semiri2265585572941072030t_real @ N )
% 5.64/5.98 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_reduce
% 5.64/5.98 thf(fact_8114_fact__reduce,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( semiri1408675320244567234ct_nat @ N )
% 5.64/5.98 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_reduce
% 5.64/5.98 thf(fact_8115_pi__half__gt__zero,axiom,
% 5.64/5.98 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pi_half_gt_zero
% 5.64/5.98 thf(fact_8116_pi__half__ge__zero,axiom,
% 5.64/5.98 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pi_half_ge_zero
% 5.64/5.98 thf(fact_8117_m2pi__less__pi,axiom,
% 5.64/5.98 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.64/5.98
% 5.64/5.98 % m2pi_less_pi
% 5.64/5.98 thf(fact_8118_summable__ratio__test,axiom,
% 5.64/5.98 ! [C: real,N5: nat,F: nat > real] :
% 5.64/5.98 ( ( ord_less_real @ C @ one_one_real )
% 5.64/5.98 => ( ! [N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.64/5.98 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.64/5.98 => ( summable_real @ F ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_ratio_test
% 5.64/5.98 thf(fact_8119_summable__ratio__test,axiom,
% 5.64/5.98 ! [C: real,N5: nat,F: nat > complex] :
% 5.64/5.98 ( ( ord_less_real @ C @ one_one_real )
% 5.64/5.98 => ( ! [N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N5 @ N3 )
% 5.64/5.98 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.64/5.98 => ( summable_complex @ F ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % summable_ratio_test
% 5.64/5.98 thf(fact_8120_sum__less__suminf2,axiom,
% 5.64/5.98 ! [F: nat > int,N: nat,I: nat] :
% 5.64/5.98 ( ( summable_int @ F )
% 5.64/5.98 => ( ! [M4: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N @ M4 )
% 5.64/5.98 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M4 ) ) )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ I )
% 5.64/5.98 => ( ( ord_less_int @ zero_zero_int @ ( F @ I ) )
% 5.64/5.98 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_less_suminf2
% 5.64/5.98 thf(fact_8121_sum__less__suminf2,axiom,
% 5.64/5.98 ! [F: nat > nat,N: nat,I: nat] :
% 5.64/5.98 ( ( summable_nat @ F )
% 5.64/5.98 => ( ! [M4: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N @ M4 )
% 5.64/5.98 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M4 ) ) )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ I )
% 5.64/5.98 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.64/5.98 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_less_suminf2
% 5.64/5.98 thf(fact_8122_sum__less__suminf2,axiom,
% 5.64/5.98 ! [F: nat > real,N: nat,I: nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ! [M4: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ N @ M4 )
% 5.64/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M4 ) ) )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ I )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.64/5.98 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_less_suminf2
% 5.64/5.98 thf(fact_8123_arctan__ubound,axiom,
% 5.64/5.98 ! [Y4: real] : ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_ubound
% 5.64/5.98 thf(fact_8124_arctan__one,axiom,
% 5.64/5.98 ( ( arctan @ one_one_real )
% 5.64/5.98 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_one
% 5.64/5.98 thf(fact_8125_minus__pi__half__less__zero,axiom,
% 5.64/5.98 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.64/5.98
% 5.64/5.98 % minus_pi_half_less_zero
% 5.64/5.98 thf(fact_8126_arctan__bounded,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) )
% 5.64/5.98 & ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_bounded
% 5.64/5.98 thf(fact_8127_arctan__lbound,axiom,
% 5.64/5.98 ! [Y4: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_lbound
% 5.64/5.98 thf(fact_8128_and__int_Opinduct,axiom,
% 5.64/5.98 ! [A0: int,A1: int,P: int > int > $o] :
% 5.64/5.98 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.64/5.98 => ( ! [K3: int,L4: int] :
% 5.64/5.98 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 5.64/5.98 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.64/5.98 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.64/5.98 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 => ( P @ K3 @ L4 ) ) )
% 5.64/5.98 => ( P @ A0 @ A1 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % and_int.pinduct
% 5.64/5.98 thf(fact_8129_Maclaurin__zero,axiom,
% 5.64/5.98 ! [X2: real,N: nat,Diff: nat > complex > real] :
% 5.64/5.98 ( ( X2 = zero_zero_real )
% 5.64/5.98 => ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_zero
% 5.64/5.98 thf(fact_8130_Maclaurin__zero,axiom,
% 5.64/5.98 ! [X2: real,N: nat,Diff: nat > real > real] :
% 5.64/5.98 ( ( X2 = zero_zero_real )
% 5.64/5.98 => ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_zero
% 5.64/5.98 thf(fact_8131_Maclaurin__zero,axiom,
% 5.64/5.98 ! [X2: real,N: nat,Diff: nat > rat > real] :
% 5.64/5.98 ( ( X2 = zero_zero_real )
% 5.64/5.98 => ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_zero
% 5.64/5.98 thf(fact_8132_Maclaurin__zero,axiom,
% 5.64/5.98 ! [X2: real,N: nat,Diff: nat > nat > real] :
% 5.64/5.98 ( ( X2 = zero_zero_real )
% 5.64/5.98 => ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_zero
% 5.64/5.98 thf(fact_8133_Maclaurin__zero,axiom,
% 5.64/5.98 ! [X2: real,N: nat,Diff: nat > int > real] :
% 5.64/5.98 ( ( X2 = zero_zero_real )
% 5.64/5.98 => ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_zero
% 5.64/5.98 thf(fact_8134_Maclaurin__lemma,axiom,
% 5.64/5.98 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.64/5.98 => ? [B9: real] :
% 5.64/5.98 ( ( F @ H2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ B9 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_lemma
% 5.64/5.98 thf(fact_8135_Maclaurin__exp__le,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ? [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/5.98 & ( ( exp_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M2 ) @ ( semiri2265585572941072030t_real @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_exp_le
% 5.64/5.98 thf(fact_8136_machin__Euler,axiom,
% 5.64/5.98 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % machin_Euler
% 5.64/5.98 thf(fact_8137_machin,axiom,
% 5.64/5.98 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % machin
% 5.64/5.98 thf(fact_8138_sum__pos__lt__pair,axiom,
% 5.64/5.98 ! [F: nat > real,K: nat] :
% 5.64/5.98 ( ( summable_real @ F )
% 5.64/5.98 => ( ! [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 ) ) ) ) )
% 5.64/5.98 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sum_pos_lt_pair
% 5.64/5.98 thf(fact_8139_cos__coeff__def,axiom,
% 5.64/5.98 ( cos_coeff
% 5.64/5.98 = ( ^ [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 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_coeff_def
% 5.64/5.98 thf(fact_8140_sin__coeff__def,axiom,
% 5.64/5.98 ( sin_coeff
% 5.64/5.98 = ( ^ [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 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_coeff_def
% 5.64/5.98 thf(fact_8141_Maclaurin__minus__cos__expansion,axiom,
% 5.64/5.98 ! [N: nat,X2: real] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_real @ X2 @ T4 )
% 5.64/5.98 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.64/5.98 & ( ( cos_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_minus_cos_expansion
% 5.64/5.98 thf(fact_8142_Maclaurin__cos__expansion2,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.64/5.98 & ( ord_less_real @ T4 @ X2 )
% 5.64/5.98 & ( ( cos_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_cos_expansion2
% 5.64/5.98 thf(fact_8143_Maclaurin__cos__expansion,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ? [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/5.98 & ( ( cos_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( cos_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_cos_expansion
% 5.64/5.98 thf(fact_8144_sin__cos__npi,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( 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 ) ) ) )
% 5.64/5.98 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_npi
% 5.64/5.98 thf(fact_8145_cos__zero,axiom,
% 5.64/5.98 ( ( cos_complex @ zero_zero_complex )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % cos_zero
% 5.64/5.98 thf(fact_8146_cos__zero,axiom,
% 5.64/5.98 ( ( cos_real @ zero_zero_real )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_zero
% 5.64/5.98 thf(fact_8147_sin__cos__squared__add3,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ X2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ X2 ) ) )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_squared_add3
% 5.64/5.98 thf(fact_8148_sin__cos__squared__add3,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ X2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ X2 ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_squared_add3
% 5.64/5.98 thf(fact_8149_sin__npi2,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_npi2
% 5.64/5.98 thf(fact_8150_sin__npi,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_npi
% 5.64/5.98 thf(fact_8151_sin__npi__int,axiom,
% 5.64/5.98 ! [N: int] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_npi_int
% 5.64/5.98 thf(fact_8152_cos__pi__half,axiom,
% 5.64/5.98 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_pi_half
% 5.64/5.98 thf(fact_8153_sin__two__pi,axiom,
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_two_pi
% 5.64/5.98 thf(fact_8154_sin__pi__half,axiom,
% 5.64/5.98 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_pi_half
% 5.64/5.98 thf(fact_8155_cos__two__pi,axiom,
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_two_pi
% 5.64/5.98 thf(fact_8156_cos__periodic,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( cos_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.64/5.98 = ( cos_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_periodic
% 5.64/5.98 thf(fact_8157_sin__periodic,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( sin_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.64/5.98 = ( sin_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_periodic
% 5.64/5.98 thf(fact_8158_cos__2pi__minus,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.64/5.98 = ( cos_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_2pi_minus
% 5.64/5.98 thf(fact_8159_cos__npi,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.64/5.98 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_npi
% 5.64/5.98 thf(fact_8160_cos__npi2,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.98 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_npi2
% 5.64/5.98 thf(fact_8161_sin__cos__squared__add,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_squared_add
% 5.64/5.98 thf(fact_8162_sin__cos__squared__add,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_squared_add
% 5.64/5.98 thf(fact_8163_sin__cos__squared__add2,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_squared_add2
% 5.64/5.98 thf(fact_8164_sin__cos__squared__add2,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_squared_add2
% 5.64/5.98 thf(fact_8165_sin__2npi,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_2npi
% 5.64/5.98 thf(fact_8166_cos__2npi,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_2npi
% 5.64/5.98 thf(fact_8167_sin__2pi__minus,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.64/5.98 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_2pi_minus
% 5.64/5.98 thf(fact_8168_sin__int__2pin,axiom,
% 5.64/5.98 ! [N: int] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_int_2pin
% 5.64/5.98 thf(fact_8169_cos__int__2pin,axiom,
% 5.64/5.98 ! [N: int] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_int_2pin
% 5.64/5.98 thf(fact_8170_cos__3over2__pi,axiom,
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_3over2_pi
% 5.64/5.98 thf(fact_8171_sin__3over2__pi,axiom,
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.64/5.98 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_3over2_pi
% 5.64/5.98 thf(fact_8172_cos__npi__int,axiom,
% 5.64/5.98 ! [N: int] :
% 5.64/5.98 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.64/5.98 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.64/5.98 = one_one_real ) )
% 5.64/5.98 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.64/5.98 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.64/5.98 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_npi_int
% 5.64/5.98 thf(fact_8173_cos__pi__eq__zero,axiom,
% 5.64/5.98 ! [M: nat] :
% 5.64/5.98 ( ( 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 ) ) ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_pi_eq_zero
% 5.64/5.98 thf(fact_8174_fact__mono__nat,axiom,
% 5.64/5.98 ! [M: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.98 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_mono_nat
% 5.64/5.98 thf(fact_8175_fact__ge__self,axiom,
% 5.64/5.98 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_ge_self
% 5.64/5.98 thf(fact_8176_cos__one__sin__zero,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( ( cos_complex @ X2 )
% 5.64/5.98 = one_one_complex )
% 5.64/5.98 => ( ( sin_complex @ X2 )
% 5.64/5.98 = zero_zero_complex ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_one_sin_zero
% 5.64/5.98 thf(fact_8177_cos__one__sin__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 => ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_one_sin_zero
% 5.64/5.98 thf(fact_8178_polar__Ex,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ? [R3: real,A5: real] :
% 5.64/5.98 ( ( X2
% 5.64/5.98 = ( times_times_real @ R3 @ ( cos_real @ A5 ) ) )
% 5.64/5.98 & ( Y4
% 5.64/5.98 = ( times_times_real @ R3 @ ( sin_real @ A5 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % polar_Ex
% 5.64/5.98 thf(fact_8179_sin__diff,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( sin_real @ ( minus_minus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_diff
% 5.64/5.98 thf(fact_8180_sin__add,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( sin_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_add
% 5.64/5.98 thf(fact_8181_cos__diff,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( cos_real @ ( minus_minus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_diff
% 5.64/5.98 thf(fact_8182_cos__add,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( cos_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_add
% 5.64/5.98 thf(fact_8183_sin__double,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X2 ) ) @ ( cos_complex @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_double
% 5.64/5.98 thf(fact_8184_sin__double,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X2 ) ) @ ( cos_real @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_double
% 5.64/5.98 thf(fact_8185_sincos__principal__value,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ? [Y3: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.64/5.98 & ( ord_less_eq_real @ Y3 @ pi )
% 5.64/5.98 & ( ( sin_real @ Y3 )
% 5.64/5.98 = ( sin_real @ X2 ) )
% 5.64/5.98 & ( ( cos_real @ Y3 )
% 5.64/5.98 = ( cos_real @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sincos_principal_value
% 5.64/5.98 thf(fact_8186_fact__less__mono__nat,axiom,
% 5.64/5.98 ! [M: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/5.98 => ( ( ord_less_nat @ M @ N )
% 5.64/5.98 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_less_mono_nat
% 5.64/5.98 thf(fact_8187_sin__cos__le1,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) ) ) ) @ one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_le1
% 5.64/5.98 thf(fact_8188_cos__squared__eq,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_squared_eq
% 5.64/5.98 thf(fact_8189_cos__squared__eq,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_squared_eq
% 5.64/5.98 thf(fact_8190_sin__squared__eq,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_squared_eq
% 5.64/5.98 thf(fact_8191_sin__squared__eq,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_squared_eq
% 5.64/5.98 thf(fact_8192_fact__ge__Suc__0__nat,axiom,
% 5.64/5.98 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_ge_Suc_0_nat
% 5.64/5.98 thf(fact_8193_dvd__fact,axiom,
% 5.64/5.98 ! [M: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.64/5.98 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.98 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % dvd_fact
% 5.64/5.98 thf(fact_8194_sin__gt__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ pi )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_gt_zero
% 5.64/5.98 thf(fact_8195_cos__diff__cos,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_diff_cos
% 5.64/5.98 thf(fact_8196_cos__diff__cos,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_diff_cos
% 5.64/5.98 thf(fact_8197_sin__diff__sin,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_diff_sin
% 5.64/5.98 thf(fact_8198_sin__diff__sin,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_diff_sin
% 5.64/5.98 thf(fact_8199_sin__plus__sin,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_plus_sin
% 5.64/5.98 thf(fact_8200_sin__plus__sin,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_plus_sin
% 5.64/5.98 thf(fact_8201_cos__times__sin,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_times_sin
% 5.64/5.98 thf(fact_8202_cos__times__sin,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_times_sin
% 5.64/5.98 thf(fact_8203_sin__times__cos,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_times_cos
% 5.64/5.98 thf(fact_8204_sin__times__cos,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_times_cos
% 5.64/5.98 thf(fact_8205_sin__times__sin,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_times_sin
% 5.64/5.98 thf(fact_8206_sin__times__sin,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_times_sin
% 5.64/5.98 thf(fact_8207_cos__double,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double
% 5.64/5.98 thf(fact_8208_cos__double,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double
% 5.64/5.98 thf(fact_8209_cos__double__sin,axiom,
% 5.64/5.98 ! [W: complex] :
% 5.64/5.98 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.64/5.98 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double_sin
% 5.64/5.98 thf(fact_8210_cos__double__sin,axiom,
% 5.64/5.98 ! [W: real] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double_sin
% 5.64/5.98 thf(fact_8211_fact__diff__Suc,axiom,
% 5.64/5.98 ! [N: nat,M: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.64/5.98 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.64/5.98 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_diff_Suc
% 5.64/5.98 thf(fact_8212_cos__two__neq__zero,axiom,
% 5.64/5.98 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 != zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_two_neq_zero
% 5.64/5.98 thf(fact_8213_fact__div__fact__le__pow,axiom,
% 5.64/5.98 ! [R2: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ R2 @ N )
% 5.64/5.98 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R2 ) ) ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % fact_div_fact_le_pow
% 5.64/5.98 thf(fact_8214_cos__mono__less__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ pi )
% 5.64/5.98 => ( ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ Y4 @ X2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_mono_less_eq
% 5.64/5.98 thf(fact_8215_cos__monotone__0__pi,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.64/5.98 => ( ord_less_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_monotone_0_pi
% 5.64/5.98 thf(fact_8216_sin__eq__0__pi,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ pi )
% 5.64/5.98 => ( ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_eq_0_pi
% 5.64/5.98 thf(fact_8217_sin__zero__pi__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ pi )
% 5.64/5.98 => ( ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( X2 = zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_zero_pi_iff
% 5.64/5.98 thf(fact_8218_sin__zero__iff__int2,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ? [I4: int] :
% 5.64/5.98 ( X2
% 5.64/5.98 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ pi ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_zero_iff_int2
% 5.64/5.98 thf(fact_8219_sincos__total__pi,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/5.98 & ( ord_less_eq_real @ T4 @ pi )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( cos_real @ T4 ) )
% 5.64/5.98 & ( Y4
% 5.64/5.98 = ( sin_real @ T4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sincos_total_pi
% 5.64/5.98 thf(fact_8220_sin__expansion__lemma,axiom,
% 5.64/5.98 ! [X2: real,M: nat] :
% 5.64/5.98 ( ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_expansion_lemma
% 5.64/5.98 thf(fact_8221_cos__expansion__lemma,axiom,
% 5.64/5.98 ! [X2: real,M: nat] :
% 5.64/5.98 ( ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_expansion_lemma
% 5.64/5.98 thf(fact_8222_sin__gt__zero__02,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_gt_zero_02
% 5.64/5.98 thf(fact_8223_cos__two__less__zero,axiom,
% 5.64/5.98 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.64/5.98
% 5.64/5.98 % cos_two_less_zero
% 5.64/5.98 thf(fact_8224_cos__is__zero,axiom,
% 5.64/5.98 ? [X4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.64/5.98 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 & ( ( cos_real @ X4 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 & ! [Y5: real] :
% 5.64/5.98 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.64/5.98 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 & ( ( cos_real @ Y5 )
% 5.64/5.98 = zero_zero_real ) )
% 5.64/5.98 => ( Y5 = X4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_is_zero
% 5.64/5.98 thf(fact_8225_cos__two__le__zero,axiom,
% 5.64/5.98 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.64/5.98
% 5.64/5.98 % cos_two_le_zero
% 5.64/5.98 thf(fact_8226_cos__monotone__minus__pi__0,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.98 => ( ord_less_real @ ( cos_real @ Y4 ) @ ( cos_real @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_monotone_minus_pi_0
% 5.64/5.98 thf(fact_8227_sincos__total__pi__half,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/5.98 & ( ord_less_eq_real @ T4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( cos_real @ T4 ) )
% 5.64/5.98 & ( Y4
% 5.64/5.98 = ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sincos_total_pi_half
% 5.64/5.98 thf(fact_8228_sincos__total__2pi__le,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/5.98 & ( ord_less_eq_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( cos_real @ T4 ) )
% 5.64/5.98 & ( Y4
% 5.64/5.98 = ( sin_real @ T4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sincos_total_2pi_le
% 5.64/5.98 thf(fact_8229_sincos__total__2pi,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 => ~ ! [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/5.98 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.98 => ( ( X2
% 5.64/5.98 = ( cos_real @ T4 ) )
% 5.64/5.98 => ( Y4
% 5.64/5.98 != ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sincos_total_2pi
% 5.64/5.98 thf(fact_8230_sin__pi__divide__n__ge__0,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_pi_divide_n_ge_0
% 5.64/5.98 thf(fact_8231_cos__plus__cos,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_plus_cos
% 5.64/5.98 thf(fact_8232_cos__plus__cos,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_plus_cos
% 5.64/5.98 thf(fact_8233_cos__times__cos,axiom,
% 5.64/5.98 ! [W: complex,Z: complex] :
% 5.64/5.98 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_times_cos
% 5.64/5.98 thf(fact_8234_cos__times__cos,axiom,
% 5.64/5.98 ! [W: real,Z: real] :
% 5.64/5.98 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.64/5.98 = ( 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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_times_cos
% 5.64/5.98 thf(fact_8235_sin__gt__zero2,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_gt_zero2
% 5.64/5.98 thf(fact_8236_sin__lt__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ pi @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.98 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_lt_zero
% 5.64/5.98 thf(fact_8237_cos__double__less__one,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.98 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double_less_one
% 5.64/5.98 thf(fact_8238_sin__30,axiom,
% 5.64/5.98 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_30
% 5.64/5.98 thf(fact_8239_cos__gt__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_gt_zero
% 5.64/5.98 thf(fact_8240_sin__inj__pi,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ( sin_real @ X2 )
% 5.64/5.98 = ( sin_real @ Y4 ) )
% 5.64/5.98 => ( X2 = Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_inj_pi
% 5.64/5.98 thf(fact_8241_sin__mono__le__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y4 ) )
% 5.64/5.98 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_mono_le_eq
% 5.64/5.98 thf(fact_8242_sin__monotone__2pi__le,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_eq_real @ ( sin_real @ Y4 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_monotone_2pi_le
% 5.64/5.98 thf(fact_8243_cos__60,axiom,
% 5.64/5.98 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_60
% 5.64/5.98 thf(fact_8244_cos__one__2pi__int,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 = ( ? [X: int] :
% 5.64/5.98 ( X2
% 5.64/5.98 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_one_2pi_int
% 5.64/5.98 thf(fact_8245_sin__coeff__Suc,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( sin_coeff @ ( suc @ N ) )
% 5.64/5.98 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_coeff_Suc
% 5.64/5.98 thf(fact_8246_cos__double__cos,axiom,
% 5.64/5.98 ! [W: complex] :
% 5.64/5.98 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.64/5.98 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double_cos
% 5.64/5.98 thf(fact_8247_cos__double__cos,axiom,
% 5.64/5.98 ! [W: real] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.64/5.98 = ( 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 ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_double_cos
% 5.64/5.98 thf(fact_8248_cos__treble__cos,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_treble_cos
% 5.64/5.98 thf(fact_8249_cos__treble__cos,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_treble_cos
% 5.64/5.98 thf(fact_8250_sin__le__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ pi @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.98 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_le_zero
% 5.64/5.98 thf(fact_8251_sin__less__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.98 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_less_zero
% 5.64/5.98 thf(fact_8252_sin__mono__less__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_mono_less_eq
% 5.64/5.98 thf(fact_8253_sin__monotone__2pi,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ ( sin_real @ Y4 ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_monotone_2pi
% 5.64/5.98 thf(fact_8254_sin__total,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ? [X4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.64/5.98 & ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( sin_real @ X4 )
% 5.64/5.98 = Y4 )
% 5.64/5.98 & ! [Y5: real] :
% 5.64/5.98 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.64/5.98 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( sin_real @ Y5 )
% 5.64/5.98 = Y4 ) )
% 5.64/5.98 => ( Y5 = X4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_total
% 5.64/5.98 thf(fact_8255_cos__gt__zero__pi,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_gt_zero_pi
% 5.64/5.98 thf(fact_8256_cos__ge__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_ge_zero
% 5.64/5.98 thf(fact_8257_cos__one__2pi,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 = ( ? [X: nat] :
% 5.64/5.98 ( X2
% 5.64/5.98 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.64/5.98 | ? [X: nat] :
% 5.64/5.98 ( X2
% 5.64/5.98 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_one_2pi
% 5.64/5.98 thf(fact_8258_Maclaurin__sin__expansion,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ? [T4: real] :
% 5.64/5.98 ( ( sin_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_sin_expansion
% 5.64/5.98 thf(fact_8259_cos__coeff__Suc,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( cos_coeff @ ( suc @ N ) )
% 5.64/5.98 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_coeff_Suc
% 5.64/5.98 thf(fact_8260_sin__pi__divide__n__gt__0,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_pi_divide_n_gt_0
% 5.64/5.98 thf(fact_8261_Maclaurin__sin__expansion2,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ? [T4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/5.98 & ( ( sin_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_sin_expansion2
% 5.64/5.98 thf(fact_8262_sin__zero__iff__int,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ? [I4: int] :
% 5.64/5.98 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_zero_iff_int
% 5.64/5.98 thf(fact_8263_Maclaurin__sin__expansion4,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.64/5.98 & ( ord_less_eq_real @ T4 @ X2 )
% 5.64/5.98 & ( ( sin_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_sin_expansion4
% 5.64/5.98 thf(fact_8264_cos__zero__iff__int,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ? [I4: int] :
% 5.64/5.98 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I4 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( times_times_real @ ( ring_1_of_int_real @ I4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_zero_iff_int
% 5.64/5.98 thf(fact_8265_Maclaurin__sin__expansion3,axiom,
% 5.64/5.98 ! [N: nat,X2: real] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ? [T4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.64/5.98 & ( ord_less_real @ T4 @ X2 )
% 5.64/5.98 & ( ( sin_real @ X2 )
% 5.64/5.98 = ( plus_plus_real
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.98 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.98 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T4 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Maclaurin_sin_expansion3
% 5.64/5.98 thf(fact_8266_sin__zero__lemma,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 => ? [N3: nat] :
% 5.64/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_zero_lemma
% 5.64/5.98 thf(fact_8267_sin__zero__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( sin_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ? [N2: nat] :
% 5.64/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.98 | ? [N2: nat] :
% 5.64/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_zero_iff
% 5.64/5.98 thf(fact_8268_cos__zero__lemma,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ( cos_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 => ? [N3: nat] :
% 5.64/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_zero_lemma
% 5.64/5.98 thf(fact_8269_cos__zero__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ? [N2: nat] :
% 5.64/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.98 | ? [N2: nat] :
% 5.64/5.98 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.64/5.98 & ( X2
% 5.64/5.98 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_zero_iff
% 5.64/5.98 thf(fact_8270_upto_Opinduct,axiom,
% 5.64/5.98 ! [A0: int,A1: int,P: int > int > $o] :
% 5.64/5.98 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.64/5.98 => ( ! [I3: int,J2: int] :
% 5.64/5.98 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.64/5.98 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.64/5.98 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.64/5.98 => ( P @ I3 @ J2 ) ) )
% 5.64/5.98 => ( P @ A0 @ A1 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % upto.pinduct
% 5.64/5.98 thf(fact_8271_tan__double,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( ( cos_complex @ X2 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_double
% 5.64/5.98 thf(fact_8272_tan__double,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.64/5.98 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X2 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_double
% 5.64/5.98 thf(fact_8273_sin__paired,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( sums_real
% 5.64/5.98 @ ^ [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 @ X2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.64/5.98 @ ( sin_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_paired
% 5.64/5.98 thf(fact_8274_ceiling__log__eq__powr__iff,axiom,
% 5.64/5.98 ! [X2: real,B: real,K: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X2 ) )
% 5.64/5.98 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.64/5.98 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.64/5.98 & ( ord_less_eq_real @ X2 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % ceiling_log_eq_powr_iff
% 5.64/5.98 thf(fact_8275_geometric__deriv__sums,axiom,
% 5.64/5.98 ! [Z: real] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( power_power_real @ Z @ N2 ) )
% 5.64/5.98 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % geometric_deriv_sums
% 5.64/5.98 thf(fact_8276_geometric__deriv__sums,axiom,
% 5.64/5.98 ! [Z: complex] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.64/5.98 => ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( power_power_complex @ Z @ N2 ) )
% 5.64/5.98 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % geometric_deriv_sums
% 5.64/5.98 thf(fact_8277_powr__one__eq__one,axiom,
% 5.64/5.98 ! [A: real] :
% 5.64/5.98 ( ( powr_real @ one_one_real @ A )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % powr_one_eq_one
% 5.64/5.98 thf(fact_8278_powr__zero__eq__one,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( X2 = zero_zero_real )
% 5.64/5.98 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.64/5.98 = zero_zero_real ) )
% 5.64/5.98 & ( ( X2 != zero_zero_real )
% 5.64/5.98 => ( ( powr_real @ X2 @ zero_zero_real )
% 5.64/5.98 = one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_zero_eq_one
% 5.64/5.98 thf(fact_8279_powr__gt__zero,axiom,
% 5.64/5.98 ! [X2: real,A: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X2 @ A ) )
% 5.64/5.98 = ( X2 != zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_gt_zero
% 5.64/5.98 thf(fact_8280_powr__less__cancel__iff,axiom,
% 5.64/5.98 ! [X2: real,A: real,B: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.64/5.98 = ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_less_cancel_iff
% 5.64/5.98 thf(fact_8281_powr__eq__one__iff,axiom,
% 5.64/5.98 ! [A: real,X2: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ A )
% 5.64/5.98 => ( ( ( powr_real @ A @ X2 )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 = ( X2 = zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_eq_one_iff
% 5.64/5.98 thf(fact_8282_powr__le__cancel__iff,axiom,
% 5.64/5.98 ! [X2: real,A: real,B: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.64/5.98 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_le_cancel_iff
% 5.64/5.98 thf(fact_8283_tan__npi,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % tan_npi
% 5.64/5.98 thf(fact_8284_numeral__powr__numeral__real,axiom,
% 5.64/5.98 ! [M: num,N: num] :
% 5.64/5.98 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.64/5.98 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % numeral_powr_numeral_real
% 5.64/5.98 thf(fact_8285_tan__periodic__n,axiom,
% 5.64/5.98 ! [X2: real,N: num] :
% 5.64/5.98 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.64/5.98 = ( tan_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_periodic_n
% 5.64/5.98 thf(fact_8286_tan__periodic__nat,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.64/5.98 = ( tan_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_periodic_nat
% 5.64/5.98 thf(fact_8287_tan__periodic__int,axiom,
% 5.64/5.98 ! [X2: real,I: int] :
% 5.64/5.98 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.64/5.98 = ( tan_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_periodic_int
% 5.64/5.98 thf(fact_8288_powr__log__cancel,axiom,
% 5.64/5.98 ! [A: real,X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ( A != one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( powr_real @ A @ ( log @ A @ X2 ) )
% 5.64/5.98 = X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_log_cancel
% 5.64/5.98 thf(fact_8289_log__powr__cancel,axiom,
% 5.64/5.98 ! [A: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ( A != one_one_real )
% 5.64/5.98 => ( ( log @ A @ ( powr_real @ A @ Y4 ) )
% 5.64/5.98 = Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_powr_cancel
% 5.64/5.98 thf(fact_8290_powser__sums__zero__iff,axiom,
% 5.64/5.98 ! [A: nat > complex,X2: complex] :
% 5.64/5.98 ( ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.64/5.98 @ X2 )
% 5.64/5.98 = ( ( A @ zero_zero_nat )
% 5.64/5.98 = X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_zero_iff
% 5.64/5.98 thf(fact_8291_powser__sums__zero__iff,axiom,
% 5.64/5.98 ! [A: nat > real,X2: real] :
% 5.64/5.98 ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.64/5.98 @ X2 )
% 5.64/5.98 = ( ( A @ zero_zero_nat )
% 5.64/5.98 = X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_zero_iff
% 5.64/5.98 thf(fact_8292_tan__periodic,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.64/5.98 = ( tan_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_periodic
% 5.64/5.98 thf(fact_8293_powr__numeral,axiom,
% 5.64/5.98 ! [X2: real,N: num] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N ) )
% 5.64/5.98 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_numeral
% 5.64/5.98 thf(fact_8294_square__powr__half,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( powr_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = ( abs_abs_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % square_powr_half
% 5.64/5.98 thf(fact_8295_sums__le,axiom,
% 5.64/5.98 ! [F: nat > nat,G: nat > nat,S2: nat,T: nat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/5.98 => ( ( sums_nat @ F @ S2 )
% 5.64/5.98 => ( ( sums_nat @ G @ T )
% 5.64/5.98 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_le
% 5.64/5.98 thf(fact_8296_sums__le,axiom,
% 5.64/5.98 ! [F: nat > int,G: nat > int,S2: int,T: int] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/5.98 => ( ( sums_int @ F @ S2 )
% 5.64/5.98 => ( ( sums_int @ G @ T )
% 5.64/5.98 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_le
% 5.64/5.98 thf(fact_8297_sums__le,axiom,
% 5.64/5.98 ! [F: nat > real,G: nat > real,S2: real,T: real] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/5.98 => ( ( sums_real @ F @ S2 )
% 5.64/5.98 => ( ( sums_real @ G @ T )
% 5.64/5.98 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_le
% 5.64/5.98 thf(fact_8298_powr__powr,axiom,
% 5.64/5.98 ! [X2: real,A: real,B: real] :
% 5.64/5.98 ( ( powr_real @ ( powr_real @ X2 @ A ) @ B )
% 5.64/5.98 = ( powr_real @ X2 @ ( times_times_real @ A @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_powr
% 5.64/5.98 thf(fact_8299_sums__mult2,axiom,
% 5.64/5.98 ! [F: nat > real,A: real,C: real] :
% 5.64/5.98 ( ( sums_real @ F @ A )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.64/5.98 @ ( times_times_real @ A @ C ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult2
% 5.64/5.98 thf(fact_8300_sums__mult,axiom,
% 5.64/5.98 ! [F: nat > real,A: real,C: real] :
% 5.64/5.98 ( ( sums_real @ F @ A )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.64/5.98 @ ( times_times_real @ C @ A ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult
% 5.64/5.98 thf(fact_8301_sums__add,axiom,
% 5.64/5.98 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.64/5.98 ( ( sums_real @ F @ A )
% 5.64/5.98 => ( ( sums_real @ G @ B )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( plus_plus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.64/5.98 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_add
% 5.64/5.98 thf(fact_8302_sums__add,axiom,
% 5.64/5.98 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.64/5.98 ( ( sums_nat @ F @ A )
% 5.64/5.98 => ( ( sums_nat @ G @ B )
% 5.64/5.98 => ( sums_nat
% 5.64/5.98 @ ^ [N2: nat] : ( plus_plus_nat @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.64/5.98 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_add
% 5.64/5.98 thf(fact_8303_sums__add,axiom,
% 5.64/5.98 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.64/5.98 ( ( sums_int @ F @ A )
% 5.64/5.98 => ( ( sums_int @ G @ B )
% 5.64/5.98 => ( sums_int
% 5.64/5.98 @ ^ [N2: nat] : ( plus_plus_int @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.64/5.98 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_add
% 5.64/5.98 thf(fact_8304_sums__divide,axiom,
% 5.64/5.98 ! [F: nat > complex,A: complex,C: complex] :
% 5.64/5.98 ( ( sums_complex @ F @ A )
% 5.64/5.98 => ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ C )
% 5.64/5.98 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_divide
% 5.64/5.98 thf(fact_8305_sums__divide,axiom,
% 5.64/5.98 ! [F: nat > real,A: real,C: real] :
% 5.64/5.98 ( ( sums_real @ F @ A )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ C )
% 5.64/5.98 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_divide
% 5.64/5.98 thf(fact_8306_powr__less__mono2__neg,axiom,
% 5.64/5.98 ! [A: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ A @ zero_zero_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.98 => ( ord_less_real @ ( powr_real @ Y4 @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_less_mono2_neg
% 5.64/5.98 thf(fact_8307_powr__non__neg,axiom,
% 5.64/5.98 ! [A: real,X2: real] :
% 5.64/5.98 ~ ( ord_less_real @ ( powr_real @ A @ X2 ) @ zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % powr_non_neg
% 5.64/5.98 thf(fact_8308_powr__less__cancel,axiom,
% 5.64/5.98 ! [X2: real,A: real,B: real] :
% 5.64/5.98 ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.64/5.98 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ord_less_real @ A @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_less_cancel
% 5.64/5.98 thf(fact_8309_powr__less__mono,axiom,
% 5.64/5.98 ! [A: real,B: real,X2: real] :
% 5.64/5.98 ( ( ord_less_real @ A @ B )
% 5.64/5.98 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_less_mono
% 5.64/5.98 thf(fact_8310_sums__mult2__iff,axiom,
% 5.64/5.98 ! [C: complex,F: nat > complex,D: complex] :
% 5.64/5.98 ( ( C != zero_zero_complex )
% 5.64/5.98 => ( ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ C )
% 5.64/5.98 @ ( times_times_complex @ D @ C ) )
% 5.64/5.98 = ( sums_complex @ F @ D ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult2_iff
% 5.64/5.98 thf(fact_8311_sums__mult2__iff,axiom,
% 5.64/5.98 ! [C: real,F: nat > real,D: real] :
% 5.64/5.98 ( ( C != zero_zero_real )
% 5.64/5.98 => ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ C )
% 5.64/5.98 @ ( times_times_real @ D @ C ) )
% 5.64/5.98 = ( sums_real @ F @ D ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult2_iff
% 5.64/5.98 thf(fact_8312_sums__mult__iff,axiom,
% 5.64/5.98 ! [C: complex,F: nat > complex,D: complex] :
% 5.64/5.98 ( ( C != zero_zero_complex )
% 5.64/5.98 => ( ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.64/5.98 @ ( times_times_complex @ C @ D ) )
% 5.64/5.98 = ( sums_complex @ F @ D ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult_iff
% 5.64/5.98 thf(fact_8313_sums__mult__iff,axiom,
% 5.64/5.98 ! [C: real,F: nat > real,D: real] :
% 5.64/5.98 ( ( C != zero_zero_real )
% 5.64/5.98 => ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.64/5.98 @ ( times_times_real @ C @ D ) )
% 5.64/5.98 = ( sums_real @ F @ D ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult_iff
% 5.64/5.98 thf(fact_8314_powr__mono2_H,axiom,
% 5.64/5.98 ! [A: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.98 => ( ord_less_eq_real @ ( powr_real @ Y4 @ A ) @ ( powr_real @ X2 @ A ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_mono2'
% 5.64/5.98 thf(fact_8315_powr__less__mono2,axiom,
% 5.64/5.98 ! [A: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.98 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_less_mono2
% 5.64/5.98 thf(fact_8316_powr__inj,axiom,
% 5.64/5.98 ! [A: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ( A != one_one_real )
% 5.64/5.98 => ( ( ( powr_real @ A @ X2 )
% 5.64/5.98 = ( powr_real @ A @ Y4 ) )
% 5.64/5.98 = ( X2 = Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_inj
% 5.64/5.98 thf(fact_8317_gr__one__powr,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gr_one_powr
% 5.64/5.98 thf(fact_8318_powr__divide,axiom,
% 5.64/5.98 ! [X2: real,Y4: real,A: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( powr_real @ ( divide_divide_real @ X2 @ Y4 ) @ A )
% 5.64/5.98 = ( divide_divide_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_divide
% 5.64/5.98 thf(fact_8319_powr__mult,axiom,
% 5.64/5.98 ! [X2: real,Y4: real,A: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( powr_real @ ( times_times_real @ X2 @ Y4 ) @ A )
% 5.64/5.98 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y4 @ A ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_mult
% 5.64/5.98 thf(fact_8320_sums__mult__D,axiom,
% 5.64/5.98 ! [C: complex,F: nat > complex,A: complex] :
% 5.64/5.98 ( ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ C @ ( F @ N2 ) )
% 5.64/5.98 @ A )
% 5.64/5.98 => ( ( C != zero_zero_complex )
% 5.64/5.98 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult_D
% 5.64/5.98 thf(fact_8321_sums__mult__D,axiom,
% 5.64/5.98 ! [C: real,F: nat > real,A: real] :
% 5.64/5.98 ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ C @ ( F @ N2 ) )
% 5.64/5.98 @ A )
% 5.64/5.98 => ( ( C != zero_zero_real )
% 5.64/5.98 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_mult_D
% 5.64/5.98 thf(fact_8322_sums__Suc__imp,axiom,
% 5.64/5.98 ! [F: nat > complex,S2: complex] :
% 5.64/5.98 ( ( ( F @ zero_zero_nat )
% 5.64/5.98 = zero_zero_complex )
% 5.64/5.98 => ( ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.64/5.98 @ S2 )
% 5.64/5.98 => ( sums_complex @ F @ S2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_Suc_imp
% 5.64/5.98 thf(fact_8323_sums__Suc__imp,axiom,
% 5.64/5.98 ! [F: nat > real,S2: real] :
% 5.64/5.98 ( ( ( F @ zero_zero_nat )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 => ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.64/5.98 @ S2 )
% 5.64/5.98 => ( sums_real @ F @ S2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_Suc_imp
% 5.64/5.98 thf(fact_8324_divide__powr__uminus,axiom,
% 5.64/5.98 ! [A: real,B: real,C: real] :
% 5.64/5.98 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.64/5.98 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % divide_powr_uminus
% 5.64/5.98 thf(fact_8325_sums__Suc,axiom,
% 5.64/5.98 ! [F: nat > real,L: real] :
% 5.64/5.98 ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.64/5.98 @ L )
% 5.64/5.98 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_Suc
% 5.64/5.98 thf(fact_8326_sums__Suc,axiom,
% 5.64/5.98 ! [F: nat > nat,L: nat] :
% 5.64/5.98 ( ( sums_nat
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.64/5.98 @ L )
% 5.64/5.98 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_Suc
% 5.64/5.98 thf(fact_8327_sums__Suc,axiom,
% 5.64/5.98 ! [F: nat > int,L: int] :
% 5.64/5.98 ( ( sums_int
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.64/5.98 @ L )
% 5.64/5.98 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_Suc
% 5.64/5.98 thf(fact_8328_sums__Suc__iff,axiom,
% 5.64/5.98 ! [F: nat > real,S2: real] :
% 5.64/5.98 ( ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( F @ ( suc @ N2 ) )
% 5.64/5.98 @ S2 )
% 5.64/5.98 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_Suc_iff
% 5.64/5.98 thf(fact_8329_sums__zero__iff__shift,axiom,
% 5.64/5.98 ! [N: nat,F: nat > complex,S2: complex] :
% 5.64/5.98 ( ! [I3: nat] :
% 5.64/5.98 ( ( ord_less_nat @ I3 @ N )
% 5.64/5.98 => ( ( F @ I3 )
% 5.64/5.98 = zero_zero_complex ) )
% 5.64/5.98 => ( ( sums_complex
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.64/5.98 @ S2 )
% 5.64/5.98 = ( sums_complex @ F @ S2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_zero_iff_shift
% 5.64/5.98 thf(fact_8330_sums__zero__iff__shift,axiom,
% 5.64/5.98 ! [N: nat,F: nat > real,S2: real] :
% 5.64/5.98 ( ! [I3: nat] :
% 5.64/5.98 ( ( ord_less_nat @ I3 @ N )
% 5.64/5.98 => ( ( F @ I3 )
% 5.64/5.98 = zero_zero_real ) )
% 5.64/5.98 => ( ( sums_real
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.64/5.98 @ S2 )
% 5.64/5.98 = ( sums_real @ F @ S2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_zero_iff_shift
% 5.64/5.98 thf(fact_8331_log__base__powr,axiom,
% 5.64/5.98 ! [A: real,B: real,X2: real] :
% 5.64/5.98 ( ( A != zero_zero_real )
% 5.64/5.98 => ( ( log @ ( powr_real @ A @ B ) @ X2 )
% 5.64/5.98 = ( divide_divide_real @ ( log @ A @ X2 ) @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_base_powr
% 5.64/5.98 thf(fact_8332_log__powr,axiom,
% 5.64/5.98 ! [X2: real,B: real,Y4: real] :
% 5.64/5.98 ( ( X2 != zero_zero_real )
% 5.64/5.98 => ( ( log @ B @ ( powr_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( times_times_real @ Y4 @ ( log @ B @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_powr
% 5.64/5.98 thf(fact_8333_ln__powr,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( X2 != zero_zero_real )
% 5.64/5.98 => ( ( ln_ln_real @ ( powr_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( times_times_real @ Y4 @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % ln_powr
% 5.64/5.98 thf(fact_8334_powr__add,axiom,
% 5.64/5.98 ! [X2: real,A: real,B: real] :
% 5.64/5.98 ( ( powr_real @ X2 @ ( plus_plus_real @ A @ B ) )
% 5.64/5.98 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_add
% 5.64/5.98 thf(fact_8335_powr__diff,axiom,
% 5.64/5.98 ! [W: real,Z1: real,Z22: real] :
% 5.64/5.98 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.64/5.98 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_diff
% 5.64/5.98 thf(fact_8336_powser__sums__if,axiom,
% 5.64/5.98 ! [M: nat,Z: complex] :
% 5.64/5.98 ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( if_complex @ ( N2 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N2 ) )
% 5.64/5.98 @ ( power_power_complex @ Z @ M ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_if
% 5.64/5.98 thf(fact_8337_powser__sums__if,axiom,
% 5.64/5.98 ! [M: nat,Z: real] :
% 5.64/5.98 ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( if_real @ ( N2 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N2 ) )
% 5.64/5.98 @ ( power_power_real @ Z @ M ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_if
% 5.64/5.98 thf(fact_8338_powser__sums__if,axiom,
% 5.64/5.98 ! [M: nat,Z: int] :
% 5.64/5.98 ( sums_int
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_int @ ( if_int @ ( N2 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N2 ) )
% 5.64/5.98 @ ( power_power_int @ Z @ M ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_if
% 5.64/5.98 thf(fact_8339_powser__sums__zero,axiom,
% 5.64/5.98 ! [A: nat > complex] :
% 5.64/5.98 ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( A @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) )
% 5.64/5.98 @ ( A @ zero_zero_nat ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_zero
% 5.64/5.98 thf(fact_8340_powser__sums__zero,axiom,
% 5.64/5.98 ! [A: nat > real] :
% 5.64/5.98 ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( A @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) )
% 5.64/5.98 @ ( A @ zero_zero_nat ) ) ).
% 5.64/5.98
% 5.64/5.98 % powser_sums_zero
% 5.64/5.98 thf(fact_8341_tan__def,axiom,
% 5.64/5.98 ( tan_complex
% 5.64/5.98 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_def
% 5.64/5.98 thf(fact_8342_tan__def,axiom,
% 5.64/5.98 ( tan_real
% 5.64/5.98 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_def
% 5.64/5.98 thf(fact_8343_powr__realpow,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( powr_real @ X2 @ ( semiri5074537144036343181t_real @ N ) )
% 5.64/5.98 = ( power_power_real @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_realpow
% 5.64/5.98 thf(fact_8344_powr__less__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ ( powr_real @ B @ Y4 ) @ X2 )
% 5.64/5.98 = ( ord_less_real @ Y4 @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_less_iff
% 5.64/5.98 thf(fact_8345_less__powr__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( powr_real @ B @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ ( log @ B @ X2 ) @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % less_powr_iff
% 5.64/5.98 thf(fact_8346_log__less__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ ( log @ B @ X2 ) @ Y4 )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( powr_real @ B @ Y4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_less_iff
% 5.64/5.98 thf(fact_8347_less__log__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ ( log @ B @ X2 ) )
% 5.64/5.98 = ( ord_less_real @ ( powr_real @ B @ Y4 ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % less_log_iff
% 5.64/5.98 thf(fact_8348_sums__iff__shift,axiom,
% 5.64/5.98 ! [F: nat > real,N: nat,S2: real] :
% 5.64/5.98 ( ( sums_real
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.64/5.98 @ S2 )
% 5.64/5.98 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_iff_shift
% 5.64/5.98 thf(fact_8349_sums__iff__shift_H,axiom,
% 5.64/5.98 ! [F: nat > real,N: nat,S2: real] :
% 5.64/5.98 ( ( sums_real
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.64/5.98 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.64/5.98 = ( sums_real @ F @ S2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_iff_shift'
% 5.64/5.98 thf(fact_8350_sums__split__initial__segment,axiom,
% 5.64/5.98 ! [F: nat > real,S2: real,N: nat] :
% 5.64/5.98 ( ( sums_real @ F @ S2 )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [I4: nat] : ( F @ ( plus_plus_nat @ I4 @ N ) )
% 5.64/5.98 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_split_initial_segment
% 5.64/5.98 thf(fact_8351_sums__If__finite__set_H,axiom,
% 5.64/5.98 ! [G: nat > real,S3: real,A4: set_nat,S5: real,F: nat > real] :
% 5.64/5.98 ( ( sums_real @ G @ S3 )
% 5.64/5.98 => ( ( finite_finite_nat @ A4 )
% 5.64/5.98 => ( ( S5
% 5.64/5.98 = ( plus_plus_real @ S3
% 5.64/5.98 @ ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.64/5.98 @ A4 ) ) )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( if_real @ ( member_nat @ N2 @ A4 ) @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.64/5.98 @ S5 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_If_finite_set'
% 5.64/5.98 thf(fact_8352_powr__minus__divide,axiom,
% 5.64/5.98 ! [X2: real,A: real] :
% 5.64/5.98 ( ( powr_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_minus_divide
% 5.64/5.98 thf(fact_8353_powr__neg__one,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_neg_one
% 5.64/5.98 thf(fact_8354_powr__mult__base,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( times_times_real @ X2 @ ( powr_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( powr_real @ X2 @ ( plus_plus_real @ one_one_real @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_mult_base
% 5.64/5.98 thf(fact_8355_le__log__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( log @ B @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( powr_real @ B @ Y4 ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_log_iff
% 5.64/5.98 thf(fact_8356_log__le__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y4 )
% 5.64/5.98 = ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_le_iff
% 5.64/5.98 thf(fact_8357_le__powr__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y4 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_powr_iff
% 5.64/5.98 thf(fact_8358_powr__le__iff,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y4 ) @ X2 )
% 5.64/5.98 = ( ord_less_eq_real @ Y4 @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_le_iff
% 5.64/5.98 thf(fact_8359_ln__powr__bound,axiom,
% 5.64/5.98 ! [X2: real,A: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A ) @ A ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % ln_powr_bound
% 5.64/5.98 thf(fact_8360_ln__powr__bound2,axiom,
% 5.64/5.98 ! [X2: real,A: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % ln_powr_bound2
% 5.64/5.98 thf(fact_8361_tan__45,axiom,
% 5.64/5.98 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % tan_45
% 5.64/5.98 thf(fact_8362_log__add__eq__powr,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.98 => ( ( B != one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( plus_plus_real @ ( log @ B @ X2 ) @ Y4 )
% 5.64/5.98 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_add_eq_powr
% 5.64/5.98 thf(fact_8363_add__log__eq__powr,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.98 => ( ( B != one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( plus_plus_real @ Y4 @ ( log @ B @ X2 ) )
% 5.64/5.98 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y4 ) @ X2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % add_log_eq_powr
% 5.64/5.98 thf(fact_8364_minus__log__eq__powr,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.98 => ( ( B != one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( minus_minus_real @ Y4 @ ( log @ B @ X2 ) )
% 5.64/5.98 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y4 ) @ X2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % minus_log_eq_powr
% 5.64/5.98 thf(fact_8365_powr__def,axiom,
% 5.64/5.98 ( powr_real
% 5.64/5.98 = ( ^ [X: real,A3: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( exp_real @ ( times_times_real @ A3 @ ( ln_ln_real @ X ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_def
% 5.64/5.98 thf(fact_8366_geometric__sums,axiom,
% 5.64/5.98 ! [C: real] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.64/5.98 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % geometric_sums
% 5.64/5.98 thf(fact_8367_geometric__sums,axiom,
% 5.64/5.98 ! [C: complex] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.64/5.98 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % geometric_sums
% 5.64/5.98 thf(fact_8368_power__half__series,axiom,
% 5.64/5.98 ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.64/5.98 @ one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % power_half_series
% 5.64/5.98 thf(fact_8369_lemma__tan__total,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ? [X4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.64/5.98 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ord_less_real @ Y4 @ ( tan_real @ X4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % lemma_tan_total
% 5.64/5.98 thf(fact_8370_tan__gt__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_gt_zero
% 5.64/5.98 thf(fact_8371_lemma__tan__total1,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ? [X4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.64/5.98 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( tan_real @ X4 )
% 5.64/5.98 = Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % lemma_tan_total1
% 5.64/5.98 thf(fact_8372_tan__mono__lt__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_mono_lt_eq
% 5.64/5.98 thf(fact_8373_tan__monotone_H,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.98 = ( ord_less_real @ ( tan_real @ Y4 ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_monotone'
% 5.64/5.98 thf(fact_8374_tan__monotone,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ ( tan_real @ Y4 ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_monotone
% 5.64/5.98 thf(fact_8375_tan__total,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ? [X4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.64/5.98 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( tan_real @ X4 )
% 5.64/5.98 = Y4 )
% 5.64/5.98 & ! [Y5: real] :
% 5.64/5.98 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.64/5.98 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( tan_real @ Y5 )
% 5.64/5.98 = Y4 ) )
% 5.64/5.98 => ( Y5 = X4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_total
% 5.64/5.98 thf(fact_8376_tan__minus__45,axiom,
% 5.64/5.98 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.64/5.98 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_minus_45
% 5.64/5.98 thf(fact_8377_tan__inverse,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y4 ) )
% 5.64/5.98 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_inverse
% 5.64/5.98 thf(fact_8378_log__minus__eq__powr,axiom,
% 5.64/5.98 ! [B: real,X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/5.98 => ( ( B != one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( minus_minus_real @ ( log @ B @ X2 ) @ Y4 )
% 5.64/5.98 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ ( uminus_uminus_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % log_minus_eq_powr
% 5.64/5.98 thf(fact_8379_add__tan__eq,axiom,
% 5.64/5.98 ! [X2: complex,Y4: complex] :
% 5.64/5.98 ( ( ( cos_complex @ X2 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ Y4 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y4 ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X2 @ Y4 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % add_tan_eq
% 5.64/5.98 thf(fact_8380_add__tan__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ Y4 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) )
% 5.64/5.98 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % add_tan_eq
% 5.64/5.98 thf(fact_8381_sums__if_H,axiom,
% 5.64/5.98 ! [G: nat > real,X2: real] :
% 5.64/5.98 ( ( sums_real @ G @ X2 )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [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 ) ) ) ) )
% 5.64/5.98 @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_if'
% 5.64/5.98 thf(fact_8382_sums__if,axiom,
% 5.64/5.98 ! [G: nat > real,X2: real,F: nat > real,Y4: real] :
% 5.64/5.98 ( ( sums_real @ G @ X2 )
% 5.64/5.98 => ( ( sums_real @ F @ Y4 )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [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 ) ) ) ) )
% 5.64/5.98 @ ( plus_plus_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sums_if
% 5.64/5.98 thf(fact_8383_powr__neg__numeral,axiom,
% 5.64/5.98 ! [X2: real,N: num] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_neg_numeral
% 5.64/5.98 thf(fact_8384_tan__pos__pi2__le,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_pos_pi2_le
% 5.64/5.98 thf(fact_8385_tan__total__pos,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ? [X4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.64/5.98 & ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( tan_real @ X4 )
% 5.64/5.98 = Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_total_pos
% 5.64/5.98 thf(fact_8386_tan__less__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.98 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_less_zero
% 5.64/5.98 thf(fact_8387_tan__mono__le__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) )
% 5.64/5.98 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_mono_le_eq
% 5.64/5.98 thf(fact_8388_tan__mono__le,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_mono_le
% 5.64/5.98 thf(fact_8389_tan__bound__pi2,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_bound_pi2
% 5.64/5.98 thf(fact_8390_arctan,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y4 ) )
% 5.64/5.98 & ( ord_less_real @ ( arctan @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( tan_real @ ( arctan @ Y4 ) )
% 5.64/5.98 = Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan
% 5.64/5.98 thf(fact_8391_arctan__tan,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.64/5.98 = X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_tan
% 5.64/5.98 thf(fact_8392_arctan__unique,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ( tan_real @ X2 )
% 5.64/5.98 = Y4 )
% 5.64/5.98 => ( ( arctan @ Y4 )
% 5.64/5.98 = X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_unique
% 5.64/5.98 thf(fact_8393_lemma__tan__add1,axiom,
% 5.64/5.98 ! [X2: complex,Y4: complex] :
% 5.64/5.98 ( ( ( cos_complex @ X2 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ Y4 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y4 ) ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X2 @ Y4 ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % lemma_tan_add1
% 5.64/5.98 thf(fact_8394_lemma__tan__add1,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ Y4 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) ) )
% 5.64/5.98 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X2 @ Y4 ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y4 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % lemma_tan_add1
% 5.64/5.98 thf(fact_8395_tan__diff,axiom,
% 5.64/5.98 ! [X2: complex,Y4: complex] :
% 5.64/5.98 ( ( ( cos_complex @ X2 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ Y4 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y4 ) )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( tan_complex @ ( minus_minus_complex @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y4 ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y4 ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_diff
% 5.64/5.98 thf(fact_8396_tan__diff,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ Y4 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ ( minus_minus_real @ X2 @ Y4 ) )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( tan_real @ ( minus_minus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_diff
% 5.64/5.98 thf(fact_8397_tan__add,axiom,
% 5.64/5.98 ! [X2: complex,Y4: complex] :
% 5.64/5.98 ( ( ( cos_complex @ X2 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ Y4 )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y4 ) )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( tan_complex @ ( plus_plus_complex @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y4 ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_add
% 5.64/5.98 thf(fact_8398_tan__add,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( cos_real @ X2 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ Y4 )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ( cos_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( tan_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y4 ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_add
% 5.64/5.98 thf(fact_8399_tan__total__pi4,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.98 => ? [Z2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.64/5.98 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 & ( ( tan_real @ Z2 )
% 5.64/5.98 = X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_total_pi4
% 5.64/5.98 thf(fact_8400_cos__paired,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( sums_real
% 5.64/5.98 @ ^ [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 @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.64/5.98 @ ( cos_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_paired
% 5.64/5.98 thf(fact_8401_tan__half,axiom,
% 5.64/5.98 ( tan_complex
% 5.64/5.98 = ( ^ [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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_half
% 5.64/5.98 thf(fact_8402_tan__half,axiom,
% 5.64/5.98 ( tan_real
% 5.64/5.98 = ( ^ [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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_half
% 5.64/5.98 thf(fact_8403_diffs__equiv,axiom,
% 5.64/5.98 ! [C: nat > real,X2: real] :
% 5.64/5.98 ( ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) )
% 5.64/5.98 => ( sums_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( C @ N2 ) ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.64/5.98 @ ( suminf_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % diffs_equiv
% 5.64/5.98 thf(fact_8404_diffs__equiv,axiom,
% 5.64/5.98 ! [C: nat > complex,X2: complex] :
% 5.64/5.98 ( ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) )
% 5.64/5.98 => ( sums_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( C @ N2 ) ) @ ( power_power_complex @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.64/5.98 @ ( suminf_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % diffs_equiv
% 5.64/5.98 thf(fact_8405_arcosh__def,axiom,
% 5.64/5.98 ( arcosh_real
% 5.64/5.98 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcosh_def
% 5.64/5.98 thf(fact_8406_sin__tan,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( sin_real @ X2 )
% 5.64/5.98 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_tan
% 5.64/5.98 thf(fact_8407_cos__tan,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( cos_real @ X2 )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_tan
% 5.64/5.98 thf(fact_8408_monoI1,axiom,
% 5.64/5.98 ! [X8: nat > set_nat] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_set_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 5.64/5.98 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI1
% 5.64/5.98 thf(fact_8409_monoI1,axiom,
% 5.64/5.98 ! [X8: nat > rat] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_rat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 5.64/5.98 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI1
% 5.64/5.98 thf(fact_8410_monoI1,axiom,
% 5.64/5.98 ! [X8: nat > num] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_num @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 5.64/5.98 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI1
% 5.64/5.98 thf(fact_8411_monoI1,axiom,
% 5.64/5.98 ! [X8: nat > nat] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_nat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 5.64/5.98 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI1
% 5.64/5.98 thf(fact_8412_monoI1,axiom,
% 5.64/5.98 ! [X8: nat > int] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_int @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 5.64/5.98 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI1
% 5.64/5.98 thf(fact_8413_monoI1,axiom,
% 5.64/5.98 ! [X8: nat > real] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_real @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) )
% 5.64/5.98 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI1
% 5.64/5.98 thf(fact_8414_real__sqrt__less__iff,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_less_iff
% 5.64/5.98 thf(fact_8415_of__real__eq__1__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( real_V1803761363581548252l_real @ X2 )
% 5.64/5.98 = one_one_real )
% 5.64/5.98 = ( X2 = one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_eq_1_iff
% 5.64/5.98 thf(fact_8416_of__real__eq__1__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( real_V4546457046886955230omplex @ X2 )
% 5.64/5.98 = one_one_complex )
% 5.64/5.98 = ( X2 = one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_eq_1_iff
% 5.64/5.98 thf(fact_8417_of__real__1,axiom,
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_1
% 5.64/5.98 thf(fact_8418_of__real__1,axiom,
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_1
% 5.64/5.98 thf(fact_8419_of__real__numeral,axiom,
% 5.64/5.98 ! [W: num] :
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.64/5.98 = ( numeral_numeral_real @ W ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_numeral
% 5.64/5.98 thf(fact_8420_of__real__numeral,axiom,
% 5.64/5.98 ! [W: num] :
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.64/5.98 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_numeral
% 5.64/5.98 thf(fact_8421_of__real__mult,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( times_times_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_mult
% 5.64/5.98 thf(fact_8422_of__real__mult,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( times_times_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_mult
% 5.64/5.98 thf(fact_8423_real__sqrt__gt__0__iff,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ zero_zero_real @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_gt_0_iff
% 5.64/5.98 thf(fact_8424_real__sqrt__lt__0__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( sqrt @ X2 ) @ zero_zero_real )
% 5.64/5.98 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_lt_0_iff
% 5.64/5.98 thf(fact_8425_of__real__divide,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_divide
% 5.64/5.98 thf(fact_8426_of__real__divide,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_divide
% 5.64/5.98 thf(fact_8427_of__real__add,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_add
% 5.64/5.98 thf(fact_8428_of__real__add,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_add
% 5.64/5.98 thf(fact_8429_of__real__power,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X2 @ N ) )
% 5.64/5.98 = ( power_power_real @ ( real_V1803761363581548252l_real @ X2 ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_power
% 5.64/5.98 thf(fact_8430_of__real__power,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X2 @ N ) )
% 5.64/5.98 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X2 ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_power
% 5.64/5.98 thf(fact_8431_real__sqrt__lt__1__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.64/5.98 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_lt_1_iff
% 5.64/5.98 thf(fact_8432_real__sqrt__gt__1__iff,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ one_one_real @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_gt_1_iff
% 5.64/5.98 thf(fact_8433_real__sqrt__abs2,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( sqrt @ ( times_times_real @ X2 @ X2 ) )
% 5.64/5.98 = ( abs_abs_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_abs2
% 5.64/5.98 thf(fact_8434_real__sqrt__mult__self,axiom,
% 5.64/5.98 ! [A: real] :
% 5.64/5.98 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.64/5.98 = ( abs_abs_real @ A ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_mult_self
% 5.64/5.98 thf(fact_8435_real__sqrt__four,axiom,
% 5.64/5.98 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_four
% 5.64/5.98 thf(fact_8436_of__real__neg__numeral,axiom,
% 5.64/5.98 ! [W: num] :
% 5.64/5.98 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.98 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_neg_numeral
% 5.64/5.98 thf(fact_8437_of__real__neg__numeral,axiom,
% 5.64/5.98 ! [W: num] :
% 5.64/5.98 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.64/5.98 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_real_neg_numeral
% 5.64/5.98 thf(fact_8438_cos__of__real__pi,axiom,
% 5.64/5.98 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.64/5.98 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_of_real_pi
% 5.64/5.98 thf(fact_8439_cos__of__real__pi,axiom,
% 5.64/5.98 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.64/5.98 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_of_real_pi
% 5.64/5.98 thf(fact_8440_real__sqrt__abs,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( sqrt @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = ( abs_abs_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_abs
% 5.64/5.98 thf(fact_8441_real__sqrt__pow2,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_pow2
% 5.64/5.98 thf(fact_8442_real__sqrt__pow2__iff,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = X2 )
% 5.64/5.98 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_pow2_iff
% 5.64/5.98 thf(fact_8443_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real,Xa2: real,Ya: real] :
% 5.64/5.98 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_mult_squared_eq
% 5.64/5.98 thf(fact_8444_norm__of__real__add1,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ one_one_real ) )
% 5.64/5.98 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % norm_of_real_add1
% 5.64/5.98 thf(fact_8445_norm__of__real__add1,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ one_one_complex ) )
% 5.64/5.98 = ( abs_abs_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % norm_of_real_add1
% 5.64/5.98 thf(fact_8446_norm__of__real__addn,axiom,
% 5.64/5.98 ! [X2: real,B: num] :
% 5.64/5.98 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( numeral_numeral_real @ B ) ) )
% 5.64/5.98 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % norm_of_real_addn
% 5.64/5.98 thf(fact_8447_norm__of__real__addn,axiom,
% 5.64/5.98 ! [X2: real,B: num] :
% 5.64/5.98 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X2 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.64/5.98 = ( abs_abs_real @ ( plus_plus_real @ X2 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % norm_of_real_addn
% 5.64/5.98 thf(fact_8448_cos__of__real__pi__half,axiom,
% 5.64/5.98 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_of_real_pi_half
% 5.64/5.98 thf(fact_8449_cos__of__real__pi__half,axiom,
% 5.64/5.98 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = zero_zero_complex ) ).
% 5.64/5.98
% 5.64/5.98 % cos_of_real_pi_half
% 5.64/5.98 thf(fact_8450_sin__of__real__pi__half,axiom,
% 5.64/5.98 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % sin_of_real_pi_half
% 5.64/5.98 thf(fact_8451_sin__of__real__pi__half,axiom,
% 5.64/5.98 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % sin_of_real_pi_half
% 5.64/5.98 thf(fact_8452_real__sqrt__mult,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( sqrt @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( times_times_real @ ( sqrt @ X2 ) @ ( sqrt @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_mult
% 5.64/5.98 thf(fact_8453_real__sqrt__divide,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( sqrt @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide_divide_real @ ( sqrt @ X2 ) @ ( sqrt @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_divide
% 5.64/5.98 thf(fact_8454_real__sqrt__less__mono,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.98 => ( ord_less_real @ ( sqrt @ X2 ) @ ( sqrt @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_less_mono
% 5.64/5.98 thf(fact_8455_real__sqrt__gt__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_gt_zero
% 5.64/5.98 thf(fact_8456_nonzero__of__real__divide,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( Y4 != zero_zero_real )
% 5.64/5.98 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X2 ) @ ( real_V1803761363581548252l_real @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % nonzero_of_real_divide
% 5.64/5.98 thf(fact_8457_nonzero__of__real__divide,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( Y4 != zero_zero_real )
% 5.64/5.98 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/5.98 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X2 ) @ ( real_V4546457046886955230omplex @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % nonzero_of_real_divide
% 5.64/5.98 thf(fact_8458_real__div__sqrt,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( divide_divide_real @ X2 @ ( sqrt @ X2 ) )
% 5.64/5.98 = ( sqrt @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_div_sqrt
% 5.64/5.98 thf(fact_8459_le__real__sqrt__sumsq,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y4 @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_real_sqrt_sumsq
% 5.64/5.98 thf(fact_8460_norm__less__p1,axiom,
% 5.64/5.98 ! [X2: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X2 ) ) @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % norm_less_p1
% 5.64/5.98 thf(fact_8461_norm__less__p1,axiom,
% 5.64/5.98 ! [X2: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X2 ) ) @ one_one_complex ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % norm_less_p1
% 5.64/5.98 thf(fact_8462_sqrt2__less__2,axiom,
% 5.64/5.98 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt2_less_2
% 5.64/5.98 thf(fact_8463_diffs__def,axiom,
% 5.64/5.98 ( diffs_rat
% 5.64/5.98 = ( ^ [C2: nat > rat,N2: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % diffs_def
% 5.64/5.98 thf(fact_8464_diffs__def,axiom,
% 5.64/5.98 ( diffs_int
% 5.64/5.98 = ( ^ [C2: nat > int,N2: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % diffs_def
% 5.64/5.98 thf(fact_8465_diffs__def,axiom,
% 5.64/5.98 ( diffs_real
% 5.64/5.98 = ( ^ [C2: nat > real,N2: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % diffs_def
% 5.64/5.98 thf(fact_8466_diffs__def,axiom,
% 5.64/5.98 ( diffs_complex
% 5.64/5.98 = ( ^ [C2: nat > complex,N2: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( C2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % diffs_def
% 5.64/5.98 thf(fact_8467_real__less__rsqrt,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 )
% 5.64/5.98 => ( ord_less_real @ X2 @ ( sqrt @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_less_rsqrt
% 5.64/5.98 thf(fact_8468_sqrt__le__D,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y4 )
% 5.64/5.98 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt_le_D
% 5.64/5.98 thf(fact_8469_real__le__rsqrt,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 )
% 5.64/5.98 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_le_rsqrt
% 5.64/5.98 thf(fact_8470_termdiff__converges__all,axiom,
% 5.64/5.98 ! [C: nat > complex,X2: complex] :
% 5.64/5.98 ( ! [X4: complex] :
% 5.64/5.98 ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X4 @ N2 ) ) )
% 5.64/5.98 => ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % termdiff_converges_all
% 5.64/5.98 thf(fact_8471_termdiff__converges__all,axiom,
% 5.64/5.98 ! [C: nat > real,X2: real] :
% 5.64/5.98 ( ! [X4: real] :
% 5.64/5.98 ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X4 @ N2 ) ) )
% 5.64/5.98 => ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % termdiff_converges_all
% 5.64/5.98 thf(fact_8472_tan__60,axiom,
% 5.64/5.98 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.64/5.98 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_60
% 5.64/5.98 thf(fact_8473_real__le__lsqrt,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_le_lsqrt
% 5.64/5.98 thf(fact_8474_real__sqrt__unique,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] :
% 5.64/5.98 ( ( ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.98 = X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( sqrt @ X2 )
% 5.64/5.98 = Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_unique
% 5.64/5.98 thf(fact_8475_lemma__real__divide__sqrt__less,axiom,
% 5.64/5.98 ! [U: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ U )
% 5.64/5.98 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.64/5.98
% 5.64/5.98 % lemma_real_divide_sqrt_less
% 5.64/5.98 thf(fact_8476_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = X2 )
% 5.64/5.98 => ( Y4 = zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_eq_cancel
% 5.64/5.98 thf(fact_8477_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = Y4 )
% 5.64/5.98 => ( X2 = zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_eq_cancel2
% 5.64/5.98 thf(fact_8478_real__sqrt__sum__squares__ge1,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_ge1
% 5.64/5.98 thf(fact_8479_real__sqrt__sum__squares__ge2,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] : ( ord_less_eq_real @ Y4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_ge2
% 5.64/5.98 thf(fact_8480_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.64/5.98 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_triangle_ineq
% 5.64/5.98 thf(fact_8481_sqrt__ge__absD,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y4 ) )
% 5.64/5.98 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt_ge_absD
% 5.64/5.98 thf(fact_8482_cos__45,axiom,
% 5.64/5.98 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_45
% 5.64/5.98 thf(fact_8483_sin__45,axiom,
% 5.64/5.98 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_45
% 5.64/5.98 thf(fact_8484_cos__int__times__real,axiom,
% 5.64/5.98 ! [M: int,X2: real] :
% 5.64/5.98 ( ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.64/5.98 = ( real_V1803761363581548252l_real @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_int_times_real
% 5.64/5.98 thf(fact_8485_cos__int__times__real,axiom,
% 5.64/5.98 ! [M: int,X2: real] :
% 5.64/5.98 ( ( cos_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.64/5.98 = ( real_V4546457046886955230omplex @ ( cos_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_int_times_real
% 5.64/5.98 thf(fact_8486_sin__int__times__real,axiom,
% 5.64/5.98 ! [M: int,X2: real] :
% 5.64/5.98 ( ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ ( real_V1803761363581548252l_real @ X2 ) ) )
% 5.64/5.98 = ( real_V1803761363581548252l_real @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_int_times_real
% 5.64/5.98 thf(fact_8487_sin__int__times__real,axiom,
% 5.64/5.98 ! [M: int,X2: real] :
% 5.64/5.98 ( ( sin_complex @ ( times_times_complex @ ( ring_17405671764205052669omplex @ M ) @ ( real_V4546457046886955230omplex @ X2 ) ) )
% 5.64/5.98 = ( real_V4546457046886955230omplex @ ( sin_real @ ( times_times_real @ ( ring_1_of_int_real @ M ) @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_int_times_real
% 5.64/5.98 thf(fact_8488_real__less__lsqrt,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ord_less_real @ ( sqrt @ X2 ) @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_less_lsqrt
% 5.64/5.98 thf(fact_8489_sqrt__sum__squares__le__sum,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt_sum_squares_le_sum
% 5.64/5.98 thf(fact_8490_tan__30,axiom,
% 5.64/5.98 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % tan_30
% 5.64/5.98 thf(fact_8491_sqrt__even__pow2,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.98 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.98 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt_even_pow2
% 5.64/5.98 thf(fact_8492_real__sqrt__ge__abs1,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_ge_abs1
% 5.64/5.98 thf(fact_8493_real__sqrt__ge__abs2,axiom,
% 5.64/5.98 ! [Y4: real,X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_ge_abs2
% 5.64/5.98 thf(fact_8494_sqrt__sum__squares__le__sum__abs,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt_sum_squares_le_sum_abs
% 5.64/5.98 thf(fact_8495_ln__sqrt,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.64/5.98 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % ln_sqrt
% 5.64/5.98 thf(fact_8496_cos__30,axiom,
% 5.64/5.98 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_30
% 5.64/5.98 thf(fact_8497_sin__60,axiom,
% 5.64/5.98 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.64/5.98 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_60
% 5.64/5.98 thf(fact_8498_cos__sin__eq,axiom,
% 5.64/5.98 ( cos_real
% 5.64/5.98 = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_sin_eq
% 5.64/5.98 thf(fact_8499_cos__sin__eq,axiom,
% 5.64/5.98 ( cos_complex
% 5.64/5.98 = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_sin_eq
% 5.64/5.98 thf(fact_8500_sin__cos__eq,axiom,
% 5.64/5.98 ( sin_real
% 5.64/5.98 = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_eq
% 5.64/5.98 thf(fact_8501_sin__cos__eq,axiom,
% 5.64/5.98 ( sin_complex
% 5.64/5.98 = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_eq
% 5.64/5.98 thf(fact_8502_termdiff__converges,axiom,
% 5.64/5.98 ! [X2: real,K5: real,C: nat > real] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ K5 )
% 5.64/5.98 => ( ! [X4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 5.64/5.98 => ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( C @ N2 ) @ ( power_power_real @ X4 @ N2 ) ) ) )
% 5.64/5.98 => ( summable_real
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_real @ ( diffs_real @ C @ N2 ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % termdiff_converges
% 5.64/5.98 thf(fact_8503_termdiff__converges,axiom,
% 5.64/5.98 ! [X2: complex,K5: real,C: nat > complex] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ K5 )
% 5.64/5.98 => ( ! [X4: complex] :
% 5.64/5.98 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 5.64/5.98 => ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( C @ N2 ) @ ( power_power_complex @ X4 @ N2 ) ) ) )
% 5.64/5.98 => ( summable_complex
% 5.64/5.98 @ ^ [N2: nat] : ( times_times_complex @ ( diffs_complex @ C @ N2 ) @ ( power_power_complex @ X2 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % termdiff_converges
% 5.64/5.98 thf(fact_8504_arsinh__real__aux,axiom,
% 5.64/5.98 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arsinh_real_aux
% 5.64/5.98 thf(fact_8505_real__sqrt__power__even,axiom,
% 5.64/5.98 ! [N: nat,X2: real] :
% 5.64/5.98 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( power_power_real @ ( sqrt @ X2 ) @ N )
% 5.64/5.98 = ( power_power_real @ X2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_power_even
% 5.64/5.98 thf(fact_8506_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.64/5.98 ! [X2: real,Y4: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_mult_ge_zero
% 5.64/5.98 thf(fact_8507_arith__geo__mean__sqrt,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y4 ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arith_geo_mean_sqrt
% 5.64/5.98 thf(fact_8508_powr__half__sqrt,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 = ( sqrt @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % powr_half_sqrt
% 5.64/5.98 thf(fact_8509_minus__sin__cos__eq,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( uminus_uminus_real @ ( sin_real @ X2 ) )
% 5.64/5.98 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % minus_sin_cos_eq
% 5.64/5.98 thf(fact_8510_minus__sin__cos__eq,axiom,
% 5.64/5.98 ! [X2: complex] :
% 5.64/5.98 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X2 ) )
% 5.64/5.98 = ( cos_complex @ ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % minus_sin_cos_eq
% 5.64/5.98 thf(fact_8511_cos__x__y__le__one,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % cos_x_y_le_one
% 5.64/5.98 thf(fact_8512_real__sqrt__sum__squares__less,axiom,
% 5.64/5.98 ! [X2: real,U: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ ( abs_abs_real @ Y4 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/5.98 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_sqrt_sum_squares_less
% 5.64/5.98 thf(fact_8513_arcosh__real__def,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.64/5.98 => ( ( arcosh_real @ X2 )
% 5.64/5.98 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcosh_real_def
% 5.64/5.98 thf(fact_8514_cos__arctan,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( cos_real @ ( arctan @ X2 ) )
% 5.64/5.98 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_arctan
% 5.64/5.98 thf(fact_8515_sin__arctan,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( sin_real @ ( arctan @ X2 ) )
% 5.64/5.98 = ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_arctan
% 5.64/5.98 thf(fact_8516_sqrt__sum__squares__half__less,axiom,
% 5.64/5.98 ! [X2: real,U: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sqrt_sum_squares_half_less
% 5.64/5.98 thf(fact_8517_sin__cos__sqrt,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.64/5.98 => ( ( sin_real @ X2 )
% 5.64/5.98 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_cos_sqrt
% 5.64/5.98 thf(fact_8518_arctan__half,axiom,
% 5.64/5.98 ( arctan
% 5.64/5.98 = ( ^ [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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arctan_half
% 5.64/5.98 thf(fact_8519_monoseq__Suc,axiom,
% 5.64/5.98 ( topolo7278393974255667507et_nat
% 5.64/5.98 = ( ^ [X5: nat > set_nat] :
% 5.64/5.98 ( ! [N2: nat] : ( ord_less_eq_set_nat @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.64/5.98 | ! [N2: nat] : ( ord_less_eq_set_nat @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_Suc
% 5.64/5.98 thf(fact_8520_monoseq__Suc,axiom,
% 5.64/5.98 ( topolo4267028734544971653eq_rat
% 5.64/5.98 = ( ^ [X5: nat > rat] :
% 5.64/5.98 ( ! [N2: nat] : ( ord_less_eq_rat @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.64/5.98 | ! [N2: nat] : ( ord_less_eq_rat @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_Suc
% 5.64/5.98 thf(fact_8521_monoseq__Suc,axiom,
% 5.64/5.98 ( topolo1459490580787246023eq_num
% 5.64/5.98 = ( ^ [X5: nat > num] :
% 5.64/5.98 ( ! [N2: nat] : ( ord_less_eq_num @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.64/5.98 | ! [N2: nat] : ( ord_less_eq_num @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_Suc
% 5.64/5.98 thf(fact_8522_monoseq__Suc,axiom,
% 5.64/5.98 ( topolo4902158794631467389eq_nat
% 5.64/5.98 = ( ^ [X5: nat > nat] :
% 5.64/5.98 ( ! [N2: nat] : ( ord_less_eq_nat @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.64/5.98 | ! [N2: nat] : ( ord_less_eq_nat @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_Suc
% 5.64/5.98 thf(fact_8523_monoseq__Suc,axiom,
% 5.64/5.98 ( topolo4899668324122417113eq_int
% 5.64/5.98 = ( ^ [X5: nat > int] :
% 5.64/5.98 ( ! [N2: nat] : ( ord_less_eq_int @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.64/5.98 | ! [N2: nat] : ( ord_less_eq_int @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_Suc
% 5.64/5.98 thf(fact_8524_monoseq__Suc,axiom,
% 5.64/5.98 ( topolo6980174941875973593q_real
% 5.64/5.98 = ( ^ [X5: nat > real] :
% 5.64/5.98 ( ! [N2: nat] : ( ord_less_eq_real @ ( X5 @ N2 ) @ ( X5 @ ( suc @ N2 ) ) )
% 5.64/5.98 | ! [N2: nat] : ( ord_less_eq_real @ ( X5 @ ( suc @ N2 ) ) @ ( X5 @ N2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_Suc
% 5.64/5.98 thf(fact_8525_mono__SucI2,axiom,
% 5.64/5.98 ! [X8: nat > set_nat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.64/5.98 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI2
% 5.64/5.98 thf(fact_8526_mono__SucI2,axiom,
% 5.64/5.98 ! [X8: nat > rat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.64/5.98 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI2
% 5.64/5.98 thf(fact_8527_mono__SucI2,axiom,
% 5.64/5.98 ! [X8: nat > num] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.64/5.98 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI2
% 5.64/5.98 thf(fact_8528_mono__SucI2,axiom,
% 5.64/5.98 ! [X8: nat > nat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.64/5.98 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI2
% 5.64/5.98 thf(fact_8529_mono__SucI2,axiom,
% 5.64/5.98 ! [X8: nat > int] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.64/5.98 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI2
% 5.64/5.98 thf(fact_8530_mono__SucI2,axiom,
% 5.64/5.98 ! [X8: nat > real] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.64/5.98 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI2
% 5.64/5.98 thf(fact_8531_mono__SucI1,axiom,
% 5.64/5.98 ! [X8: nat > set_nat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.64/5.98 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI1
% 5.64/5.98 thf(fact_8532_mono__SucI1,axiom,
% 5.64/5.98 ! [X8: nat > rat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.64/5.98 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI1
% 5.64/5.98 thf(fact_8533_mono__SucI1,axiom,
% 5.64/5.98 ! [X8: nat > num] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.64/5.98 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI1
% 5.64/5.98 thf(fact_8534_mono__SucI1,axiom,
% 5.64/5.98 ! [X8: nat > nat] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.64/5.98 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI1
% 5.64/5.98 thf(fact_8535_mono__SucI1,axiom,
% 5.64/5.98 ! [X8: nat > int] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.64/5.98 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI1
% 5.64/5.98 thf(fact_8536_mono__SucI1,axiom,
% 5.64/5.98 ! [X8: nat > real] :
% 5.64/5.98 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.64/5.98 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % mono_SucI1
% 5.64/5.98 thf(fact_8537_monoseq__def,axiom,
% 5.64/5.98 ( topolo7278393974255667507et_nat
% 5.64/5.98 = ( ^ [X5: nat > set_nat] :
% 5.64/5.98 ( ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_set_nat @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) )
% 5.64/5.98 | ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_set_nat @ ( X5 @ N2 ) @ ( X5 @ M2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_def
% 5.64/5.98 thf(fact_8538_monoseq__def,axiom,
% 5.64/5.98 ( topolo4267028734544971653eq_rat
% 5.64/5.98 = ( ^ [X5: nat > rat] :
% 5.64/5.98 ( ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_rat @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) )
% 5.64/5.98 | ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_rat @ ( X5 @ N2 ) @ ( X5 @ M2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_def
% 5.64/5.98 thf(fact_8539_monoseq__def,axiom,
% 5.64/5.98 ( topolo1459490580787246023eq_num
% 5.64/5.98 = ( ^ [X5: nat > num] :
% 5.64/5.98 ( ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_num @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) )
% 5.64/5.98 | ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_num @ ( X5 @ N2 ) @ ( X5 @ M2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_def
% 5.64/5.98 thf(fact_8540_monoseq__def,axiom,
% 5.64/5.98 ( topolo4902158794631467389eq_nat
% 5.64/5.98 = ( ^ [X5: nat > nat] :
% 5.64/5.98 ( ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_nat @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) )
% 5.64/5.98 | ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_nat @ ( X5 @ N2 ) @ ( X5 @ M2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_def
% 5.64/5.98 thf(fact_8541_monoseq__def,axiom,
% 5.64/5.98 ( topolo4899668324122417113eq_int
% 5.64/5.98 = ( ^ [X5: nat > int] :
% 5.64/5.98 ( ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_int @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) )
% 5.64/5.98 | ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_int @ ( X5 @ N2 ) @ ( X5 @ M2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_def
% 5.64/5.98 thf(fact_8542_monoseq__def,axiom,
% 5.64/5.98 ( topolo6980174941875973593q_real
% 5.64/5.98 = ( ^ [X5: nat > real] :
% 5.64/5.98 ( ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_real @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) )
% 5.64/5.98 | ! [M2: nat,N2: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M2 @ N2 )
% 5.64/5.98 => ( ord_less_eq_real @ ( X5 @ N2 ) @ ( X5 @ M2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoseq_def
% 5.64/5.98 thf(fact_8543_monoI2,axiom,
% 5.64/5.98 ! [X8: nat > set_nat] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_set_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 5.64/5.98 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI2
% 5.64/5.98 thf(fact_8544_monoI2,axiom,
% 5.64/5.98 ! [X8: nat > rat] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 5.64/5.98 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI2
% 5.64/5.98 thf(fact_8545_monoI2,axiom,
% 5.64/5.98 ! [X8: nat > num] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 5.64/5.98 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI2
% 5.64/5.98 thf(fact_8546_monoI2,axiom,
% 5.64/5.98 ! [X8: nat > nat] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 5.64/5.98 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI2
% 5.64/5.98 thf(fact_8547_monoI2,axiom,
% 5.64/5.98 ! [X8: nat > int] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 5.64/5.98 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI2
% 5.64/5.98 thf(fact_8548_monoI2,axiom,
% 5.64/5.98 ! [X8: nat > real] :
% 5.64/5.98 ( ! [M4: nat,N3: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ M4 @ N3 )
% 5.64/5.98 => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M4 ) ) )
% 5.64/5.98 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.64/5.98
% 5.64/5.98 % monoI2
% 5.64/5.98 thf(fact_8549_arsinh__def,axiom,
% 5.64/5.98 ( arsinh_real
% 5.64/5.98 = ( ^ [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 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arsinh_def
% 5.64/5.98 thf(fact_8550_arsinh__real__def,axiom,
% 5.64/5.98 ( arsinh_real
% 5.64/5.98 = ( ^ [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 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arsinh_real_def
% 5.64/5.98 thf(fact_8551_cos__arcsin,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.98 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.64/5.98 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_arcsin
% 5.64/5.98 thf(fact_8552_sin__arccos__abs,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.64/5.98 => ( ( sin_real @ ( arccos @ Y4 ) )
% 5.64/5.98 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_arccos_abs
% 5.64/5.98 thf(fact_8553_sin__arccos,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.98 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.64/5.98 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_arccos
% 5.64/5.98 thf(fact_8554_arccos__0,axiom,
% 5.64/5.98 ( ( arccos @ zero_zero_real )
% 5.64/5.98 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arccos_0
% 5.64/5.98 thf(fact_8555_arcsin__1,axiom,
% 5.64/5.98 ( ( arcsin @ one_one_real )
% 5.64/5.98 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_1
% 5.64/5.98 thf(fact_8556_arcsin__minus__1,axiom,
% 5.64/5.98 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.64/5.98 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_minus_1
% 5.64/5.98 thf(fact_8557_arccos__less__arccos,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ord_less_real @ ( arccos @ Y4 ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arccos_less_arccos
% 5.64/5.98 thf(fact_8558_arccos__less__mono,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ Y4 @ X2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arccos_less_mono
% 5.64/5.98 thf(fact_8559_arcsin__less__arcsin,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y4 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_less_arcsin
% 5.64/5.98 thf(fact_8560_arcsin__less__mono,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y4 ) @ one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y4 ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_less_mono
% 5.64/5.98 thf(fact_8561_arccos__lt__bounded,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y4 ) )
% 5.64/5.98 & ( ord_less_real @ ( arccos @ Y4 ) @ pi ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arccos_lt_bounded
% 5.64/5.98 thf(fact_8562_sin__arccos__nonzero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/5.98 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.64/5.98 != zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % sin_arccos_nonzero
% 5.64/5.98 thf(fact_8563_cos__arcsin__nonzero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/5.98 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.64/5.98 != zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % cos_arcsin_nonzero
% 5.64/5.98 thf(fact_8564_arccos__le__pi2,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ord_less_eq_real @ ( arccos @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arccos_le_pi2
% 5.64/5.98 thf(fact_8565_arcsin__lt__bounded,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.64/5.98 & ( ord_less_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_lt_bounded
% 5.64/5.98 thf(fact_8566_arcsin__bounded,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.64/5.98 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_bounded
% 5.64/5.98 thf(fact_8567_arcsin__ubound,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_ubound
% 5.64/5.98 thf(fact_8568_arcsin__lbound,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_lbound
% 5.64/5.98 thf(fact_8569_arcsin__sin,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.64/5.98 = X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_sin
% 5.64/5.98 thf(fact_8570_le__arcsin__iff,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( arcsin @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( sin_real @ Y4 ) @ X2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_arcsin_iff
% 5.64/5.98 thf(fact_8571_arcsin__le__iff,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/5.98 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y4 )
% 5.64/5.98 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y4 ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_le_iff
% 5.64/5.98 thf(fact_8572_arcsin__pi,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.64/5.98 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ pi )
% 5.64/5.98 & ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.64/5.98 = Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin_pi
% 5.64/5.98 thf(fact_8573_arcsin,axiom,
% 5.64/5.98 ! [Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y4 )
% 5.64/5.98 => ( ( ord_less_eq_real @ Y4 @ one_one_real )
% 5.64/5.98 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y4 ) )
% 5.64/5.98 & ( ord_less_eq_real @ ( arcsin @ Y4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.98 & ( ( sin_real @ ( arcsin @ Y4 ) )
% 5.64/5.98 = Y4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arcsin
% 5.64/5.98 thf(fact_8574_arccos__cos__eq__abs__2pi,axiom,
% 5.64/5.98 ! [Theta: real] :
% 5.64/5.98 ~ ! [K3: int] :
% 5.64/5.98 ( ( arccos @ ( cos_real @ Theta ) )
% 5.64/5.98 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % arccos_cos_eq_abs_2pi
% 5.64/5.98 thf(fact_8575_pochhammer__double,axiom,
% 5.64/5.98 ! [Z: rat,N: nat] :
% 5.64/5.98 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.98 = ( 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 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_double
% 5.64/5.98 thf(fact_8576_pochhammer__double,axiom,
% 5.64/5.98 ! [Z: real,N: nat] :
% 5.64/5.98 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.98 = ( 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 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_double
% 5.64/5.98 thf(fact_8577_pochhammer__double,axiom,
% 5.64/5.98 ! [Z: complex,N: nat] :
% 5.64/5.98 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.98 = ( 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 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_double
% 5.64/5.98 thf(fact_8578_floor__log__nat__eq__powr__iff,axiom,
% 5.64/5.98 ! [B: nat,K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.98 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.98 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.64/5.98 = ( semiri1314217659103216013at_int @ N ) )
% 5.64/5.98 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.64/5.98 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_log_nat_eq_powr_iff
% 5.64/5.98 thf(fact_8579_of__nat__code,axiom,
% 5.64/5.98 ( semiri681578069525770553at_rat
% 5.64/5.98 = ( ^ [N2: nat] :
% 5.64/5.98 ( semiri7787848453975740701ux_rat
% 5.64/5.98 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.64/5.98 @ N2
% 5.64/5.98 @ zero_zero_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_nat_code
% 5.64/5.98 thf(fact_8580_of__nat__code,axiom,
% 5.64/5.98 ( semiri1314217659103216013at_int
% 5.64/5.98 = ( ^ [N2: nat] :
% 5.64/5.98 ( semiri8420488043553186161ux_int
% 5.64/5.98 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.64/5.98 @ N2
% 5.64/5.98 @ zero_zero_int ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_nat_code
% 5.64/5.98 thf(fact_8581_of__nat__code,axiom,
% 5.64/5.98 ( semiri5074537144036343181t_real
% 5.64/5.98 = ( ^ [N2: nat] :
% 5.64/5.98 ( semiri7260567687927622513x_real
% 5.64/5.98 @ ^ [I4: real] : ( plus_plus_real @ I4 @ one_one_real )
% 5.64/5.98 @ N2
% 5.64/5.98 @ zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_nat_code
% 5.64/5.98 thf(fact_8582_of__nat__code,axiom,
% 5.64/5.98 ( semiri1316708129612266289at_nat
% 5.64/5.98 = ( ^ [N2: nat] :
% 5.64/5.98 ( semiri8422978514062236437ux_nat
% 5.64/5.98 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.64/5.98 @ N2
% 5.64/5.98 @ zero_zero_nat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_nat_code
% 5.64/5.98 thf(fact_8583_of__nat__code,axiom,
% 5.64/5.98 ( semiri8010041392384452111omplex
% 5.64/5.98 = ( ^ [N2: nat] :
% 5.64/5.98 ( semiri2816024913162550771omplex
% 5.64/5.98 @ ^ [I4: complex] : ( plus_plus_complex @ I4 @ one_one_complex )
% 5.64/5.98 @ N2
% 5.64/5.98 @ zero_zero_complex ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % of_nat_code
% 5.64/5.98 thf(fact_8584_gchoose__row__sum__weighted,axiom,
% 5.64/5.98 ! [R2: rat,M: nat] :
% 5.64/5.98 ( ( groups2906978787729119204at_rat
% 5.64/5.98 @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 5.64/5.98 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.64/5.98 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gchoose_row_sum_weighted
% 5.64/5.98 thf(fact_8585_gchoose__row__sum__weighted,axiom,
% 5.64/5.98 ! [R2: complex,M: nat] :
% 5.64/5.98 ( ( groups2073611262835488442omplex
% 5.64/5.98 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 5.64/5.98 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.64/5.98 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gchoose_row_sum_weighted
% 5.64/5.98 thf(fact_8586_gchoose__row__sum__weighted,axiom,
% 5.64/5.98 ! [R2: real,M: nat] :
% 5.64/5.98 ( ( groups6591440286371151544t_real
% 5.64/5.98 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.64/5.98 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.64/5.98 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gchoose_row_sum_weighted
% 5.64/5.98 thf(fact_8587_central__binomial__lower__bound,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.98 => ( 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 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % central_binomial_lower_bound
% 5.64/5.98 thf(fact_8588_binomial__Suc__n,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( binomial @ ( suc @ N ) @ N )
% 5.64/5.98 = ( suc @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_Suc_n
% 5.64/5.98 thf(fact_8589_binomial__n__n,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( binomial @ N @ N )
% 5.64/5.98 = one_one_nat ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_n_n
% 5.64/5.98 thf(fact_8590_gbinomial__0_I2_J,axiom,
% 5.64/5.98 ! [K: nat] :
% 5.64/5.98 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.64/5.98 = zero_zero_complex ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(2)
% 5.64/5.98 thf(fact_8591_gbinomial__0_I2_J,axiom,
% 5.64/5.98 ! [K: nat] :
% 5.64/5.98 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.64/5.98 = zero_zero_real ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(2)
% 5.64/5.98 thf(fact_8592_gbinomial__0_I2_J,axiom,
% 5.64/5.98 ! [K: nat] :
% 5.64/5.98 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.64/5.98 = zero_zero_rat ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(2)
% 5.64/5.98 thf(fact_8593_gbinomial__0_I2_J,axiom,
% 5.64/5.98 ! [K: nat] :
% 5.64/5.98 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.64/5.98 = zero_zero_nat ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(2)
% 5.64/5.98 thf(fact_8594_gbinomial__0_I2_J,axiom,
% 5.64/5.98 ! [K: nat] :
% 5.64/5.98 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.64/5.98 = zero_zero_int ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(2)
% 5.64/5.98 thf(fact_8595_floor__numeral,axiom,
% 5.64/5.98 ! [V: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.64/5.98 = ( numeral_numeral_int @ V ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_numeral
% 5.64/5.98 thf(fact_8596_floor__numeral,axiom,
% 5.64/5.98 ! [V: num] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.64/5.98 = ( numeral_numeral_int @ V ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_numeral
% 5.64/5.98 thf(fact_8597_binomial__0__Suc,axiom,
% 5.64/5.98 ! [K: nat] :
% 5.64/5.98 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.64/5.98 = zero_zero_nat ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_0_Suc
% 5.64/5.98 thf(fact_8598_binomial__1,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.64/5.98 = N ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_1
% 5.64/5.98 thf(fact_8599_binomial__eq__0__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ( binomial @ N @ K )
% 5.64/5.98 = zero_zero_nat )
% 5.64/5.98 = ( ord_less_nat @ N @ K ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_eq_0_iff
% 5.64/5.98 thf(fact_8600_gbinomial__0_I1_J,axiom,
% 5.64/5.98 ! [A: complex] :
% 5.64/5.98 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(1)
% 5.64/5.98 thf(fact_8601_gbinomial__0_I1_J,axiom,
% 5.64/5.98 ! [A: real] :
% 5.64/5.98 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(1)
% 5.64/5.98 thf(fact_8602_gbinomial__0_I1_J,axiom,
% 5.64/5.98 ! [A: rat] :
% 5.64/5.98 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_rat ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(1)
% 5.64/5.98 thf(fact_8603_gbinomial__0_I1_J,axiom,
% 5.64/5.98 ! [A: nat] :
% 5.64/5.98 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_nat ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(1)
% 5.64/5.98 thf(fact_8604_gbinomial__0_I1_J,axiom,
% 5.64/5.98 ! [A: int] :
% 5.64/5.98 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_int ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_0(1)
% 5.64/5.98 thf(fact_8605_floor__one,axiom,
% 5.64/5.98 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.64/5.98 = one_one_int ) ).
% 5.64/5.98
% 5.64/5.98 % floor_one
% 5.64/5.98 thf(fact_8606_floor__one,axiom,
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.64/5.98 = one_one_int ) ).
% 5.64/5.98
% 5.64/5.98 % floor_one
% 5.64/5.98 thf(fact_8607_binomial__Suc__Suc,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_Suc_Suc
% 5.64/5.98 thf(fact_8608_pochhammer__0,axiom,
% 5.64/5.98 ! [A: complex] :
% 5.64/5.98 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_complex ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0
% 5.64/5.98 thf(fact_8609_pochhammer__0,axiom,
% 5.64/5.98 ! [A: real] :
% 5.64/5.98 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_real ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0
% 5.64/5.98 thf(fact_8610_pochhammer__0,axiom,
% 5.64/5.98 ! [A: rat] :
% 5.64/5.98 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_rat ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0
% 5.64/5.98 thf(fact_8611_pochhammer__0,axiom,
% 5.64/5.98 ! [A: nat] :
% 5.64/5.98 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_nat ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0
% 5.64/5.98 thf(fact_8612_pochhammer__0,axiom,
% 5.64/5.98 ! [A: int] :
% 5.64/5.98 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.64/5.98 = one_one_int ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0
% 5.64/5.98 thf(fact_8613_binomial__n__0,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( binomial @ N @ zero_zero_nat )
% 5.64/5.98 = one_one_nat ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_n_0
% 5.64/5.98 thf(fact_8614_zero__less__binomial__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.64/5.98 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % zero_less_binomial_iff
% 5.64/5.98 thf(fact_8615_zero__le__floor,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % zero_le_floor
% 5.64/5.98 thf(fact_8616_zero__le__floor,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ zero_zero_rat @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % zero_le_floor
% 5.64/5.98 thf(fact_8617_floor__less__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.64/5.98 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_zero
% 5.64/5.98 thf(fact_8618_floor__less__zero,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.64/5.98 = ( ord_less_rat @ X2 @ zero_zero_rat ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_zero
% 5.64/5.98 thf(fact_8619_numeral__le__floor,axiom,
% 5.64/5.98 ! [V: num,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % numeral_le_floor
% 5.64/5.98 thf(fact_8620_numeral__le__floor,axiom,
% 5.64/5.98 ! [V: num,X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % numeral_le_floor
% 5.64/5.98 thf(fact_8621_zero__less__floor,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % zero_less_floor
% 5.64/5.98 thf(fact_8622_zero__less__floor,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % zero_less_floor
% 5.64/5.98 thf(fact_8623_floor__le__zero,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ zero_zero_int )
% 5.64/5.98 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_zero
% 5.64/5.98 thf(fact_8624_floor__le__zero,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ zero_zero_int )
% 5.64/5.98 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_zero
% 5.64/5.98 thf(fact_8625_floor__less__numeral,axiom,
% 5.64/5.98 ! [X2: real,V: num] :
% 5.64/5.98 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_numeral
% 5.64/5.98 thf(fact_8626_floor__less__numeral,axiom,
% 5.64/5.98 ! [X2: rat,V: num] :
% 5.64/5.98 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.98 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_numeral
% 5.64/5.98 thf(fact_8627_one__le__floor,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % one_le_floor
% 5.64/5.98 thf(fact_8628_one__le__floor,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % one_le_floor
% 5.64/5.98 thf(fact_8629_floor__less__one,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.64/5.98 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_one
% 5.64/5.98 thf(fact_8630_floor__less__one,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.64/5.98 = ( ord_less_rat @ X2 @ one_one_rat ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_one
% 5.64/5.98 thf(fact_8631_floor__neg__numeral,axiom,
% 5.64/5.98 ! [V: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_neg_numeral
% 5.64/5.98 thf(fact_8632_floor__neg__numeral,axiom,
% 5.64/5.98 ! [V: num] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.98 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_neg_numeral
% 5.64/5.98 thf(fact_8633_floor__diff__numeral,axiom,
% 5.64/5.98 ! [X2: real,V: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ ( numeral_numeral_real @ V ) ) )
% 5.64/5.98 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_diff_numeral
% 5.64/5.98 thf(fact_8634_floor__diff__numeral,axiom,
% 5.64/5.98 ! [X2: rat,V: num] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ ( numeral_numeral_rat @ V ) ) )
% 5.64/5.98 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_diff_numeral
% 5.64/5.98 thf(fact_8635_floor__diff__one,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X2 @ one_one_real ) )
% 5.64/5.98 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_diff_one
% 5.64/5.98 thf(fact_8636_floor__diff__one,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) )
% 5.64/5.98 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_diff_one
% 5.64/5.98 thf(fact_8637_floor__numeral__power,axiom,
% 5.64/5.98 ! [X2: num,N: nat] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N ) )
% 5.64/5.98 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_numeral_power
% 5.64/5.98 thf(fact_8638_floor__numeral__power,axiom,
% 5.64/5.98 ! [X2: num,N: nat] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N ) )
% 5.64/5.98 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_numeral_power
% 5.64/5.98 thf(fact_8639_floor__divide__eq__div__numeral,axiom,
% 5.64/5.98 ! [A: num,B: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.64/5.98 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_divide_eq_div_numeral
% 5.64/5.98 thf(fact_8640_numeral__less__floor,axiom,
% 5.64/5.98 ! [V: num,X2: real] :
% 5.64/5.98 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % numeral_less_floor
% 5.64/5.98 thf(fact_8641_numeral__less__floor,axiom,
% 5.64/5.98 ! [V: num,X2: rat] :
% 5.64/5.98 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % numeral_less_floor
% 5.64/5.98 thf(fact_8642_floor__le__numeral,axiom,
% 5.64/5.98 ! [X2: real,V: num] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_numeral
% 5.64/5.98 thf(fact_8643_floor__le__numeral,axiom,
% 5.64/5.98 ! [X2: rat,V: num] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( numeral_numeral_int @ V ) )
% 5.64/5.98 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_numeral
% 5.64/5.98 thf(fact_8644_one__less__floor,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % one_less_floor
% 5.64/5.98 thf(fact_8645_one__less__floor,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % one_less_floor
% 5.64/5.98 thf(fact_8646_floor__le__one,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_one
% 5.64/5.98 thf(fact_8647_floor__le__one,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.64/5.98 = ( ord_less_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_one
% 5.64/5.98 thf(fact_8648_neg__numeral__le__floor,axiom,
% 5.64/5.98 ! [V: num,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % neg_numeral_le_floor
% 5.64/5.98 thf(fact_8649_neg__numeral__le__floor,axiom,
% 5.64/5.98 ! [V: num,X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % neg_numeral_le_floor
% 5.64/5.98 thf(fact_8650_floor__less__neg__numeral,axiom,
% 5.64/5.98 ! [X2: real,V: num] :
% 5.64/5.98 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_neg_numeral
% 5.64/5.98 thf(fact_8651_floor__less__neg__numeral,axiom,
% 5.64/5.98 ! [X2: rat,V: num] :
% 5.64/5.98 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.98 = ( ord_less_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_neg_numeral
% 5.64/5.98 thf(fact_8652_floor__one__divide__eq__div__numeral,axiom,
% 5.64/5.98 ! [B: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.64/5.98 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_one_divide_eq_div_numeral
% 5.64/5.98 thf(fact_8653_floor__minus__divide__eq__div__numeral,axiom,
% 5.64/5.98 ! [A: num,B: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.64/5.98 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_minus_divide_eq_div_numeral
% 5.64/5.98 thf(fact_8654_neg__numeral__less__floor,axiom,
% 5.64/5.98 ! [V: num,X2: real] :
% 5.64/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % neg_numeral_less_floor
% 5.64/5.98 thf(fact_8655_neg__numeral__less__floor,axiom,
% 5.64/5.98 ! [V: num,X2: rat] :
% 5.64/5.98 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % neg_numeral_less_floor
% 5.64/5.98 thf(fact_8656_floor__le__neg__numeral,axiom,
% 5.64/5.98 ! [X2: real,V: num] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_neg_numeral
% 5.64/5.98 thf(fact_8657_floor__le__neg__numeral,axiom,
% 5.64/5.98 ! [X2: rat,V: num] :
% 5.64/5.98 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.64/5.98 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_le_neg_numeral
% 5.64/5.98 thf(fact_8658_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.64/5.98 ! [B: num] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.64/5.98 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_minus_one_divide_eq_div_numeral
% 5.64/5.98 thf(fact_8659_choose__one,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( binomial @ N @ one_one_nat )
% 5.64/5.98 = N ) ).
% 5.64/5.98
% 5.64/5.98 % choose_one
% 5.64/5.98 thf(fact_8660_floor__mono,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/5.98 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_mono
% 5.64/5.98 thf(fact_8661_floor__mono,axiom,
% 5.64/5.98 ! [X2: rat,Y4: rat] :
% 5.64/5.98 ( ( ord_less_eq_rat @ X2 @ Y4 )
% 5.64/5.98 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_mono
% 5.64/5.98 thf(fact_8662_binomial__eq__0,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ K )
% 5.64/5.98 => ( ( binomial @ N @ K )
% 5.64/5.98 = zero_zero_nat ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_eq_0
% 5.64/5.98 thf(fact_8663_of__int__floor__le,axiom,
% 5.64/5.98 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 ) ).
% 5.64/5.98
% 5.64/5.98 % of_int_floor_le
% 5.64/5.98 thf(fact_8664_of__int__floor__le,axiom,
% 5.64/5.98 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 ) ).
% 5.64/5.98
% 5.64/5.98 % of_int_floor_le
% 5.64/5.98 thf(fact_8665_floor__less__cancel,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] :
% 5.64/5.98 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y4 ) )
% 5.64/5.98 => ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_cancel
% 5.64/5.98 thf(fact_8666_floor__less__cancel,axiom,
% 5.64/5.98 ! [X2: rat,Y4: rat] :
% 5.64/5.98 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y4 ) )
% 5.64/5.98 => ( ord_less_rat @ X2 @ Y4 ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_cancel
% 5.64/5.98 thf(fact_8667_Suc__times__binomial__eq,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.64/5.98 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Suc_times_binomial_eq
% 5.64/5.98 thf(fact_8668_Suc__times__binomial,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.64/5.98 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Suc_times_binomial
% 5.64/5.98 thf(fact_8669_binomial__symmetric,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( binomial @ N @ K )
% 5.64/5.98 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_symmetric
% 5.64/5.98 thf(fact_8670_choose__mult__lemma,axiom,
% 5.64/5.98 ! [M: nat,R2: nat,K: nat] :
% 5.64/5.98 ( ( 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 ) )
% 5.64/5.98 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_mult_lemma
% 5.64/5.98 thf(fact_8671_binomial__le__pow,axiom,
% 5.64/5.98 ! [R2: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ R2 @ N )
% 5.64/5.98 => ( ord_less_eq_nat @ ( binomial @ N @ R2 ) @ ( power_power_nat @ N @ R2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_le_pow
% 5.64/5.98 thf(fact_8672_pochhammer__pos,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_pos
% 5.64/5.98 thf(fact_8673_pochhammer__pos,axiom,
% 5.64/5.98 ! [X2: rat,N: nat] :
% 5.64/5.98 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.64/5.98 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_pos
% 5.64/5.98 thf(fact_8674_pochhammer__pos,axiom,
% 5.64/5.98 ! [X2: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.98 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_pos
% 5.64/5.98 thf(fact_8675_pochhammer__pos,axiom,
% 5.64/5.98 ! [X2: int,N: nat] :
% 5.64/5.98 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.64/5.98 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_pos
% 5.64/5.98 thf(fact_8676_pochhammer__eq__0__mono,axiom,
% 5.64/5.98 ! [A: complex,N: nat,M: nat] :
% 5.64/5.98 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.64/5.98 = zero_zero_complex )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.98 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.64/5.98 = zero_zero_complex ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_eq_0_mono
% 5.64/5.98 thf(fact_8677_pochhammer__eq__0__mono,axiom,
% 5.64/5.98 ! [A: real,N: nat,M: nat] :
% 5.64/5.98 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.98 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.64/5.98 = zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_eq_0_mono
% 5.64/5.98 thf(fact_8678_pochhammer__eq__0__mono,axiom,
% 5.64/5.98 ! [A: rat,N: nat,M: nat] :
% 5.64/5.98 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.64/5.98 = zero_zero_rat )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.98 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.64/5.98 = zero_zero_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_eq_0_mono
% 5.64/5.98 thf(fact_8679_pochhammer__neq__0__mono,axiom,
% 5.64/5.98 ! [A: complex,M: nat,N: nat] :
% 5.64/5.98 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.64/5.98 != zero_zero_complex )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.98 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.64/5.98 != zero_zero_complex ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_neq_0_mono
% 5.64/5.98 thf(fact_8680_pochhammer__neq__0__mono,axiom,
% 5.64/5.98 ! [A: real,M: nat,N: nat] :
% 5.64/5.98 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.64/5.98 != zero_zero_real )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.98 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.64/5.98 != zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_neq_0_mono
% 5.64/5.98 thf(fact_8681_pochhammer__neq__0__mono,axiom,
% 5.64/5.98 ! [A: rat,M: nat,N: nat] :
% 5.64/5.98 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.64/5.98 != zero_zero_rat )
% 5.64/5.98 => ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.98 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.64/5.98 != zero_zero_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_neq_0_mono
% 5.64/5.98 thf(fact_8682_pochhammer__fact,axiom,
% 5.64/5.98 ( semiri5044797733671781792omplex
% 5.64/5.98 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_fact
% 5.64/5.98 thf(fact_8683_pochhammer__fact,axiom,
% 5.64/5.98 ( semiri773545260158071498ct_rat
% 5.64/5.98 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_fact
% 5.64/5.98 thf(fact_8684_pochhammer__fact,axiom,
% 5.64/5.98 ( semiri1406184849735516958ct_int
% 5.64/5.98 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_fact
% 5.64/5.98 thf(fact_8685_pochhammer__fact,axiom,
% 5.64/5.98 ( semiri2265585572941072030t_real
% 5.64/5.98 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_fact
% 5.64/5.98 thf(fact_8686_pochhammer__fact,axiom,
% 5.64/5.98 ( semiri1408675320244567234ct_nat
% 5.64/5.98 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_fact
% 5.64/5.98 thf(fact_8687_zero__less__binomial,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % zero_less_binomial
% 5.64/5.98 thf(fact_8688_le__floor__iff,axiom,
% 5.64/5.98 ! [Z: int,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_floor_iff
% 5.64/5.98 thf(fact_8689_le__floor__iff,axiom,
% 5.64/5.98 ! [Z: int,X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_floor_iff
% 5.64/5.98 thf(fact_8690_Suc__times__binomial__add,axiom,
% 5.64/5.98 ! [A: nat,B: nat] :
% 5.64/5.98 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.64/5.98 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % Suc_times_binomial_add
% 5.64/5.98 thf(fact_8691_floor__less__iff,axiom,
% 5.64/5.98 ! [X2: real,Z: int] :
% 5.64/5.98 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.64/5.98 = ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_iff
% 5.64/5.98 thf(fact_8692_floor__less__iff,axiom,
% 5.64/5.98 ! [X2: rat,Z: int] :
% 5.64/5.98 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.64/5.98 = ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_less_iff
% 5.64/5.98 thf(fact_8693_le__floor__add,axiom,
% 5.64/5.98 ! [X2: real,Y4: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ ( archim6058952711729229775r_real @ Y4 ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_floor_add
% 5.64/5.98 thf(fact_8694_le__floor__add,axiom,
% 5.64/5.98 ! [X2: rat,Y4: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ ( archim3151403230148437115or_rat @ Y4 ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ Y4 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_floor_add
% 5.64/5.98 thf(fact_8695_binomial__Suc__Suc__eq__times,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.64/5.98 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_Suc_Suc_eq_times
% 5.64/5.98 thf(fact_8696_int__add__floor,axiom,
% 5.64/5.98 ! [Z: int,X2: real] :
% 5.64/5.98 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.98 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % int_add_floor
% 5.64/5.98 thf(fact_8697_int__add__floor,axiom,
% 5.64/5.98 ! [Z: int,X2: rat] :
% 5.64/5.98 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.98 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % int_add_floor
% 5.64/5.98 thf(fact_8698_floor__add__int,axiom,
% 5.64/5.98 ! [X2: real,Z: int] :
% 5.64/5.98 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.64/5.98 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_add_int
% 5.64/5.98 thf(fact_8699_floor__add__int,axiom,
% 5.64/5.98 ! [X2: rat,Z: int] :
% 5.64/5.98 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.64/5.98 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_add_int
% 5.64/5.98 thf(fact_8700_choose__mult,axiom,
% 5.64/5.98 ! [K: nat,M: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.98 => ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.98 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.64/5.98 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % choose_mult
% 5.64/5.98 thf(fact_8701_binomial__absorb__comp,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.64/5.98 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_absorb_comp
% 5.64/5.98 thf(fact_8702_floor__divide__of__int__eq,axiom,
% 5.64/5.98 ! [K: int,L: int] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.64/5.98 = ( divide_divide_int @ K @ L ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_divide_of_int_eq
% 5.64/5.98 thf(fact_8703_floor__divide__of__int__eq,axiom,
% 5.64/5.98 ! [K: int,L: int] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.64/5.98 = ( divide_divide_int @ K @ L ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_divide_of_int_eq
% 5.64/5.98 thf(fact_8704_gbinomial__pochhammer,axiom,
% 5.64/5.98 ( gbinomial_complex
% 5.64/5.98 = ( ^ [A3: complex,K2: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K2 ) ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_pochhammer
% 5.64/5.98 thf(fact_8705_gbinomial__pochhammer,axiom,
% 5.64/5.98 ( gbinomial_rat
% 5.64/5.98 = ( ^ [A3: rat,K2: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K2 ) ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_pochhammer
% 5.64/5.98 thf(fact_8706_gbinomial__pochhammer,axiom,
% 5.64/5.98 ( gbinomial_real
% 5.64/5.98 = ( ^ [A3: real,K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A3 ) @ K2 ) ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_pochhammer
% 5.64/5.98 thf(fact_8707_gbinomial__pochhammer_H,axiom,
% 5.64/5.98 ( gbinomial_rat
% 5.64/5.98 = ( ^ [A3: rat,K2: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_pochhammer'
% 5.64/5.98 thf(fact_8708_gbinomial__pochhammer_H,axiom,
% 5.64/5.98 ( gbinomial_complex
% 5.64/5.98 = ( ^ [A3: complex,K2: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_pochhammer'
% 5.64/5.98 thf(fact_8709_gbinomial__pochhammer_H,axiom,
% 5.64/5.98 ( gbinomial_real
% 5.64/5.98 = ( ^ [A3: real,K2: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_pochhammer'
% 5.64/5.98 thf(fact_8710_floor__power,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( X2
% 5.64/5.98 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) )
% 5.64/5.98 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X2 @ N ) )
% 5.64/5.98 = ( power_power_int @ ( archim6058952711729229775r_real @ X2 ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_power
% 5.64/5.98 thf(fact_8711_floor__power,axiom,
% 5.64/5.98 ! [X2: rat,N: nat] :
% 5.64/5.98 ( ( X2
% 5.64/5.98 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) )
% 5.64/5.98 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X2 @ N ) )
% 5.64/5.98 = ( power_power_int @ ( archim3151403230148437115or_rat @ X2 ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_power
% 5.64/5.98 thf(fact_8712_gbinomial__Suc__Suc,axiom,
% 5.64/5.98 ! [A: complex,K: nat] :
% 5.64/5.98 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_Suc_Suc
% 5.64/5.98 thf(fact_8713_gbinomial__Suc__Suc,axiom,
% 5.64/5.98 ! [A: real,K: nat] :
% 5.64/5.98 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_Suc_Suc
% 5.64/5.98 thf(fact_8714_gbinomial__Suc__Suc,axiom,
% 5.64/5.98 ! [A: rat,K: nat] :
% 5.64/5.98 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_Suc_Suc
% 5.64/5.98 thf(fact_8715_gbinomial__of__nat__symmetric,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K )
% 5.64/5.98 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_of_nat_symmetric
% 5.64/5.98 thf(fact_8716_gbinomial__of__nat__symmetric,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ K )
% 5.64/5.98 = ( gbinomial_complex @ ( semiri8010041392384452111omplex @ N ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_of_nat_symmetric
% 5.64/5.98 thf(fact_8717_pochhammer__nonneg,axiom,
% 5.64/5.98 ! [X2: rat,N: nat] :
% 5.64/5.98 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.64/5.98 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_nonneg
% 5.64/5.98 thf(fact_8718_pochhammer__nonneg,axiom,
% 5.64/5.98 ! [X2: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.64/5.98 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_nonneg
% 5.64/5.98 thf(fact_8719_pochhammer__nonneg,axiom,
% 5.64/5.98 ! [X2: int,N: nat] :
% 5.64/5.98 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.64/5.98 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_nonneg
% 5.64/5.98 thf(fact_8720_pochhammer__nonneg,axiom,
% 5.64/5.98 ! [X2: real,N: nat] :
% 5.64/5.98 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.98 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_nonneg
% 5.64/5.98 thf(fact_8721_pochhammer__0__left,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ( N = zero_zero_nat )
% 5.64/5.98 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.64/5.98 = one_one_complex ) )
% 5.64/5.98 & ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 5.64/5.98 = zero_zero_complex ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0_left
% 5.64/5.98 thf(fact_8722_pochhammer__0__left,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ( N = zero_zero_nat )
% 5.64/5.98 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.64/5.98 = one_one_real ) )
% 5.64/5.98 & ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 5.64/5.98 = zero_zero_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0_left
% 5.64/5.98 thf(fact_8723_pochhammer__0__left,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ( N = zero_zero_nat )
% 5.64/5.98 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.64/5.98 = one_one_rat ) )
% 5.64/5.98 & ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 5.64/5.98 = zero_zero_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0_left
% 5.64/5.98 thf(fact_8724_pochhammer__0__left,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ( N = zero_zero_nat )
% 5.64/5.98 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.64/5.98 = one_one_nat ) )
% 5.64/5.98 & ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 5.64/5.98 = zero_zero_nat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0_left
% 5.64/5.98 thf(fact_8725_pochhammer__0__left,axiom,
% 5.64/5.98 ! [N: nat] :
% 5.64/5.98 ( ( ( N = zero_zero_nat )
% 5.64/5.98 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.64/5.98 = one_one_int ) )
% 5.64/5.98 & ( ( N != zero_zero_nat )
% 5.64/5.98 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 5.64/5.98 = zero_zero_int ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_0_left
% 5.64/5.98 thf(fact_8726_one__add__floor,axiom,
% 5.64/5.98 ! [X2: real] :
% 5.64/5.98 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int )
% 5.64/5.98 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X2 @ one_one_real ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % one_add_floor
% 5.64/5.98 thf(fact_8727_one__add__floor,axiom,
% 5.64/5.98 ! [X2: rat] :
% 5.64/5.98 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int )
% 5.64/5.98 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % one_add_floor
% 5.64/5.98 thf(fact_8728_floor__divide__of__nat__eq,axiom,
% 5.64/5.98 ! [M: nat,N: nat] :
% 5.64/5.98 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.98 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_divide_of_nat_eq
% 5.64/5.98 thf(fact_8729_floor__divide__of__nat__eq,axiom,
% 5.64/5.98 ! [M: nat,N: nat] :
% 5.64/5.98 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) )
% 5.64/5.98 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_divide_of_nat_eq
% 5.64/5.98 thf(fact_8730_binomial__absorption,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.64/5.98 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_absorption
% 5.64/5.98 thf(fact_8731_gbinomial__addition__formula,axiom,
% 5.64/5.98 ! [A: complex,K: nat] :
% 5.64/5.98 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_addition_formula
% 5.64/5.98 thf(fact_8732_gbinomial__addition__formula,axiom,
% 5.64/5.98 ! [A: real,K: nat] :
% 5.64/5.98 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_addition_formula
% 5.64/5.98 thf(fact_8733_gbinomial__addition__formula,axiom,
% 5.64/5.98 ! [A: rat,K: nat] :
% 5.64/5.98 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.64/5.98 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_addition_formula
% 5.64/5.98 thf(fact_8734_gbinomial__absorb__comp,axiom,
% 5.64/5.98 ! [A: rat,K: nat] :
% 5.64/5.98 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.64/5.98 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_absorb_comp
% 5.64/5.98 thf(fact_8735_gbinomial__absorb__comp,axiom,
% 5.64/5.98 ! [A: real,K: nat] :
% 5.64/5.98 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.64/5.98 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_absorb_comp
% 5.64/5.98 thf(fact_8736_gbinomial__absorb__comp,axiom,
% 5.64/5.98 ! [A: complex,K: nat] :
% 5.64/5.98 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.64/5.98 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_absorb_comp
% 5.64/5.98 thf(fact_8737_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.64/5.98 ! [K: nat,A: rat] :
% 5.64/5.98 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.64/5.98 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_ge_n_over_k_pow_k
% 5.64/5.98 thf(fact_8738_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.64/5.98 ! [K: nat,A: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.64/5.98 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_ge_n_over_k_pow_k
% 5.64/5.98 thf(fact_8739_gbinomial__mult__1,axiom,
% 5.64/5.98 ! [A: rat,K: nat] :
% 5.64/5.98 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_mult_1
% 5.64/5.98 thf(fact_8740_gbinomial__mult__1,axiom,
% 5.64/5.98 ! [A: real,K: nat] :
% 5.64/5.98 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.64/5.98 = ( 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 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_mult_1
% 5.64/5.98 thf(fact_8741_gbinomial__mult__1,axiom,
% 5.64/5.98 ! [A: complex,K: nat] :
% 5.64/5.98 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.64/5.98 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_mult_1
% 5.64/5.98 thf(fact_8742_gbinomial__mult__1_H,axiom,
% 5.64/5.98 ! [A: rat,K: nat] :
% 5.64/5.98 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.64/5.98 = ( 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 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_mult_1'
% 5.64/5.98 thf(fact_8743_gbinomial__mult__1_H,axiom,
% 5.64/5.98 ! [A: real,K: nat] :
% 5.64/5.98 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.64/5.98 = ( 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 ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_mult_1'
% 5.64/5.98 thf(fact_8744_gbinomial__mult__1_H,axiom,
% 5.64/5.98 ! [A: complex,K: nat] :
% 5.64/5.98 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.64/5.98 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % gbinomial_mult_1'
% 5.64/5.98 thf(fact_8745_floor__eq,axiom,
% 5.64/5.98 ! [N: int,X2: real] :
% 5.64/5.98 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.64/5.98 => ( ( archim6058952711729229775r_real @ X2 )
% 5.64/5.98 = N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_eq
% 5.64/5.98 thf(fact_8746_real__of__int__floor__add__one__gt,axiom,
% 5.64/5.98 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_of_int_floor_add_one_gt
% 5.64/5.98 thf(fact_8747_real__of__int__floor__gt__diff__one,axiom,
% 5.64/5.98 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % real_of_int_floor_gt_diff_one
% 5.64/5.98 thf(fact_8748_binomial__fact__lemma,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.64/5.98 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_fact_lemma
% 5.64/5.98 thf(fact_8749_pochhammer__rec,axiom,
% 5.64/5.98 ! [A: complex,N: nat] :
% 5.64/5.98 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec
% 5.64/5.98 thf(fact_8750_pochhammer__rec,axiom,
% 5.64/5.98 ! [A: real,N: nat] :
% 5.64/5.98 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec
% 5.64/5.98 thf(fact_8751_pochhammer__rec,axiom,
% 5.64/5.98 ! [A: rat,N: nat] :
% 5.64/5.98 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec
% 5.64/5.98 thf(fact_8752_pochhammer__rec,axiom,
% 5.64/5.98 ! [A: nat,N: nat] :
% 5.64/5.98 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec
% 5.64/5.98 thf(fact_8753_pochhammer__rec,axiom,
% 5.64/5.98 ! [A: int,N: nat] :
% 5.64/5.98 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec
% 5.64/5.98 thf(fact_8754_pochhammer__Suc,axiom,
% 5.64/5.98 ! [A: rat,N: nat] :
% 5.64/5.98 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_Suc
% 5.64/5.98 thf(fact_8755_pochhammer__Suc,axiom,
% 5.64/5.98 ! [A: int,N: nat] :
% 5.64/5.98 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_Suc
% 5.64/5.98 thf(fact_8756_pochhammer__Suc,axiom,
% 5.64/5.98 ! [A: real,N: nat] :
% 5.64/5.98 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_Suc
% 5.64/5.98 thf(fact_8757_pochhammer__Suc,axiom,
% 5.64/5.98 ! [A: nat,N: nat] :
% 5.64/5.98 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_Suc
% 5.64/5.98 thf(fact_8758_pochhammer__Suc,axiom,
% 5.64/5.98 ! [A: complex,N: nat] :
% 5.64/5.98 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_Suc
% 5.64/5.98 thf(fact_8759_pochhammer__rec_H,axiom,
% 5.64/5.98 ! [Z: rat,N: nat] :
% 5.64/5.98 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec'
% 5.64/5.98 thf(fact_8760_pochhammer__rec_H,axiom,
% 5.64/5.98 ! [Z: int,N: nat] :
% 5.64/5.98 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec'
% 5.64/5.98 thf(fact_8761_pochhammer__rec_H,axiom,
% 5.64/5.98 ! [Z: real,N: nat] :
% 5.64/5.98 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec'
% 5.64/5.98 thf(fact_8762_pochhammer__rec_H,axiom,
% 5.64/5.98 ! [Z: nat,N: nat] :
% 5.64/5.98 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec'
% 5.64/5.98 thf(fact_8763_pochhammer__rec_H,axiom,
% 5.64/5.98 ! [Z: complex,N: nat] :
% 5.64/5.98 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) )
% 5.64/5.98 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ ( comm_s2602460028002588243omplex @ Z @ N ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_rec'
% 5.64/5.98 thf(fact_8764_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ K )
% 5.64/5.98 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.64/5.98 = zero_zero_rat ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma
% 5.64/5.98 thf(fact_8765_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ K )
% 5.64/5.98 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.64/5.98 = zero_z3403309356797280102nteger ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma
% 5.64/5.98 thf(fact_8766_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ K )
% 5.64/5.98 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.64/5.98 = zero_zero_int ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma
% 5.64/5.98 thf(fact_8767_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ K )
% 5.64/5.98 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.64/5.98 = zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma
% 5.64/5.98 thf(fact_8768_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ord_less_nat @ N @ K )
% 5.64/5.98 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.64/5.98 = zero_zero_complex ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma
% 5.64/5.98 thf(fact_8769_pochhammer__of__nat__eq__0__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.64/5.98 = zero_zero_rat )
% 5.64/5.98 = ( ord_less_nat @ N @ K ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_iff
% 5.64/5.98 thf(fact_8770_pochhammer__of__nat__eq__0__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.64/5.98 = zero_z3403309356797280102nteger )
% 5.64/5.98 = ( ord_less_nat @ N @ K ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_iff
% 5.64/5.98 thf(fact_8771_pochhammer__of__nat__eq__0__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.64/5.98 = zero_zero_int )
% 5.64/5.98 = ( ord_less_nat @ N @ K ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_iff
% 5.64/5.98 thf(fact_8772_pochhammer__of__nat__eq__0__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ord_less_nat @ N @ K ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_iff
% 5.64/5.98 thf(fact_8773_pochhammer__of__nat__eq__0__iff,axiom,
% 5.64/5.98 ! [N: nat,K: nat] :
% 5.64/5.98 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.64/5.98 = zero_zero_complex )
% 5.64/5.98 = ( ord_less_nat @ N @ K ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_iff
% 5.64/5.98 thf(fact_8774_pochhammer__eq__0__iff,axiom,
% 5.64/5.98 ! [A: rat,N: nat] :
% 5.64/5.98 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 5.64/5.98 = zero_zero_rat )
% 5.64/5.98 = ( ? [K2: nat] :
% 5.64/5.98 ( ( ord_less_nat @ K2 @ N )
% 5.64/5.98 & ( A
% 5.64/5.98 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_eq_0_iff
% 5.64/5.98 thf(fact_8775_pochhammer__eq__0__iff,axiom,
% 5.64/5.98 ! [A: real,N: nat] :
% 5.64/5.98 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 5.64/5.98 = zero_zero_real )
% 5.64/5.98 = ( ? [K2: nat] :
% 5.64/5.98 ( ( ord_less_nat @ K2 @ N )
% 5.64/5.98 & ( A
% 5.64/5.98 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_eq_0_iff
% 5.64/5.98 thf(fact_8776_pochhammer__eq__0__iff,axiom,
% 5.64/5.98 ! [A: complex,N: nat] :
% 5.64/5.98 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 5.64/5.98 = zero_zero_complex )
% 5.64/5.98 = ( ? [K2: nat] :
% 5.64/5.98 ( ( ord_less_nat @ K2 @ N )
% 5.64/5.98 & ( A
% 5.64/5.98 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_eq_0_iff
% 5.64/5.98 thf(fact_8777_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 5.64/5.98 != zero_zero_rat ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma'
% 5.64/5.98 thf(fact_8778_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 5.64/5.98 != zero_z3403309356797280102nteger ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma'
% 5.64/5.98 thf(fact_8779_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 5.64/5.98 != zero_zero_int ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma'
% 5.64/5.98 thf(fact_8780_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K )
% 5.64/5.98 != zero_zero_real ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma'
% 5.64/5.98 thf(fact_8781_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K )
% 5.64/5.98 != zero_zero_complex ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_of_nat_eq_0_lemma'
% 5.64/5.98 thf(fact_8782_pochhammer__product_H,axiom,
% 5.64/5.98 ! [Z: rat,N: nat,M: nat] :
% 5.64/5.98 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.98 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_product'
% 5.64/5.98 thf(fact_8783_pochhammer__product_H,axiom,
% 5.64/5.98 ! [Z: int,N: nat,M: nat] :
% 5.64/5.98 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.98 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_product'
% 5.64/5.98 thf(fact_8784_pochhammer__product_H,axiom,
% 5.64/5.98 ! [Z: real,N: nat,M: nat] :
% 5.64/5.98 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.98 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N ) ) @ M ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_product'
% 5.64/5.98 thf(fact_8785_pochhammer__product_H,axiom,
% 5.64/5.98 ! [Z: nat,N: nat,M: nat] :
% 5.64/5.98 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.98 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_product'
% 5.64/5.98 thf(fact_8786_pochhammer__product_H,axiom,
% 5.64/5.98 ! [Z: complex,N: nat,M: nat] :
% 5.64/5.98 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N @ M ) )
% 5.64/5.98 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N ) ) @ M ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % pochhammer_product'
% 5.64/5.98 thf(fact_8787_floor__unique,axiom,
% 5.64/5.98 ! [Z: int,X2: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X2 )
% 5.64/5.98 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.64/5.98 => ( ( archim6058952711729229775r_real @ X2 )
% 5.64/5.98 = Z ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_unique
% 5.64/5.98 thf(fact_8788_floor__unique,axiom,
% 5.64/5.98 ! [Z: int,X2: rat] :
% 5.64/5.98 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X2 )
% 5.64/5.98 => ( ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.64/5.98 => ( ( archim3151403230148437115or_rat @ X2 )
% 5.64/5.98 = Z ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_unique
% 5.64/5.98 thf(fact_8789_floor__eq__iff,axiom,
% 5.64/5.98 ! [X2: real,A: int] :
% 5.64/5.98 ( ( ( archim6058952711729229775r_real @ X2 )
% 5.64/5.98 = A )
% 5.64/5.98 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X2 )
% 5.64/5.98 & ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_eq_iff
% 5.64/5.98 thf(fact_8790_floor__eq__iff,axiom,
% 5.64/5.98 ! [X2: rat,A: int] :
% 5.64/5.98 ( ( ( archim3151403230148437115or_rat @ X2 )
% 5.64/5.98 = A )
% 5.64/5.98 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X2 )
% 5.64/5.98 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_eq_iff
% 5.64/5.98 thf(fact_8791_floor__split,axiom,
% 5.64/5.98 ! [P: int > $o,T: real] :
% 5.64/5.98 ( ( P @ ( archim6058952711729229775r_real @ T ) )
% 5.64/5.98 = ( ! [I4: int] :
% 5.64/5.98 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I4 ) @ T )
% 5.64/5.98 & ( ord_less_real @ T @ ( plus_plus_real @ ( ring_1_of_int_real @ I4 ) @ one_one_real ) ) )
% 5.64/5.98 => ( P @ I4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_split
% 5.64/5.98 thf(fact_8792_floor__split,axiom,
% 5.64/5.98 ! [P: int > $o,T: rat] :
% 5.64/5.98 ( ( P @ ( archim3151403230148437115or_rat @ T ) )
% 5.64/5.98 = ( ! [I4: int] :
% 5.64/5.98 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T )
% 5.64/5.98 & ( ord_less_rat @ T @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 5.64/5.98 => ( P @ I4 ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % floor_split
% 5.64/5.98 thf(fact_8793_binomial__ge__n__over__k__pow__k,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_ge_n_over_k_pow_k
% 5.64/5.98 thf(fact_8794_binomial__ge__n__over__k__pow__k,axiom,
% 5.64/5.98 ! [K: nat,N: nat] :
% 5.64/5.98 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.98 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % binomial_ge_n_over_k_pow_k
% 5.64/5.98 thf(fact_8795_le__mult__floor,axiom,
% 5.64/5.98 ! [A: real,B: real] :
% 5.64/5.98 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.64/5.98 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.64/5.98 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.64/5.98
% 5.64/5.98 % le_mult_floor
% 5.64/5.98 thf(fact_8796_le__mult__floor,axiom,
% 5.64/5.98 ! [A: rat,B: rat] :
% 5.64/5.98 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.64/5.98 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.64/5.98 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % le_mult_floor
% 5.64/5.99 thf(fact_8797_less__floor__iff,axiom,
% 5.64/5.99 ! [Z: int,X2: real] :
% 5.64/5.99 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.99 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_floor_iff
% 5.64/5.99 thf(fact_8798_less__floor__iff,axiom,
% 5.64/5.99 ! [Z: int,X2: rat] :
% 5.64/5.99 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X2 ) )
% 5.64/5.99 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_floor_iff
% 5.64/5.99 thf(fact_8799_floor__le__iff,axiom,
% 5.64/5.99 ! [X2: real,Z: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X2 ) @ Z )
% 5.64/5.99 = ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_le_iff
% 5.64/5.99 thf(fact_8800_floor__le__iff,axiom,
% 5.64/5.99 ! [X2: rat,Z: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X2 ) @ Z )
% 5.64/5.99 = ( ord_less_rat @ X2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_le_iff
% 5.64/5.99 thf(fact_8801_binomial__mono,axiom,
% 5.64/5.99 ! [K: nat,K6: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ K6 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.64/5.99 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_mono
% 5.64/5.99 thf(fact_8802_binomial__maximum_H,axiom,
% 5.64/5.99 ! [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 ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_maximum'
% 5.64/5.99 thf(fact_8803_binomial__maximum,axiom,
% 5.64/5.99 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_maximum
% 5.64/5.99 thf(fact_8804_binomial__antimono,axiom,
% 5.64/5.99 ! [K: nat,K6: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ K6 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.64/5.99 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_antimono
% 5.64/5.99 thf(fact_8805_binomial__le__pow2,axiom,
% 5.64/5.99 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_le_pow2
% 5.64/5.99 thf(fact_8806_floor__correct,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X2 ) ) @ X2 )
% 5.64/5.99 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X2 ) @ one_one_int ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_correct
% 5.64/5.99 thf(fact_8807_floor__correct,axiom,
% 5.64/5.99 ! [X2: rat] :
% 5.64/5.99 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X2 ) ) @ X2 )
% 5.64/5.99 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X2 ) @ one_one_int ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_correct
% 5.64/5.99 thf(fact_8808_choose__reduce__nat,axiom,
% 5.64/5.99 ! [N: nat,K: nat] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.99 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( binomial @ N @ K )
% 5.64/5.99 = ( 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 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_reduce_nat
% 5.64/5.99 thf(fact_8809_times__binomial__minus1__eq,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.64/5.99 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % times_binomial_minus1_eq
% 5.64/5.99 thf(fact_8810_floor__eq2,axiom,
% 5.64/5.99 ! [N: int,X2: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.64/5.99 => ( ( archim6058952711729229775r_real @ X2 )
% 5.64/5.99 = N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_eq2
% 5.64/5.99 thf(fact_8811_Suc__times__gbinomial,axiom,
% 5.64/5.99 ! [K: nat,A: rat] :
% 5.64/5.99 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.64/5.99 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Suc_times_gbinomial
% 5.64/5.99 thf(fact_8812_Suc__times__gbinomial,axiom,
% 5.64/5.99 ! [K: nat,A: real] :
% 5.64/5.99 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.64/5.99 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Suc_times_gbinomial
% 5.64/5.99 thf(fact_8813_Suc__times__gbinomial,axiom,
% 5.64/5.99 ! [K: nat,A: complex] :
% 5.64/5.99 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.64/5.99 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Suc_times_gbinomial
% 5.64/5.99 thf(fact_8814_gbinomial__absorption,axiom,
% 5.64/5.99 ! [K: nat,A: rat] :
% 5.64/5.99 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.64/5.99 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_absorption
% 5.64/5.99 thf(fact_8815_gbinomial__absorption,axiom,
% 5.64/5.99 ! [K: nat,A: real] :
% 5.64/5.99 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.64/5.99 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_absorption
% 5.64/5.99 thf(fact_8816_gbinomial__absorption,axiom,
% 5.64/5.99 ! [K: nat,A: complex] :
% 5.64/5.99 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.64/5.99 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_absorption
% 5.64/5.99 thf(fact_8817_binomial__altdef__nat,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( binomial @ N @ K )
% 5.64/5.99 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_altdef_nat
% 5.64/5.99 thf(fact_8818_floor__divide__real__eq__div,axiom,
% 5.64/5.99 ! [B: int,A: real] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.64/5.99 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.64/5.99 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_divide_real_eq_div
% 5.64/5.99 thf(fact_8819_gbinomial__trinomial__revision,axiom,
% 5.64/5.99 ! [K: nat,M: nat,A: rat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.99 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.64/5.99 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_trinomial_revision
% 5.64/5.99 thf(fact_8820_gbinomial__trinomial__revision,axiom,
% 5.64/5.99 ! [K: nat,M: nat,A: real] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.99 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.64/5.99 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_trinomial_revision
% 5.64/5.99 thf(fact_8821_gbinomial__trinomial__revision,axiom,
% 5.64/5.99 ! [K: nat,M: nat,A: complex] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ M )
% 5.64/5.99 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.64/5.99 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_trinomial_revision
% 5.64/5.99 thf(fact_8822_pochhammer__product,axiom,
% 5.64/5.99 ! [M: nat,N: nat,Z: rat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 5.64/5.99 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_product
% 5.64/5.99 thf(fact_8823_pochhammer__product,axiom,
% 5.64/5.99 ! [M: nat,N: nat,Z: int] :
% 5.64/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 5.64/5.99 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_product
% 5.64/5.99 thf(fact_8824_pochhammer__product,axiom,
% 5.64/5.99 ! [M: nat,N: nat,Z: real] :
% 5.64/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 => ( ( comm_s7457072308508201937r_real @ Z @ N )
% 5.64/5.99 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_product
% 5.64/5.99 thf(fact_8825_pochhammer__product,axiom,
% 5.64/5.99 ! [M: nat,N: nat,Z: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 5.64/5.99 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_product
% 5.64/5.99 thf(fact_8826_pochhammer__product,axiom,
% 5.64/5.99 ! [M: nat,N: nat,Z: complex] :
% 5.64/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 => ( ( comm_s2602460028002588243omplex @ Z @ N )
% 5.64/5.99 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_product
% 5.64/5.99 thf(fact_8827_floor__divide__lower,axiom,
% 5.64/5.99 ! [Q3: real,P2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.64/5.99 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_divide_lower
% 5.64/5.99 thf(fact_8828_floor__divide__lower,axiom,
% 5.64/5.99 ! [Q3: rat,P2: rat] :
% 5.64/5.99 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.64/5.99 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_divide_lower
% 5.64/5.99 thf(fact_8829_binomial__less__binomial__Suc,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.99 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_less_binomial_Suc
% 5.64/5.99 thf(fact_8830_binomial__strict__mono,axiom,
% 5.64/5.99 ! [K: nat,K6: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_nat @ K @ K6 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.64/5.99 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_strict_mono
% 5.64/5.99 thf(fact_8831_binomial__strict__antimono,axiom,
% 5.64/5.99 ! [K: nat,K6: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_nat @ K @ K6 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.64/5.99 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_strict_antimono
% 5.64/5.99 thf(fact_8832_central__binomial__odd,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.99 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/5.99 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % central_binomial_odd
% 5.64/5.99 thf(fact_8833_binomial__addition__formula,axiom,
% 5.64/5.99 ! [N: nat,K: nat] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/5.99 => ( ( binomial @ N @ ( suc @ K ) )
% 5.64/5.99 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_addition_formula
% 5.64/5.99 thf(fact_8834_fact__binomial,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 5.64/5.99 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_binomial
% 5.64/5.99 thf(fact_8835_fact__binomial,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) ) )
% 5.64/5.99 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_binomial
% 5.64/5.99 thf(fact_8836_fact__binomial,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) ) )
% 5.64/5.99 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_binomial
% 5.64/5.99 thf(fact_8837_binomial__fact,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 5.64/5.99 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_fact
% 5.64/5.99 thf(fact_8838_binomial__fact,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K ) )
% 5.64/5.99 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_fact
% 5.64/5.99 thf(fact_8839_binomial__fact,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ K @ N )
% 5.64/5.99 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K ) )
% 5.64/5.99 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_fact
% 5.64/5.99 thf(fact_8840_gbinomial__factors,axiom,
% 5.64/5.99 ! [A: rat,K: nat] :
% 5.64/5.99 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.64/5.99 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_factors
% 5.64/5.99 thf(fact_8841_gbinomial__factors,axiom,
% 5.64/5.99 ! [A: real,K: nat] :
% 5.64/5.99 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.64/5.99 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_factors
% 5.64/5.99 thf(fact_8842_gbinomial__factors,axiom,
% 5.64/5.99 ! [A: complex,K: nat] :
% 5.64/5.99 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.64/5.99 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_factors
% 5.64/5.99 thf(fact_8843_gbinomial__rec,axiom,
% 5.64/5.99 ! [A: rat,K: nat] :
% 5.64/5.99 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.64/5.99 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_rec
% 5.64/5.99 thf(fact_8844_gbinomial__rec,axiom,
% 5.64/5.99 ! [A: real,K: nat] :
% 5.64/5.99 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.64/5.99 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_rec
% 5.64/5.99 thf(fact_8845_gbinomial__rec,axiom,
% 5.64/5.99 ! [A: complex,K: nat] :
% 5.64/5.99 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.64/5.99 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_rec
% 5.64/5.99 thf(fact_8846_gbinomial__negated__upper,axiom,
% 5.64/5.99 ( gbinomial_rat
% 5.64/5.99 = ( ^ [A3: rat,K2: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A3 ) @ one_one_rat ) @ K2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_negated_upper
% 5.64/5.99 thf(fact_8847_gbinomial__negated__upper,axiom,
% 5.64/5.99 ( gbinomial_real
% 5.64/5.99 = ( ^ [A3: real,K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K2 ) @ A3 ) @ one_one_real ) @ K2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_negated_upper
% 5.64/5.99 thf(fact_8848_gbinomial__negated__upper,axiom,
% 5.64/5.99 ( gbinomial_complex
% 5.64/5.99 = ( ^ [A3: complex,K2: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K2 ) @ A3 ) @ one_one_complex ) @ K2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_negated_upper
% 5.64/5.99 thf(fact_8849_gbinomial__index__swap,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( 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 ) )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_index_swap
% 5.64/5.99 thf(fact_8850_gbinomial__index__swap,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( 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 ) )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_index_swap
% 5.64/5.99 thf(fact_8851_gbinomial__index__swap,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K ) )
% 5.64/5.99 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_index_swap
% 5.64/5.99 thf(fact_8852_pochhammer__absorb__comp,axiom,
% 5.64/5.99 ! [R2: rat,K: nat] :
% 5.64/5.99 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.64/5.99 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_absorb_comp
% 5.64/5.99 thf(fact_8853_pochhammer__absorb__comp,axiom,
% 5.64/5.99 ! [R2: code_integer,K: nat] :
% 5.64/5.99 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.64/5.99 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_absorb_comp
% 5.64/5.99 thf(fact_8854_pochhammer__absorb__comp,axiom,
% 5.64/5.99 ! [R2: int,K: nat] :
% 5.64/5.99 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.64/5.99 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_absorb_comp
% 5.64/5.99 thf(fact_8855_pochhammer__absorb__comp,axiom,
% 5.64/5.99 ! [R2: real,K: nat] :
% 5.64/5.99 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.64/5.99 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_absorb_comp
% 5.64/5.99 thf(fact_8856_pochhammer__absorb__comp,axiom,
% 5.64/5.99 ! [R2: complex,K: nat] :
% 5.64/5.99 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.64/5.99 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_absorb_comp
% 5.64/5.99 thf(fact_8857_floor__divide__upper,axiom,
% 5.64/5.99 ! [Q3: real,P2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.64/5.99 => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_divide_upper
% 5.64/5.99 thf(fact_8858_floor__divide__upper,axiom,
% 5.64/5.99 ! [Q3: rat,P2: rat] :
% 5.64/5.99 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.64/5.99 => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_divide_upper
% 5.64/5.99 thf(fact_8859_pochhammer__same,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 5.64/5.99 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_same
% 5.64/5.99 thf(fact_8860_pochhammer__same,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 5.64/5.99 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_same
% 5.64/5.99 thf(fact_8861_pochhammer__same,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 5.64/5.99 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_same
% 5.64/5.99 thf(fact_8862_pochhammer__same,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 5.64/5.99 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_same
% 5.64/5.99 thf(fact_8863_pochhammer__same,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 5.64/5.99 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_same
% 5.64/5.99 thf(fact_8864_choose__two,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.99 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_two
% 5.64/5.99 thf(fact_8865_round__def,axiom,
% 5.64/5.99 ( archim8280529875227126926d_real
% 5.64/5.99 = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % round_def
% 5.64/5.99 thf(fact_8866_round__def,axiom,
% 5.64/5.99 ( archim7778729529865785530nd_rat
% 5.64/5.99 = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % round_def
% 5.64/5.99 thf(fact_8867_gbinomial__minus,axiom,
% 5.64/5.99 ! [A: rat,K: nat] :
% 5.64/5.99 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_minus
% 5.64/5.99 thf(fact_8868_gbinomial__minus,axiom,
% 5.64/5.99 ! [A: real,K: nat] :
% 5.64/5.99 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_minus
% 5.64/5.99 thf(fact_8869_gbinomial__minus,axiom,
% 5.64/5.99 ! [A: complex,K: nat] :
% 5.64/5.99 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_minus
% 5.64/5.99 thf(fact_8870_gbinomial__reduce__nat,axiom,
% 5.64/5.99 ! [K: nat,A: complex] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( gbinomial_complex @ A @ K )
% 5.64/5.99 = ( 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 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_reduce_nat
% 5.64/5.99 thf(fact_8871_gbinomial__reduce__nat,axiom,
% 5.64/5.99 ! [K: nat,A: real] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( gbinomial_real @ A @ K )
% 5.64/5.99 = ( 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 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_reduce_nat
% 5.64/5.99 thf(fact_8872_gbinomial__reduce__nat,axiom,
% 5.64/5.99 ! [K: nat,A: rat] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( gbinomial_rat @ A @ K )
% 5.64/5.99 = ( 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 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_reduce_nat
% 5.64/5.99 thf(fact_8873_pochhammer__minus,axiom,
% 5.64/5.99 ! [B: rat,K: nat] :
% 5.64/5.99 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.64/5.99 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus
% 5.64/5.99 thf(fact_8874_pochhammer__minus,axiom,
% 5.64/5.99 ! [B: code_integer,K: nat] :
% 5.64/5.99 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.64/5.99 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus
% 5.64/5.99 thf(fact_8875_pochhammer__minus,axiom,
% 5.64/5.99 ! [B: int,K: nat] :
% 5.64/5.99 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.64/5.99 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus
% 5.64/5.99 thf(fact_8876_pochhammer__minus,axiom,
% 5.64/5.99 ! [B: real,K: nat] :
% 5.64/5.99 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.64/5.99 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus
% 5.64/5.99 thf(fact_8877_pochhammer__minus,axiom,
% 5.64/5.99 ! [B: complex,K: nat] :
% 5.64/5.99 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.64/5.99 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus
% 5.64/5.99 thf(fact_8878_pochhammer__minus_H,axiom,
% 5.64/5.99 ! [B: rat,K: nat] :
% 5.64/5.99 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.64/5.99 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus'
% 5.64/5.99 thf(fact_8879_pochhammer__minus_H,axiom,
% 5.64/5.99 ! [B: code_integer,K: nat] :
% 5.64/5.99 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.64/5.99 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus'
% 5.64/5.99 thf(fact_8880_pochhammer__minus_H,axiom,
% 5.64/5.99 ! [B: int,K: nat] :
% 5.64/5.99 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.64/5.99 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus'
% 5.64/5.99 thf(fact_8881_pochhammer__minus_H,axiom,
% 5.64/5.99 ! [B: real,K: nat] :
% 5.64/5.99 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.64/5.99 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus'
% 5.64/5.99 thf(fact_8882_pochhammer__minus_H,axiom,
% 5.64/5.99 ! [B: complex,K: nat] :
% 5.64/5.99 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.64/5.99 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_minus'
% 5.64/5.99 thf(fact_8883_gbinomial__sum__up__index,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( groups2906978787729119204at_rat
% 5.64/5.99 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.99 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_sum_up_index
% 5.64/5.99 thf(fact_8884_gbinomial__sum__up__index,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( groups2073611262835488442omplex
% 5.64/5.99 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.99 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_sum_up_index
% 5.64/5.99 thf(fact_8885_gbinomial__sum__up__index,axiom,
% 5.64/5.99 ! [K: nat,N: nat] :
% 5.64/5.99 ( ( groups6591440286371151544t_real
% 5.64/5.99 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.64/5.99 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_sum_up_index
% 5.64/5.99 thf(fact_8886_floor__log__eq__powr__iff,axiom,
% 5.64/5.99 ! [X2: real,B: real,K: int] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ one_one_real @ B )
% 5.64/5.99 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X2 ) )
% 5.64/5.99 = K )
% 5.64/5.99 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.64/5.99 & ( ord_less_real @ X2 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_log_eq_powr_iff
% 5.64/5.99 thf(fact_8887_gbinomial__absorption_H,axiom,
% 5.64/5.99 ! [K: nat,A: rat] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( gbinomial_rat @ A @ K )
% 5.64/5.99 = ( 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 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_absorption'
% 5.64/5.99 thf(fact_8888_gbinomial__absorption_H,axiom,
% 5.64/5.99 ! [K: nat,A: real] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( gbinomial_real @ A @ K )
% 5.64/5.99 = ( 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 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_absorption'
% 5.64/5.99 thf(fact_8889_gbinomial__absorption_H,axiom,
% 5.64/5.99 ! [K: nat,A: complex] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.64/5.99 => ( ( gbinomial_complex @ A @ K )
% 5.64/5.99 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_absorption'
% 5.64/5.99 thf(fact_8890_floor__log2__div2,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/5.99 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_log2_div2
% 5.64/5.99 thf(fact_8891_fact__double,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_double
% 5.64/5.99 thf(fact_8892_fact__double,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_double
% 5.64/5.99 thf(fact_8893_fact__double,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_double
% 5.64/5.99 thf(fact_8894_floor__log__nat__eq__if,axiom,
% 5.64/5.99 ! [B: nat,N: nat,K: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.64/5.99 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.64/5.99 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.64/5.99 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.64/5.99 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_log_nat_eq_if
% 5.64/5.99 thf(fact_8895_binomial__code,axiom,
% 5.64/5.99 ( binomial
% 5.64/5.99 = ( ^ [N2: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K2 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_code
% 5.64/5.99 thf(fact_8896_gbinomial__code,axiom,
% 5.64/5.99 ( gbinomial_rat
% 5.64/5.99 = ( ^ [A3: rat,K2: nat] :
% 5.64/5.99 ( if_rat @ ( K2 = zero_zero_nat ) @ one_one_rat
% 5.64/5.99 @ ( divide_divide_rat
% 5.64/5.99 @ ( set_fo1949268297981939178at_rat
% 5.64/5.99 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.64/5.99 @ one_one_rat )
% 5.64/5.99 @ ( semiri773545260158071498ct_rat @ K2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_code
% 5.64/5.99 thf(fact_8897_gbinomial__code,axiom,
% 5.64/5.99 ( gbinomial_complex
% 5.64/5.99 = ( ^ [A3: complex,K2: nat] :
% 5.64/5.99 ( if_complex @ ( K2 = zero_zero_nat ) @ one_one_complex
% 5.64/5.99 @ ( divide1717551699836669952omplex
% 5.64/5.99 @ ( set_fo1517530859248394432omplex
% 5.64/5.99 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.64/5.99 @ one_one_complex )
% 5.64/5.99 @ ( semiri5044797733671781792omplex @ K2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_code
% 5.64/5.99 thf(fact_8898_gbinomial__code,axiom,
% 5.64/5.99 ( gbinomial_real
% 5.64/5.99 = ( ^ [A3: real,K2: nat] :
% 5.64/5.99 ( if_real @ ( K2 = zero_zero_nat ) @ one_one_real
% 5.64/5.99 @ ( divide_divide_real
% 5.64/5.99 @ ( set_fo3111899725591712190t_real
% 5.64/5.99 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ K2 @ one_one_nat )
% 5.64/5.99 @ one_one_real )
% 5.64/5.99 @ ( semiri2265585572941072030t_real @ K2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_code
% 5.64/5.99 thf(fact_8899_pochhammer__times__pochhammer__half,axiom,
% 5.64/5.99 ! [Z: rat,N: nat] :
% 5.64/5.99 ( ( 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 ) ) )
% 5.64/5.99 = ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [K2: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_times_pochhammer_half
% 5.64/5.99 thf(fact_8900_pochhammer__times__pochhammer__half,axiom,
% 5.64/5.99 ! [Z: real,N: nat] :
% 5.64/5.99 ( ( 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 ) ) )
% 5.64/5.99 = ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [K2: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_times_pochhammer_half
% 5.64/5.99 thf(fact_8901_pochhammer__times__pochhammer__half,axiom,
% 5.64/5.99 ! [Z: complex,N: nat] :
% 5.64/5.99 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 5.64/5.99 = ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [K2: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_times_pochhammer_half
% 5.64/5.99 thf(fact_8902_pochhammer__code,axiom,
% 5.64/5.99 ( comm_s4028243227959126397er_rat
% 5.64/5.99 = ( ^ [A3: rat,N2: nat] :
% 5.64/5.99 ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 5.64/5.99 @ ( set_fo1949268297981939178at_rat
% 5.64/5.99 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.64/5.99 @ one_one_rat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_code
% 5.64/5.99 thf(fact_8903_pochhammer__code,axiom,
% 5.64/5.99 ( comm_s4660882817536571857er_int
% 5.64/5.99 = ( ^ [A3: int,N2: nat] :
% 5.64/5.99 ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 5.64/5.99 @ ( set_fo2581907887559384638at_int
% 5.64/5.99 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.64/5.99 @ one_one_int ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_code
% 5.64/5.99 thf(fact_8904_pochhammer__code,axiom,
% 5.64/5.99 ( comm_s7457072308508201937r_real
% 5.64/5.99 = ( ^ [A3: real,N2: nat] :
% 5.64/5.99 ( if_real @ ( N2 = zero_zero_nat ) @ one_one_real
% 5.64/5.99 @ ( set_fo3111899725591712190t_real
% 5.64/5.99 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.64/5.99 @ one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_code
% 5.64/5.99 thf(fact_8905_pochhammer__code,axiom,
% 5.64/5.99 ( comm_s2602460028002588243omplex
% 5.64/5.99 = ( ^ [A3: complex,N2: nat] :
% 5.64/5.99 ( if_complex @ ( N2 = zero_zero_nat ) @ one_one_complex
% 5.64/5.99 @ ( set_fo1517530859248394432omplex
% 5.64/5.99 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.64/5.99 @ one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_code
% 5.64/5.99 thf(fact_8906_pochhammer__code,axiom,
% 5.64/5.99 ( comm_s4663373288045622133er_nat
% 5.64/5.99 = ( ^ [A3: nat,N2: nat] :
% 5.64/5.99 ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 5.64/5.99 @ ( set_fo2584398358068434914at_nat
% 5.64/5.99 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.64/5.99 @ zero_zero_nat
% 5.64/5.99 @ ( minus_minus_nat @ N2 @ one_one_nat )
% 5.64/5.99 @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pochhammer_code
% 5.64/5.99 thf(fact_8907_gbinomial__partial__row__sum,axiom,
% 5.64/5.99 ! [A: rat,M: nat] :
% 5.64/5.99 ( ( groups2906978787729119204at_rat
% 5.64/5.99 @ ^ [K2: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K2 ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_partial_row_sum
% 5.64/5.99 thf(fact_8908_gbinomial__partial__row__sum,axiom,
% 5.64/5.99 ! [A: complex,M: nat] :
% 5.64/5.99 ( ( groups2073611262835488442omplex
% 5.64/5.99 @ ^ [K2: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K2 ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_partial_row_sum
% 5.64/5.99 thf(fact_8909_gbinomial__partial__row__sum,axiom,
% 5.64/5.99 ! [A: real,M: nat] :
% 5.64/5.99 ( ( groups6591440286371151544t_real
% 5.64/5.99 @ ^ [K2: nat] : ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % gbinomial_partial_row_sum
% 5.64/5.99 thf(fact_8910_atMost__iff,axiom,
% 5.64/5.99 ! [I: set_nat,K: set_nat] :
% 5.64/5.99 ( ( member_set_nat @ I @ ( set_or4236626031148496127et_nat @ K ) )
% 5.64/5.99 = ( ord_less_eq_set_nat @ I @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_iff
% 5.64/5.99 thf(fact_8911_atMost__iff,axiom,
% 5.64/5.99 ! [I: rat,K: rat] :
% 5.64/5.99 ( ( member_rat @ I @ ( set_ord_atMost_rat @ K ) )
% 5.64/5.99 = ( ord_less_eq_rat @ I @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_iff
% 5.64/5.99 thf(fact_8912_atMost__iff,axiom,
% 5.64/5.99 ! [I: num,K: num] :
% 5.64/5.99 ( ( member_num @ I @ ( set_ord_atMost_num @ K ) )
% 5.64/5.99 = ( ord_less_eq_num @ I @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_iff
% 5.64/5.99 thf(fact_8913_atMost__iff,axiom,
% 5.64/5.99 ! [I: int,K: int] :
% 5.64/5.99 ( ( member_int @ I @ ( set_ord_atMost_int @ K ) )
% 5.64/5.99 = ( ord_less_eq_int @ I @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_iff
% 5.64/5.99 thf(fact_8914_atMost__iff,axiom,
% 5.64/5.99 ! [I: real,K: real] :
% 5.64/5.99 ( ( member_real @ I @ ( set_ord_atMost_real @ K ) )
% 5.64/5.99 = ( ord_less_eq_real @ I @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_iff
% 5.64/5.99 thf(fact_8915_atMost__iff,axiom,
% 5.64/5.99 ! [I: nat,K: nat] :
% 5.64/5.99 ( ( member_nat @ I @ ( set_ord_atMost_nat @ K ) )
% 5.64/5.99 = ( ord_less_eq_nat @ I @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_iff
% 5.64/5.99 thf(fact_8916_prod_Oneutral__const,axiom,
% 5.64/5.99 ! [A4: set_nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [Uu3: nat] : one_one_nat
% 5.64/5.99 @ A4 )
% 5.64/5.99 = one_one_nat ) ).
% 5.64/5.99
% 5.64/5.99 % prod.neutral_const
% 5.64/5.99 thf(fact_8917_prod_Oneutral__const,axiom,
% 5.64/5.99 ! [A4: set_nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [Uu3: nat] : one_one_int
% 5.64/5.99 @ A4 )
% 5.64/5.99 = one_one_int ) ).
% 5.64/5.99
% 5.64/5.99 % prod.neutral_const
% 5.64/5.99 thf(fact_8918_prod_Oneutral__const,axiom,
% 5.64/5.99 ! [A4: set_int] :
% 5.64/5.99 ( ( groups1705073143266064639nt_int
% 5.64/5.99 @ ^ [Uu3: int] : one_one_int
% 5.64/5.99 @ A4 )
% 5.64/5.99 = one_one_int ) ).
% 5.64/5.99
% 5.64/5.99 % prod.neutral_const
% 5.64/5.99 thf(fact_8919_prod_Oempty,axiom,
% 5.64/5.99 ! [G: nat > complex] :
% 5.64/5.99 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.64/5.99 = one_one_complex ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8920_prod_Oempty,axiom,
% 5.64/5.99 ! [G: nat > real] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.64/5.99 = one_one_real ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8921_prod_Oempty,axiom,
% 5.64/5.99 ! [G: nat > rat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.64/5.99 = one_one_rat ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8922_prod_Oempty,axiom,
% 5.64/5.99 ! [G: int > complex] :
% 5.64/5.99 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.64/5.99 = one_one_complex ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8923_prod_Oempty,axiom,
% 5.64/5.99 ! [G: int > real] :
% 5.64/5.99 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.64/5.99 = one_one_real ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8924_prod_Oempty,axiom,
% 5.64/5.99 ! [G: int > rat] :
% 5.64/5.99 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.64/5.99 = one_one_rat ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8925_prod_Oempty,axiom,
% 5.64/5.99 ! [G: int > nat] :
% 5.64/5.99 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.64/5.99 = one_one_nat ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8926_prod_Oempty,axiom,
% 5.64/5.99 ! [G: real > complex] :
% 5.64/5.99 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.64/5.99 = one_one_complex ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8927_prod_Oempty,axiom,
% 5.64/5.99 ! [G: real > real] :
% 5.64/5.99 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.64/5.99 = one_one_real ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8928_prod_Oempty,axiom,
% 5.64/5.99 ! [G: real > rat] :
% 5.64/5.99 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.64/5.99 = one_one_rat ) ).
% 5.64/5.99
% 5.64/5.99 % prod.empty
% 5.64/5.99 thf(fact_8929_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > complex] :
% 5.64/5.99 ( ~ ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex @ G @ A4 )
% 5.64/5.99 = one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8930_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > complex] :
% 5.64/5.99 ( ~ ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G @ A4 )
% 5.64/5.99 = one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8931_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > complex] :
% 5.64/5.99 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G @ A4 )
% 5.64/5.99 = one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8932_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > real] :
% 5.64/5.99 ( ~ ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ A4 )
% 5.64/5.99 = one_one_real ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8933_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > real] :
% 5.64/5.99 ( ~ ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ A4 )
% 5.64/5.99 = one_one_real ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8934_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > real] :
% 5.64/5.99 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ A4 )
% 5.64/5.99 = one_one_real ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8935_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > rat] :
% 5.64/5.99 ( ~ ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ A4 )
% 5.64/5.99 = one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8936_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > rat] :
% 5.64/5.99 ( ~ ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ A4 )
% 5.64/5.99 = one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8937_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > rat] :
% 5.64/5.99 ( ~ ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ A4 )
% 5.64/5.99 = one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8938_prod_Oinfinite,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > nat] :
% 5.64/5.99 ( ~ ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups1707563613775114915nt_nat @ G @ A4 )
% 5.64/5.99 = one_one_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.infinite
% 5.64/5.99 thf(fact_8939_atMost__subset__iff,axiom,
% 5.64/5.99 ! [X2: set_nat,Y4: set_nat] :
% 5.64/5.99 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X2 ) @ ( set_or4236626031148496127et_nat @ Y4 ) )
% 5.64/5.99 = ( ord_less_eq_set_nat @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_subset_iff
% 5.64/5.99 thf(fact_8940_atMost__subset__iff,axiom,
% 5.64/5.99 ! [X2: rat,Y4: rat] :
% 5.64/5.99 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X2 ) @ ( set_ord_atMost_rat @ Y4 ) )
% 5.64/5.99 = ( ord_less_eq_rat @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_subset_iff
% 5.64/5.99 thf(fact_8941_atMost__subset__iff,axiom,
% 5.64/5.99 ! [X2: num,Y4: num] :
% 5.64/5.99 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X2 ) @ ( set_ord_atMost_num @ Y4 ) )
% 5.64/5.99 = ( ord_less_eq_num @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_subset_iff
% 5.64/5.99 thf(fact_8942_atMost__subset__iff,axiom,
% 5.64/5.99 ! [X2: int,Y4: int] :
% 5.64/5.99 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X2 ) @ ( set_ord_atMost_int @ Y4 ) )
% 5.64/5.99 = ( ord_less_eq_int @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_subset_iff
% 5.64/5.99 thf(fact_8943_atMost__subset__iff,axiom,
% 5.64/5.99 ! [X2: real,Y4: real] :
% 5.64/5.99 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ X2 ) @ ( set_ord_atMost_real @ Y4 ) )
% 5.64/5.99 = ( ord_less_eq_real @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_subset_iff
% 5.64/5.99 thf(fact_8944_atMost__subset__iff,axiom,
% 5.64/5.99 ! [X2: nat,Y4: nat] :
% 5.64/5.99 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X2 ) @ ( set_ord_atMost_nat @ Y4 ) )
% 5.64/5.99 = ( ord_less_eq_nat @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_subset_iff
% 5.64/5.99 thf(fact_8945_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_real,A: real,B: real > complex] :
% 5.64/5.99 ( ( finite_finite_real @ S3 )
% 5.64/5.99 => ( ( ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups713298508707869441omplex
% 5.64/5.99 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups713298508707869441omplex
% 5.64/5.99 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8946_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.64/5.99 ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ( ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8947_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_int,A: int,B: int > complex] :
% 5.64/5.99 ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ( ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex
% 5.64/5.99 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex
% 5.64/5.99 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8948_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex
% 5.64/5.99 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex
% 5.64/5.99 @ ^ [K2: complex] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8949_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_real,A: real,B: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ S3 )
% 5.64/5.99 => ( ( ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real
% 5.64/5.99 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real
% 5.64/5.99 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8950_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ( ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [K2: nat] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8951_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_int,A: int,B: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ( ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real
% 5.64/5.99 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real
% 5.64/5.99 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8952_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups766887009212190081x_real
% 5.64/5.99 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups766887009212190081x_real
% 5.64/5.99 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8953_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_real,A: real,B: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ S3 )
% 5.64/5.99 => ( ( ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat
% 5.64/5.99 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat
% 5.64/5.99 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_rat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8954_prod_Odelta,axiom,
% 5.64/5.99 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ( ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_rat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta
% 5.64/5.99 thf(fact_8955_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_real,A: real,B: real > complex] :
% 5.64/5.99 ( ( finite_finite_real @ S3 )
% 5.64/5.99 => ( ( ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups713298508707869441omplex
% 5.64/5.99 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups713298508707869441omplex
% 5.64/5.99 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8956_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_nat,A: nat,B: nat > complex] :
% 5.64/5.99 ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ( ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8957_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_int,A: int,B: int > complex] :
% 5.64/5.99 ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ( ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex
% 5.64/5.99 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex
% 5.64/5.99 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8958_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_complex,A: complex,B: complex > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex
% 5.64/5.99 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex
% 5.64/5.99 @ ^ [K2: complex] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ one_one_complex )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_complex ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8959_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_real,A: real,B: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ S3 )
% 5.64/5.99 => ( ( ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real
% 5.64/5.99 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real
% 5.64/5.99 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8960_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_nat,A: nat,B: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ( ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [K2: nat] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8961_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_int,A: int,B: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ( ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real
% 5.64/5.99 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_int @ A @ S3 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real
% 5.64/5.99 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8962_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_complex,A: complex,B: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ( ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups766887009212190081x_real
% 5.64/5.99 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_complex @ A @ S3 )
% 5.64/5.99 => ( ( groups766887009212190081x_real
% 5.64/5.99 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ one_one_real )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8963_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_real,A: real,B: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ S3 )
% 5.64/5.99 => ( ( ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat
% 5.64/5.99 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_real @ A @ S3 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat
% 5.64/5.99 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_rat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8964_prod_Odelta_H,axiom,
% 5.64/5.99 ! [S3: set_nat,A: nat,B: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ( ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = ( B @ A ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ A @ S3 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ one_one_rat )
% 5.64/5.99 @ S3 )
% 5.64/5.99 = one_one_rat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.delta'
% 5.64/5.99 thf(fact_8965_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.64/5.99 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.99 => ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.99 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8966_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_real,X2: real,G: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8967_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_nat,X2: nat,G: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8968_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_int,X2: int,G: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8969_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_complex,X2: complex,G: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8970_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.64/5.99 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.99 => ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.99 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8971_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_real,X2: real,G: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8972_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_nat,X2: nat,G: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8973_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_int,X2: int,G: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8974_prod_Oinsert,axiom,
% 5.64/5.99 ! [A4: set_complex,X2: complex,G: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ A4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert
% 5.64/5.99 thf(fact_8975_Icc__subset__Iic__iff,axiom,
% 5.64/5.99 ! [L: set_nat,H2: set_nat,H3: set_nat] :
% 5.64/5.99 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.64/5.99 = ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.64/5.99 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Icc_subset_Iic_iff
% 5.64/5.99 thf(fact_8976_Icc__subset__Iic__iff,axiom,
% 5.64/5.99 ! [L: rat,H2: rat,H3: rat] :
% 5.64/5.99 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.64/5.99 = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.64/5.99 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Icc_subset_Iic_iff
% 5.64/5.99 thf(fact_8977_Icc__subset__Iic__iff,axiom,
% 5.64/5.99 ! [L: num,H2: num,H3: num] :
% 5.64/5.99 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.64/5.99 = ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.64/5.99 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Icc_subset_Iic_iff
% 5.64/5.99 thf(fact_8978_Icc__subset__Iic__iff,axiom,
% 5.64/5.99 ! [L: nat,H2: nat,H3: nat] :
% 5.64/5.99 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.64/5.99 = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.64/5.99 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Icc_subset_Iic_iff
% 5.64/5.99 thf(fact_8979_Icc__subset__Iic__iff,axiom,
% 5.64/5.99 ! [L: int,H2: int,H3: int] :
% 5.64/5.99 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.64/5.99 = ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.64/5.99 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Icc_subset_Iic_iff
% 5.64/5.99 thf(fact_8980_Icc__subset__Iic__iff,axiom,
% 5.64/5.99 ! [L: real,H2: real,H3: real] :
% 5.64/5.99 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.64/5.99 = ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.64/5.99 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Icc_subset_Iic_iff
% 5.64/5.99 thf(fact_8981_sum_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > rat,N: nat] :
% 5.64/5.99 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum.atMost_Suc
% 5.64/5.99 thf(fact_8982_sum_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum.atMost_Suc
% 5.64/5.99 thf(fact_8983_sum_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum.atMost_Suc
% 5.64/5.99 thf(fact_8984_sum_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > real,N: nat] :
% 5.64/5.99 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum.atMost_Suc
% 5.64/5.99 thf(fact_8985_prod_OlessThan__Suc,axiom,
% 5.64/5.99 ! [G: nat > real,N: nat] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.lessThan_Suc
% 5.64/5.99 thf(fact_8986_prod_OlessThan__Suc,axiom,
% 5.64/5.99 ! [G: nat > rat,N: nat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.lessThan_Suc
% 5.64/5.99 thf(fact_8987_prod_OlessThan__Suc,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.lessThan_Suc
% 5.64/5.99 thf(fact_8988_prod_OlessThan__Suc,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.lessThan_Suc
% 5.64/5.99 thf(fact_8989_prod_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > real,N: nat] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc
% 5.64/5.99 thf(fact_8990_prod_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > rat,N: nat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc
% 5.64/5.99 thf(fact_8991_prod_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc
% 5.64/5.99 thf(fact_8992_prod_OatMost__Suc,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc
% 5.64/5.99 thf(fact_8993_prod_Ocl__ivl__Suc,axiom,
% 5.64/5.99 ! [N: nat,M: nat,G: nat > complex] :
% 5.64/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.cl_ivl_Suc
% 5.64/5.99 thf(fact_8994_prod_Ocl__ivl__Suc,axiom,
% 5.64/5.99 ! [N: nat,M: nat,G: nat > real] :
% 5.64/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.cl_ivl_Suc
% 5.64/5.99 thf(fact_8995_prod_Ocl__ivl__Suc,axiom,
% 5.64/5.99 ! [N: nat,M: nat,G: nat > rat] :
% 5.64/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.cl_ivl_Suc
% 5.64/5.99 thf(fact_8996_prod_Ocl__ivl__Suc,axiom,
% 5.64/5.99 ! [N: nat,M: nat,G: nat > nat] :
% 5.64/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = one_one_nat ) )
% 5.64/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.cl_ivl_Suc
% 5.64/5.99 thf(fact_8997_prod_Ocl__ivl__Suc,axiom,
% 5.64/5.99 ! [N: nat,M: nat,G: nat > int] :
% 5.64/5.99 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = one_one_int ) )
% 5.64/5.99 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.64/5.99 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.cl_ivl_Suc
% 5.64/5.99 thf(fact_8998_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: complex > complex,A4: set_complex] :
% 5.64/5.99 ( ( ( groups3708469109370488835omplex @ G @ A4 )
% 5.64/5.99 != one_one_complex )
% 5.64/5.99 => ~ ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_8999_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: real > complex,A4: set_real] :
% 5.64/5.99 ( ( ( groups713298508707869441omplex @ G @ A4 )
% 5.64/5.99 != one_one_complex )
% 5.64/5.99 => ~ ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9000_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: nat > complex,A4: set_nat] :
% 5.64/5.99 ( ( ( groups6464643781859351333omplex @ G @ A4 )
% 5.64/5.99 != one_one_complex )
% 5.64/5.99 => ~ ! [A5: nat] :
% 5.64/5.99 ( ( member_nat @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9001_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: int > complex,A4: set_int] :
% 5.64/5.99 ( ( ( groups7440179247065528705omplex @ G @ A4 )
% 5.64/5.99 != one_one_complex )
% 5.64/5.99 => ~ ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9002_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: complex > real,A4: set_complex] :
% 5.64/5.99 ( ( ( groups766887009212190081x_real @ G @ A4 )
% 5.64/5.99 != one_one_real )
% 5.64/5.99 => ~ ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_real ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9003_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: real > real,A4: set_real] :
% 5.64/5.99 ( ( ( groups1681761925125756287l_real @ G @ A4 )
% 5.64/5.99 != one_one_real )
% 5.64/5.99 => ~ ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_real ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9004_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: nat > real,A4: set_nat] :
% 5.64/5.99 ( ( ( groups129246275422532515t_real @ G @ A4 )
% 5.64/5.99 != one_one_real )
% 5.64/5.99 => ~ ! [A5: nat] :
% 5.64/5.99 ( ( member_nat @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_real ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9005_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: int > real,A4: set_int] :
% 5.64/5.99 ( ( ( groups2316167850115554303t_real @ G @ A4 )
% 5.64/5.99 != one_one_real )
% 5.64/5.99 => ~ ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_real ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9006_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: complex > rat,A4: set_complex] :
% 5.64/5.99 ( ( ( groups225925009352817453ex_rat @ G @ A4 )
% 5.64/5.99 != one_one_rat )
% 5.64/5.99 => ~ ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_rat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9007_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.64/5.99 ! [G: real > rat,A4: set_real] :
% 5.64/5.99 ( ( ( groups4061424788464935467al_rat @ G @ A4 )
% 5.64/5.99 != one_one_rat )
% 5.64/5.99 => ~ ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ A4 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_rat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.not_neutral_contains_not_neutral
% 5.64/5.99 thf(fact_9008_prod_Oneutral,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > nat] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_nat ) )
% 5.64/5.99 => ( ( groups708209901874060359at_nat @ G @ A4 )
% 5.64/5.99 = one_one_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.neutral
% 5.64/5.99 thf(fact_9009_prod_Oneutral,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > int] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_int ) )
% 5.64/5.99 => ( ( groups705719431365010083at_int @ G @ A4 )
% 5.64/5.99 = one_one_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.neutral
% 5.64/5.99 thf(fact_9010_prod_Oneutral,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > int] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_int ) )
% 5.64/5.99 => ( ( groups1705073143266064639nt_int @ G @ A4 )
% 5.64/5.99 = one_one_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.neutral
% 5.64/5.99 thf(fact_9011_prod_Odistrib,axiom,
% 5.64/5.99 ! [G: nat > nat,H2: nat > nat,A4: set_nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [X: nat] : ( times_times_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.99 @ A4 )
% 5.64/5.99 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A4 ) @ ( groups708209901874060359at_nat @ H2 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.distrib
% 5.64/5.99 thf(fact_9012_prod_Odistrib,axiom,
% 5.64/5.99 ! [G: nat > int,H2: nat > int,A4: set_nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [X: nat] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.99 @ A4 )
% 5.64/5.99 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A4 ) @ ( groups705719431365010083at_int @ H2 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.distrib
% 5.64/5.99 thf(fact_9013_prod_Odistrib,axiom,
% 5.64/5.99 ! [G: int > int,H2: int > int,A4: set_int] :
% 5.64/5.99 ( ( groups1705073143266064639nt_int
% 5.64/5.99 @ ^ [X: int] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.64/5.99 @ A4 )
% 5.64/5.99 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A4 ) @ ( groups1705073143266064639nt_int @ H2 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.distrib
% 5.64/5.99 thf(fact_9014_prod__power__distrib,axiom,
% 5.64/5.99 ! [F: nat > nat,A4: set_nat,N: nat] :
% 5.64/5.99 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A4 ) @ N )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_power_distrib
% 5.64/5.99 thf(fact_9015_prod__power__distrib,axiom,
% 5.64/5.99 ! [F: nat > int,A4: set_nat,N: nat] :
% 5.64/5.99 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A4 ) @ N )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_power_distrib
% 5.64/5.99 thf(fact_9016_prod__power__distrib,axiom,
% 5.64/5.99 ! [F: int > int,A4: set_int,N: nat] :
% 5.64/5.99 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A4 ) @ N )
% 5.64/5.99 = ( groups1705073143266064639nt_int
% 5.64/5.99 @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_power_distrib
% 5.64/5.99 thf(fact_9017_prod_OatMost__Suc__shift,axiom,
% 5.64/5.99 ! [G: nat > real,N: nat] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc_shift
% 5.64/5.99 thf(fact_9018_prod_OatMost__Suc__shift,axiom,
% 5.64/5.99 ! [G: nat > rat,N: nat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc_shift
% 5.64/5.99 thf(fact_9019_prod_OatMost__Suc__shift,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc_shift
% 5.64/5.99 thf(fact_9020_prod_OatMost__Suc__shift,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_Suc_shift
% 5.64/5.99 thf(fact_9021_prod_Onested__swap_H,axiom,
% 5.64/5.99 ! [A: nat > nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [J3: nat] :
% 5.64/5.99 ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.nested_swap'
% 5.64/5.99 thf(fact_9022_prod_Onested__swap_H,axiom,
% 5.64/5.99 ! [A: nat > nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [J3: nat] :
% 5.64/5.99 ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.nested_swap'
% 5.64/5.99 thf(fact_9023_atMost__def,axiom,
% 5.64/5.99 ( set_or4236626031148496127et_nat
% 5.64/5.99 = ( ^ [U2: set_nat] :
% 5.64/5.99 ( collect_set_nat
% 5.64/5.99 @ ^ [X: set_nat] : ( ord_less_eq_set_nat @ X @ U2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_def
% 5.64/5.99 thf(fact_9024_atMost__def,axiom,
% 5.64/5.99 ( set_ord_atMost_rat
% 5.64/5.99 = ( ^ [U2: rat] :
% 5.64/5.99 ( collect_rat
% 5.64/5.99 @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_def
% 5.64/5.99 thf(fact_9025_atMost__def,axiom,
% 5.64/5.99 ( set_ord_atMost_num
% 5.64/5.99 = ( ^ [U2: num] :
% 5.64/5.99 ( collect_num
% 5.64/5.99 @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_def
% 5.64/5.99 thf(fact_9026_atMost__def,axiom,
% 5.64/5.99 ( set_ord_atMost_int
% 5.64/5.99 = ( ^ [U2: int] :
% 5.64/5.99 ( collect_int
% 5.64/5.99 @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_def
% 5.64/5.99 thf(fact_9027_atMost__def,axiom,
% 5.64/5.99 ( set_ord_atMost_real
% 5.64/5.99 = ( ^ [U2: real] :
% 5.64/5.99 ( collect_real
% 5.64/5.99 @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_def
% 5.64/5.99 thf(fact_9028_atMost__def,axiom,
% 5.64/5.99 ( set_ord_atMost_nat
% 5.64/5.99 = ( ^ [U2: nat] :
% 5.64/5.99 ( collect_nat
% 5.64/5.99 @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_def
% 5.64/5.99 thf(fact_9029_prod__nonneg,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > nat] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_nonneg
% 5.64/5.99 thf(fact_9030_prod__nonneg,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > int] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_nonneg
% 5.64/5.99 thf(fact_9031_prod__nonneg,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > int] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_nonneg
% 5.64/5.99 thf(fact_9032_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > rat,G: complex > rat] :
% 5.64/5.99 ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A4 ) @ ( groups225925009352817453ex_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9033_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > rat,G: real > rat] :
% 5.64/5.99 ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A4 ) @ ( groups4061424788464935467al_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9034_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > rat,G: nat > rat] :
% 5.64/5.99 ( ! [I3: nat] :
% 5.64/5.99 ( ( member_nat @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ ( groups73079841787564623at_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9035_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > rat,G: int > rat] :
% 5.64/5.99 ( ! [I3: int] :
% 5.64/5.99 ( ( member_int @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9036_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > nat,G: complex > nat] :
% 5.64/5.99 ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A4 ) @ ( groups861055069439313189ex_nat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9037_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > nat,G: real > nat] :
% 5.64/5.99 ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A4 ) @ ( groups4696554848551431203al_nat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9038_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > nat,G: int > nat] :
% 5.64/5.99 ( ! [I3: int] :
% 5.64/5.99 ( ( member_int @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) @ ( groups1707563613775114915nt_nat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9039_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > int,G: complex > int] :
% 5.64/5.99 ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A4 ) @ ( groups858564598930262913ex_int @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9040_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > int,G: real > int] :
% 5.64/5.99 ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A4 ) @ ( groups4694064378042380927al_int @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9041_prod__mono,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > real,G: complex > real] :
% 5.64/5.99 ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I3 ) )
% 5.64/5.99 & ( ord_less_eq_real @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.64/5.99 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A4 ) @ ( groups766887009212190081x_real @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_mono
% 5.64/5.99 thf(fact_9042_prod__pos,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > nat] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_pos
% 5.64/5.99 thf(fact_9043_prod__pos,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > int] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_pos
% 5.64/5.99 thf(fact_9044_prod__pos,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > int] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_int @ zero_zero_int @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_pos
% 5.64/5.99 thf(fact_9045_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > rat] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9046_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > rat] :
% 5.64/5.99 ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9047_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > rat] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9048_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > rat] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9049_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ one_one_nat @ ( groups861055069439313189ex_nat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9050_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > nat] :
% 5.64/5.99 ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9051_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > nat] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9052_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > int] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9053_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > int] :
% 5.64/5.99 ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_int @ one_one_int @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9054_prod__ge__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > real] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ord_less_eq_real @ one_one_real @ ( F @ X4 ) ) )
% 5.64/5.99 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_ge_1
% 5.64/5.99 thf(fact_9055_prod__atLeastAtMost__code,axiom,
% 5.64/5.99 ! [F: nat > complex,A: nat,B: nat] :
% 5.64/5.99 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.64/5.99 = ( set_fo1517530859248394432omplex
% 5.64/5.99 @ ^ [A3: nat] : ( times_times_complex @ ( F @ A3 ) )
% 5.64/5.99 @ A
% 5.64/5.99 @ B
% 5.64/5.99 @ one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_atLeastAtMost_code
% 5.64/5.99 thf(fact_9056_prod__atLeastAtMost__code,axiom,
% 5.64/5.99 ! [F: nat > real,A: nat,B: nat] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.64/5.99 = ( set_fo3111899725591712190t_real
% 5.64/5.99 @ ^ [A3: nat] : ( times_times_real @ ( F @ A3 ) )
% 5.64/5.99 @ A
% 5.64/5.99 @ B
% 5.64/5.99 @ one_one_real ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_atLeastAtMost_code
% 5.64/5.99 thf(fact_9057_prod__atLeastAtMost__code,axiom,
% 5.64/5.99 ! [F: nat > rat,A: nat,B: nat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.64/5.99 = ( set_fo1949268297981939178at_rat
% 5.64/5.99 @ ^ [A3: nat] : ( times_times_rat @ ( F @ A3 ) )
% 5.64/5.99 @ A
% 5.64/5.99 @ B
% 5.64/5.99 @ one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_atLeastAtMost_code
% 5.64/5.99 thf(fact_9058_prod__atLeastAtMost__code,axiom,
% 5.64/5.99 ! [F: nat > nat,A: nat,B: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.64/5.99 = ( set_fo2584398358068434914at_nat
% 5.64/5.99 @ ^ [A3: nat] : ( times_times_nat @ ( F @ A3 ) )
% 5.64/5.99 @ A
% 5.64/5.99 @ B
% 5.64/5.99 @ one_one_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_atLeastAtMost_code
% 5.64/5.99 thf(fact_9059_prod__atLeastAtMost__code,axiom,
% 5.64/5.99 ! [F: nat > int,A: nat,B: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.64/5.99 = ( set_fo2581907887559384638at_int
% 5.64/5.99 @ ^ [A3: nat] : ( times_times_int @ ( F @ A3 ) )
% 5.64/5.99 @ A
% 5.64/5.99 @ B
% 5.64/5.99 @ one_one_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_atLeastAtMost_code
% 5.64/5.99 thf(fact_9060_prod_OatMost__shift,axiom,
% 5.64/5.99 ! [G: nat > real,N: nat] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_shift
% 5.64/5.99 thf(fact_9061_prod_OatMost__shift,axiom,
% 5.64/5.99 ! [G: nat > rat,N: nat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_shift
% 5.64/5.99 thf(fact_9062_prod_OatMost__shift,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_shift
% 5.64/5.99 thf(fact_9063_prod_OatMost__shift,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.64/5.99 @ ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atMost_shift
% 5.64/5.99 thf(fact_9064_lessThan__Suc__atMost,axiom,
% 5.64/5.99 ! [K: nat] :
% 5.64/5.99 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.64/5.99 = ( set_ord_atMost_nat @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % lessThan_Suc_atMost
% 5.64/5.99 thf(fact_9065_atMost__Suc,axiom,
% 5.64/5.99 ! [K: nat] :
% 5.64/5.99 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.64/5.99 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_Suc
% 5.64/5.99 thf(fact_9066_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > complex,P: real > $o] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( member_real @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups713298508707869441omplex
% 5.64/5.99 @ ^ [X: real] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9067_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > complex,P: nat > $o] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex @ G
% 5.64/5.99 @ ( collect_nat
% 5.64/5.99 @ ^ [X: nat] :
% 5.64/5.99 ( ( member_nat @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [X: nat] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9068_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > complex,P: int > $o] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G
% 5.64/5.99 @ ( collect_int
% 5.64/5.99 @ ^ [X: int] :
% 5.64/5.99 ( ( member_int @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups7440179247065528705omplex
% 5.64/5.99 @ ^ [X: int] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9069_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > complex,P: complex > $o] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G
% 5.64/5.99 @ ( collect_complex
% 5.64/5.99 @ ^ [X: complex] :
% 5.64/5.99 ( ( member_complex @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups3708469109370488835omplex
% 5.64/5.99 @ ^ [X: complex] : ( if_complex @ ( P @ X ) @ ( G @ X ) @ one_one_complex )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9070_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > real,P: real > $o] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( member_real @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups1681761925125756287l_real
% 5.64/5.99 @ ^ [X: real] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9071_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > real,P: nat > $o] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G
% 5.64/5.99 @ ( collect_nat
% 5.64/5.99 @ ^ [X: nat] :
% 5.64/5.99 ( ( member_nat @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [X: nat] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9072_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > real,P: int > $o] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G
% 5.64/5.99 @ ( collect_int
% 5.64/5.99 @ ^ [X: int] :
% 5.64/5.99 ( ( member_int @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups2316167850115554303t_real
% 5.64/5.99 @ ^ [X: int] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9073_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > real,P: complex > $o] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G
% 5.64/5.99 @ ( collect_complex
% 5.64/5.99 @ ^ [X: complex] :
% 5.64/5.99 ( ( member_complex @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups766887009212190081x_real
% 5.64/5.99 @ ^ [X: complex] : ( if_real @ ( P @ X ) @ ( G @ X ) @ one_one_real )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9074_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > rat,P: real > $o] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( member_real @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups4061424788464935467al_rat
% 5.64/5.99 @ ^ [X: real] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ one_one_rat )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9075_prod_Ointer__filter,axiom,
% 5.64/5.99 ! [A4: set_nat,G: nat > rat,P: nat > $o] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G
% 5.64/5.99 @ ( collect_nat
% 5.64/5.99 @ ^ [X: nat] :
% 5.64/5.99 ( ( member_nat @ X @ A4 )
% 5.64/5.99 & ( P @ X ) ) ) )
% 5.64/5.99 = ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [X: nat] : ( if_rat @ ( P @ X ) @ ( G @ X ) @ one_one_rat )
% 5.64/5.99 @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.inter_filter
% 5.64/5.99 thf(fact_9076_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.64/5.99 ! [G: nat > nat,M: nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.shift_bounds_cl_Suc_ivl
% 5.64/5.99 thf(fact_9077_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.64/5.99 ! [G: nat > int,M: nat,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.shift_bounds_cl_Suc_ivl
% 5.64/5.99 thf(fact_9078_power__sum,axiom,
% 5.64/5.99 ! [C: real,F: nat > nat,A4: set_nat] :
% 5.64/5.99 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 5.64/5.99 = ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [A3: nat] : ( power_power_real @ C @ ( F @ A3 ) )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % power_sum
% 5.64/5.99 thf(fact_9079_power__sum,axiom,
% 5.64/5.99 ! [C: complex,F: nat > nat,A4: set_nat] :
% 5.64/5.99 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 5.64/5.99 = ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [A3: nat] : ( power_power_complex @ C @ ( F @ A3 ) )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % power_sum
% 5.64/5.99 thf(fact_9080_power__sum,axiom,
% 5.64/5.99 ! [C: nat,F: nat > nat,A4: set_nat] :
% 5.64/5.99 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [A3: nat] : ( power_power_nat @ C @ ( F @ A3 ) )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % power_sum
% 5.64/5.99 thf(fact_9081_power__sum,axiom,
% 5.64/5.99 ! [C: int,F: nat > nat,A4: set_nat] :
% 5.64/5.99 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A4 ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [A3: nat] : ( power_power_int @ C @ ( F @ A3 ) )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % power_sum
% 5.64/5.99 thf(fact_9082_power__sum,axiom,
% 5.64/5.99 ! [C: int,F: int > nat,A4: set_int] :
% 5.64/5.99 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A4 ) )
% 5.64/5.99 = ( groups1705073143266064639nt_int
% 5.64/5.99 @ ^ [A3: int] : ( power_power_int @ C @ ( F @ A3 ) )
% 5.64/5.99 @ A4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % power_sum
% 5.64/5.99 thf(fact_9083_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.64/5.99 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.shift_bounds_cl_nat_ivl
% 5.64/5.99 thf(fact_9084_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.64/5.99 ! [G: nat > int,M: nat,K: nat,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.shift_bounds_cl_nat_ivl
% 5.64/5.99 thf(fact_9085_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > rat] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9086_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > rat] :
% 5.64/5.99 ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9087_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_nat,F: nat > rat] :
% 5.64/5.99 ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9088_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > rat] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_rat @ ( F @ X4 ) @ one_one_rat ) ) )
% 5.64/5.99 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A4 ) @ one_one_rat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9089_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > nat] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A4 ) @ one_one_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9090_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > nat] :
% 5.64/5.99 ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A4 ) @ one_one_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9091_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_int,F: int > nat] :
% 5.64/5.99 ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_nat @ ( F @ X4 ) @ one_one_nat ) ) )
% 5.64/5.99 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A4 ) @ one_one_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9092_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > int] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ ( groups858564598930262913ex_int @ F @ A4 ) @ one_one_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9093_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_real,F: real > int] :
% 5.64/5.99 ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_int @ ( F @ X4 ) @ one_one_int ) ) )
% 5.64/5.99 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F @ A4 ) @ one_one_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9094_prod__le__1,axiom,
% 5.64/5.99 ! [A4: set_complex,F: complex > real] :
% 5.64/5.99 ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ A4 )
% 5.64/5.99 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) )
% 5.64/5.99 & ( ord_less_eq_real @ ( F @ X4 ) @ one_one_real ) ) )
% 5.64/5.99 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A4 ) @ one_one_real ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_le_1
% 5.64/5.99 thf(fact_9095_prod_Orelated,axiom,
% 5.64/5.99 ! [R: complex > complex > $o,S3: set_nat,H2: nat > complex,G: nat > complex] :
% 5.64/5.99 ( ( R @ one_one_complex @ one_one_complex )
% 5.64/5.99 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_complex @ X16 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups6464643781859351333omplex @ H2 @ S3 ) @ ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9096_prod_Orelated,axiom,
% 5.64/5.99 ! [R: complex > complex > $o,S3: set_int,H2: int > complex,G: int > complex] :
% 5.64/5.99 ( ( R @ one_one_complex @ one_one_complex )
% 5.64/5.99 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_complex @ X16 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups7440179247065528705omplex @ H2 @ S3 ) @ ( groups7440179247065528705omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9097_prod_Orelated,axiom,
% 5.64/5.99 ! [R: complex > complex > $o,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.64/5.99 ( ( R @ one_one_complex @ one_one_complex )
% 5.64/5.99 => ( ! [X16: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_complex @ X16 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups3708469109370488835omplex @ H2 @ S3 ) @ ( groups3708469109370488835omplex @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9098_prod_Orelated,axiom,
% 5.64/5.99 ! [R: real > real > $o,S3: set_nat,H2: nat > real,G: nat > real] :
% 5.64/5.99 ( ( R @ one_one_real @ one_one_real )
% 5.64/5.99 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_real @ X16 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups129246275422532515t_real @ H2 @ S3 ) @ ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9099_prod_Orelated,axiom,
% 5.64/5.99 ! [R: real > real > $o,S3: set_int,H2: int > real,G: int > real] :
% 5.64/5.99 ( ( R @ one_one_real @ one_one_real )
% 5.64/5.99 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_real @ X16 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups2316167850115554303t_real @ H2 @ S3 ) @ ( groups2316167850115554303t_real @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9100_prod_Orelated,axiom,
% 5.64/5.99 ! [R: real > real > $o,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.64/5.99 ( ( R @ one_one_real @ one_one_real )
% 5.64/5.99 => ( ! [X16: real,Y15: real,X23: real,Y23: real] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_real @ X16 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups766887009212190081x_real @ H2 @ S3 ) @ ( groups766887009212190081x_real @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9101_prod_Orelated,axiom,
% 5.64/5.99 ! [R: rat > rat > $o,S3: set_nat,H2: nat > rat,G: nat > rat] :
% 5.64/5.99 ( ( R @ one_one_rat @ one_one_rat )
% 5.64/5.99 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_rat @ X16 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_nat @ S3 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups73079841787564623at_rat @ H2 @ S3 ) @ ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9102_prod_Orelated,axiom,
% 5.64/5.99 ! [R: rat > rat > $o,S3: set_int,H2: int > rat,G: int > rat] :
% 5.64/5.99 ( ( R @ one_one_rat @ one_one_rat )
% 5.64/5.99 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_rat @ X16 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups1072433553688619179nt_rat @ H2 @ S3 ) @ ( groups1072433553688619179nt_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9103_prod_Orelated,axiom,
% 5.64/5.99 ! [R: rat > rat > $o,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.64/5.99 ( ( R @ one_one_rat @ one_one_rat )
% 5.64/5.99 => ( ! [X16: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_rat @ X16 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ S3 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups225925009352817453ex_rat @ H2 @ S3 ) @ ( groups225925009352817453ex_rat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9104_prod_Orelated,axiom,
% 5.64/5.99 ! [R: nat > nat > $o,S3: set_int,H2: int > nat,G: int > nat] :
% 5.64/5.99 ( ( R @ one_one_nat @ one_one_nat )
% 5.64/5.99 => ( ! [X16: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.64/5.99 ( ( ( R @ X16 @ X23 )
% 5.64/5.99 & ( R @ Y15 @ Y23 ) )
% 5.64/5.99 => ( R @ ( times_times_nat @ X16 @ Y15 ) @ ( times_times_nat @ X23 @ Y23 ) ) )
% 5.64/5.99 => ( ( finite_finite_int @ S3 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( R @ ( H2 @ X4 ) @ ( G @ X4 ) ) )
% 5.64/5.99 => ( R @ ( groups1707563613775114915nt_nat @ H2 @ S3 ) @ ( groups1707563613775114915nt_nat @ G @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.related
% 5.64/5.99 thf(fact_9105_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > real] :
% 5.64/5.99 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.99 => ( ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.99 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.99 = ( groups2703838992350267259T_real @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.99 => ( ( groups2703838992350267259T_real @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups2703838992350267259T_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9106_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_real,X2: real,G: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( ( member_real @ X2 @ A4 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.99 = ( groups1681761925125756287l_real @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups1681761925125756287l_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9107_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_nat,X2: nat,G: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( ( member_nat @ X2 @ A4 )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.99 = ( groups129246275422532515t_real @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups129246275422532515t_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9108_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_int,X2: int,G: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( ( member_int @ X2 @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.99 = ( groups2316167850115554303t_real @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups2316167850115554303t_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9109_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_complex,X2: complex,G: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( ( member_complex @ X2 @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.99 = ( groups766887009212190081x_real @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_real @ ( G @ X2 ) @ ( groups766887009212190081x_real @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9110_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_VEBT_VEBT,X2: vEBT_VEBT,G: vEBT_VEBT > rat] :
% 5.64/5.99 ( ( finite5795047828879050333T_VEBT @ A4 )
% 5.64/5.99 => ( ( ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.99 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.99 = ( groups5726676334696518183BT_rat @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_VEBT_VEBT @ X2 @ A4 )
% 5.64/5.99 => ( ( groups5726676334696518183BT_rat @ G @ ( insert_VEBT_VEBT @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups5726676334696518183BT_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9111_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_real,X2: real,G: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( ( member_real @ X2 @ A4 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.99 = ( groups4061424788464935467al_rat @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_real @ X2 @ A4 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G @ ( insert_real @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups4061424788464935467al_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9112_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_nat,X2: nat,G: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( ( member_nat @ X2 @ A4 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.99 = ( groups73079841787564623at_rat @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_nat @ X2 @ A4 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ ( insert_nat @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups73079841787564623at_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9113_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_int,X2: int,G: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( ( member_int @ X2 @ A4 )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.99 = ( groups1072433553688619179nt_rat @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_int @ X2 @ A4 )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ ( insert_int @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9114_prod_Oinsert__if,axiom,
% 5.64/5.99 ! [A4: set_complex,X2: complex,G: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( ( member_complex @ X2 @ A4 )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.99 = ( groups225925009352817453ex_rat @ G @ A4 ) ) )
% 5.64/5.99 & ( ~ ( member_complex @ X2 @ A4 )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ ( insert_complex @ X2 @ A4 ) )
% 5.64/5.99 = ( times_times_rat @ ( G @ X2 ) @ ( groups225925009352817453ex_rat @ G @ A4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.insert_if
% 5.64/5.99 thf(fact_9115_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_real,T5: set_real,S3: set_real,I: real > real,J: real > real,T6: set_real,G: real > complex,H2: real > complex] :
% 5.64/5.99 ( ( finite_finite_real @ S5 )
% 5.64/5.99 => ( ( finite_finite_real @ T5 )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.64/5.99 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9116_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_real,T5: set_int,S3: set_real,I: int > real,J: real > int,T6: set_int,G: real > complex,H2: int > complex] :
% 5.64/5.99 ( ( finite_finite_real @ S5 )
% 5.64/5.99 => ( ( finite_finite_int @ T5 )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.64/5.99 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.64/5.99 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9117_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_real,T5: set_complex,S3: set_real,I: complex > real,J: real > complex,T6: set_complex,G: real > complex,H2: complex > complex] :
% 5.64/5.99 ( ( finite_finite_real @ S5 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ T5 )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.64/5.99 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.64/5.99 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9118_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_int,T5: set_real,S3: set_int,I: real > int,J: int > real,T6: set_real,G: int > complex,H2: real > complex] :
% 5.64/5.99 ( ( finite_finite_int @ S5 )
% 5.64/5.99 => ( ( finite_finite_real @ T5 )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.64/5.99 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.64/5.99 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9119_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_int,T5: set_int,S3: set_int,I: int > int,J: int > int,T6: set_int,G: int > complex,H2: int > complex] :
% 5.64/5.99 ( ( finite_finite_int @ S5 )
% 5.64/5.99 => ( ( finite_finite_int @ T5 )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.64/5.99 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.64/5.99 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.64/5.99 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9120_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_int,T5: set_complex,S3: set_int,I: complex > int,J: int > complex,T6: set_complex,G: int > complex,H2: complex > complex] :
% 5.64/5.99 ( ( finite_finite_int @ S5 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ T5 )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 5.64/5.99 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.64/5.99 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: int] :
% 5.64/5.99 ( ( member_int @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.64/5.99 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9121_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_complex,T5: set_real,S3: set_complex,I: real > complex,J: complex > real,T6: set_real,G: complex > complex,H2: real > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S5 )
% 5.64/5.99 => ( ( finite_finite_real @ T5 )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.64/5.99 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.64/5.99 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9122_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_complex,T5: set_int,S3: set_complex,I: int > complex,J: complex > int,T6: set_int,G: complex > complex,H2: int > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S5 )
% 5.64/5.99 => ( ( finite_finite_int @ T5 )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.64/5.99 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ ( minus_minus_set_int @ T6 @ T5 ) )
% 5.64/5.99 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: int] :
% 5.64/5.99 ( ( member_int @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.64/5.99 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9123_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_complex,T5: set_complex,S3: set_complex,I: complex > complex,J: complex > complex,T6: set_complex,G: complex > complex,H2: complex > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ S5 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ T5 )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 5.64/5.99 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T6 @ T5 ) )
% 5.64/5.99 => ( member_complex @ ( I @ B5 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [B5: complex] :
% 5.64/5.99 ( ( member_complex @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [A5: complex] :
% 5.64/5.99 ( ( member_complex @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.64/5.99 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9124_prod_Oreindex__bij__witness__not__neutral,axiom,
% 5.64/5.99 ! [S5: set_real,T5: set_real,S3: set_real,I: real > real,J: real > real,T6: set_real,G: real > real,H2: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ S5 )
% 5.64/5.99 => ( ( finite_finite_real @ T5 )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( ( I @ ( J @ A5 ) )
% 5.64/5.99 = A5 ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 5.64/5.99 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T6 @ T5 ) ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( ( J @ ( I @ B5 ) )
% 5.64/5.99 = B5 ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ ( minus_minus_set_real @ T6 @ T5 ) )
% 5.64/5.99 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S5 )
% 5.64/5.99 => ( ( G @ A5 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [B5: real] :
% 5.64/5.99 ( ( member_real @ B5 @ T5 )
% 5.64/5.99 => ( ( H2 @ B5 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [A5: real] :
% 5.64/5.99 ( ( member_real @ A5 @ S3 )
% 5.64/5.99 => ( ( H2 @ ( J @ A5 ) )
% 5.64/5.99 = ( G @ A5 ) ) )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G @ S3 )
% 5.64/5.99 = ( groups1681761925125756287l_real @ H2 @ T6 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.reindex_bij_witness_not_neutral
% 5.64/5.99 thf(fact_9125_prod_Oin__pairs__0,axiom,
% 5.64/5.99 ! [G: nat > real,N: nat] :
% 5.64/5.99 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.99 = ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [I4: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.in_pairs_0
% 5.64/5.99 thf(fact_9126_prod_Oin__pairs__0,axiom,
% 5.64/5.99 ! [G: nat > rat,N: nat] :
% 5.64/5.99 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.99 = ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.in_pairs_0
% 5.64/5.99 thf(fact_9127_prod_Oin__pairs__0,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.in_pairs_0
% 5.64/5.99 thf(fact_9128_prod_Oin__pairs__0,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.in_pairs_0
% 5.64/5.99 thf(fact_9129_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > complex] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G
% 5.64/5.99 @ ( minus_minus_set_real @ A4
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_complex ) ) ) )
% 5.64/5.99 = ( groups713298508707869441omplex @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9130_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > complex] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G
% 5.64/5.99 @ ( minus_minus_set_int @ A4
% 5.64/5.99 @ ( collect_int
% 5.64/5.99 @ ^ [X: int] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_complex ) ) ) )
% 5.64/5.99 = ( groups7440179247065528705omplex @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9131_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G
% 5.64/5.99 @ ( minus_811609699411566653omplex @ A4
% 5.64/5.99 @ ( collect_complex
% 5.64/5.99 @ ^ [X: complex] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_complex ) ) ) )
% 5.64/5.99 = ( groups3708469109370488835omplex @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9132_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G
% 5.64/5.99 @ ( minus_minus_set_real @ A4
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_real ) ) ) )
% 5.64/5.99 = ( groups1681761925125756287l_real @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9133_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G
% 5.64/5.99 @ ( minus_minus_set_int @ A4
% 5.64/5.99 @ ( collect_int
% 5.64/5.99 @ ^ [X: int] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_real ) ) ) )
% 5.64/5.99 = ( groups2316167850115554303t_real @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9134_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G
% 5.64/5.99 @ ( minus_811609699411566653omplex @ A4
% 5.64/5.99 @ ( collect_complex
% 5.64/5.99 @ ^ [X: complex] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_real ) ) ) )
% 5.64/5.99 = ( groups766887009212190081x_real @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9135_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G
% 5.64/5.99 @ ( minus_minus_set_real @ A4
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_rat ) ) ) )
% 5.64/5.99 = ( groups4061424788464935467al_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9136_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_int,G: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G
% 5.64/5.99 @ ( minus_minus_set_int @ A4
% 5.64/5.99 @ ( collect_int
% 5.64/5.99 @ ^ [X: int] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_rat ) ) ) )
% 5.64/5.99 = ( groups1072433553688619179nt_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9137_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_complex,G: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G
% 5.64/5.99 @ ( minus_811609699411566653omplex @ A4
% 5.64/5.99 @ ( collect_complex
% 5.64/5.99 @ ^ [X: complex] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_rat ) ) ) )
% 5.64/5.99 = ( groups225925009352817453ex_rat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9138_prod_Osetdiff__irrelevant,axiom,
% 5.64/5.99 ! [A4: set_real,G: real > nat] :
% 5.64/5.99 ( ( finite_finite_real @ A4 )
% 5.64/5.99 => ( ( groups4696554848551431203al_nat @ G
% 5.64/5.99 @ ( minus_minus_set_real @ A4
% 5.64/5.99 @ ( collect_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( G @ X )
% 5.64/5.99 = one_one_nat ) ) ) )
% 5.64/5.99 = ( groups4696554848551431203al_nat @ G @ A4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.setdiff_irrelevant
% 5.64/5.99 thf(fact_9139_atMost__nat__numeral,axiom,
% 5.64/5.99 ! [K: num] :
% 5.64/5.99 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.64/5.99 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atMost_nat_numeral
% 5.64/5.99 thf(fact_9140_prod_Onat__diff__reindex,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.99 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.nat_diff_reindex
% 5.64/5.99 thf(fact_9141_prod_Onat__diff__reindex,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I4 ) ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/5.99 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.nat_diff_reindex
% 5.64/5.99 thf(fact_9142_Iic__subset__Iio__iff,axiom,
% 5.64/5.99 ! [A: rat,B: rat] :
% 5.64/5.99 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.64/5.99 = ( ord_less_rat @ A @ B ) ) ).
% 5.64/5.99
% 5.64/5.99 % Iic_subset_Iio_iff
% 5.64/5.99 thf(fact_9143_Iic__subset__Iio__iff,axiom,
% 5.64/5.99 ! [A: num,B: num] :
% 5.64/5.99 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.64/5.99 = ( ord_less_num @ A @ B ) ) ).
% 5.64/5.99
% 5.64/5.99 % Iic_subset_Iio_iff
% 5.64/5.99 thf(fact_9144_Iic__subset__Iio__iff,axiom,
% 5.64/5.99 ! [A: int,B: int] :
% 5.64/5.99 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.64/5.99 = ( ord_less_int @ A @ B ) ) ).
% 5.64/5.99
% 5.64/5.99 % Iic_subset_Iio_iff
% 5.64/5.99 thf(fact_9145_Iic__subset__Iio__iff,axiom,
% 5.64/5.99 ! [A: nat,B: nat] :
% 5.64/5.99 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.64/5.99 = ( ord_less_nat @ A @ B ) ) ).
% 5.64/5.99
% 5.64/5.99 % Iic_subset_Iio_iff
% 5.64/5.99 thf(fact_9146_Iic__subset__Iio__iff,axiom,
% 5.64/5.99 ! [A: real,B: real] :
% 5.64/5.99 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.64/5.99 = ( ord_less_real @ A @ B ) ) ).
% 5.64/5.99
% 5.64/5.99 % Iic_subset_Iio_iff
% 5.64/5.99 thf(fact_9147_prod_OatLeastAtMost__rev,axiom,
% 5.64/5.99 ! [G: nat > nat,N: nat,M: nat] :
% 5.64/5.99 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atLeastAtMost_rev
% 5.64/5.99 thf(fact_9148_prod_OatLeastAtMost__rev,axiom,
% 5.64/5.99 ! [G: nat > int,N: nat,M: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I4 ) )
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.atLeastAtMost_rev
% 5.64/5.99 thf(fact_9149_prod_Ozero__middle,axiom,
% 5.64/5.99 ! [P2: nat,K: nat,G: nat > complex,H2: nat > complex] :
% 5.64/5.99 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.64/5.99 => ( ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ one_one_complex @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ P2 ) )
% 5.64/5.99 = ( groups6464643781859351333omplex
% 5.64/5.99 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.zero_middle
% 5.64/5.99 thf(fact_9150_prod_Ozero__middle,axiom,
% 5.64/5.99 ! [P2: nat,K: nat,G: nat > real,H2: nat > real] :
% 5.64/5.99 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.64/5.99 => ( ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ one_one_real @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ P2 ) )
% 5.64/5.99 = ( groups129246275422532515t_real
% 5.64/5.99 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.zero_middle
% 5.64/5.99 thf(fact_9151_prod_Ozero__middle,axiom,
% 5.64/5.99 ! [P2: nat,K: nat,G: nat > rat,H2: nat > rat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ P2 ) )
% 5.64/5.99 = ( groups73079841787564623at_rat
% 5.64/5.99 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.zero_middle
% 5.64/5.99 thf(fact_9152_prod_Ozero__middle,axiom,
% 5.64/5.99 ! [P2: nat,K: nat,G: nat > nat,H2: nat > nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.64/5.99 => ( ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ P2 ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.zero_middle
% 5.64/5.99 thf(fact_9153_prod_Ozero__middle,axiom,
% 5.64/5.99 ! [P2: nat,K: nat,G: nat > int,H2: nat > int] :
% 5.64/5.99 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.64/5.99 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.64/5.99 => ( ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H2 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ P2 ) )
% 5.64/5.99 = ( groups705719431365010083at_int
% 5.64/5.99 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H2 @ J3 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.zero_middle
% 5.64/5.99 thf(fact_9154_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_real,I: real,F: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ I5 )
% 5.64/5.99 => ( ( member_real @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9155_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_nat,I: nat,F: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ I5 )
% 5.64/5.99 => ( ( member_nat @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: nat] :
% 5.64/5.99 ( ( member_nat @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9156_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_int,I: int,F: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ I5 )
% 5.64/5.99 => ( ( member_int @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: int] :
% 5.64/5.99 ( ( member_int @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9157_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_complex,I: complex,F: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.99 => ( ( member_complex @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_rat @ one_one_rat @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9158_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_real,I: real,F: real > int] :
% 5.64/5.99 ( ( finite_finite_real @ I5 )
% 5.64/5.99 => ( ( member_real @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9159_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_complex,I: complex,F: complex > int] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.99 => ( ( member_complex @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_int @ one_one_int @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9160_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_real,I: real,F: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ I5 )
% 5.64/5.99 => ( ( member_real @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9161_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_nat,I: nat,F: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ I5 )
% 5.64/5.99 => ( ( member_nat @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: nat] :
% 5.64/5.99 ( ( member_nat @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9162_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_int,I: int,F: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ I5 )
% 5.64/5.99 => ( ( member_int @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: int] :
% 5.64/5.99 ( ( member_int @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9163_less__1__prod2,axiom,
% 5.64/5.99 ! [I5: set_complex,I: complex,F: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.99 => ( ( member_complex @ I @ I5 )
% 5.64/5.99 => ( ( ord_less_real @ one_one_real @ ( F @ I ) )
% 5.64/5.99 => ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_eq_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod2
% 5.64/5.99 thf(fact_9164_sum__choose__upper,axiom,
% 5.64/5.99 ! [M: nat,N: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( binomial @ K2 @ M )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum_choose_upper
% 5.64/5.99 thf(fact_9165_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_complex,F: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_complex )
% 5.64/5.99 => ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9166_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_nat,F: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_nat )
% 5.64/5.99 => ( ! [I3: nat] :
% 5.64/5.99 ( ( member_nat @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9167_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_int,F: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_int )
% 5.64/5.99 => ( ! [I3: int] :
% 5.64/5.99 ( ( member_int @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9168_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_real,F: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_real )
% 5.64/5.99 => ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9169_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_complex,F: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_complex )
% 5.64/5.99 => ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9170_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_nat,F: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_nat )
% 5.64/5.99 => ( ! [I3: nat] :
% 5.64/5.99 ( ( member_nat @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9171_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_int,F: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_int )
% 5.64/5.99 => ( ! [I3: int] :
% 5.64/5.99 ( ( member_int @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9172_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_real,F: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_real )
% 5.64/5.99 => ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9173_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_complex,F: complex > int] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_complex )
% 5.64/5.99 => ( ! [I3: complex] :
% 5.64/5.99 ( ( member_complex @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_int @ one_one_int @ ( groups858564598930262913ex_int @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9174_less__1__prod,axiom,
% 5.64/5.99 ! [I5: set_real,F: real > int] :
% 5.64/5.99 ( ( finite_finite_real @ I5 )
% 5.64/5.99 => ( ( I5 != bot_bot_set_real )
% 5.64/5.99 => ( ! [I3: real] :
% 5.64/5.99 ( ( member_real @ I3 @ I5 )
% 5.64/5.99 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 5.64/5.99 => ( ord_less_int @ one_one_int @ ( groups4694064378042380927al_int @ F @ I5 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % less_1_prod
% 5.64/5.99 thf(fact_9175_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_int,A4: set_int,G: int > real] :
% 5.64/5.99 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.99 => ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ A4 )
% 5.64/5.99 = ( times_times_real @ ( groups2316167850115554303t_real @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups2316167850115554303t_real @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9176_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_complex,A4: set_complex,G: complex > real] :
% 5.64/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ A4 )
% 5.64/5.99 = ( times_times_real @ ( groups766887009212190081x_real @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups766887009212190081x_real @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9177_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_int,A4: set_int,G: int > rat] :
% 5.64/5.99 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.99 => ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ A4 )
% 5.64/5.99 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups1072433553688619179nt_rat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9178_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_complex,A4: set_complex,G: complex > rat] :
% 5.64/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ A4 )
% 5.64/5.99 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups225925009352817453ex_rat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9179_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_int,A4: set_int,G: int > nat] :
% 5.64/5.99 ( ( ord_less_eq_set_int @ B4 @ A4 )
% 5.64/5.99 => ( ( finite_finite_int @ A4 )
% 5.64/5.99 => ( ( groups1707563613775114915nt_nat @ G @ A4 )
% 5.64/5.99 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A4 @ B4 ) ) @ ( groups1707563613775114915nt_nat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9180_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_complex,A4: set_complex,G: complex > nat] :
% 5.64/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups861055069439313189ex_nat @ G @ A4 )
% 5.64/5.99 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups861055069439313189ex_nat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9181_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_complex,A4: set_complex,G: complex > int] :
% 5.64/5.99 ( ( ord_le211207098394363844omplex @ B4 @ A4 )
% 5.64/5.99 => ( ( finite3207457112153483333omplex @ A4 )
% 5.64/5.99 => ( ( groups858564598930262913ex_int @ G @ A4 )
% 5.64/5.99 = ( times_times_int @ ( groups858564598930262913ex_int @ G @ ( minus_811609699411566653omplex @ A4 @ B4 ) ) @ ( groups858564598930262913ex_int @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9182_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_nat,A4: set_nat,G: nat > real] :
% 5.64/5.99 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.64/5.99 => ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ A4 )
% 5.64/5.99 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups129246275422532515t_real @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9183_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_nat,A4: set_nat,G: nat > rat] :
% 5.64/5.99 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.64/5.99 => ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ A4 )
% 5.64/5.99 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups73079841787564623at_rat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9184_prod_Osubset__diff,axiom,
% 5.64/5.99 ! [B4: set_nat,A4: set_nat,G: nat > nat] :
% 5.64/5.99 ( ( ord_less_eq_set_nat @ B4 @ A4 )
% 5.64/5.99 => ( ( finite_finite_nat @ A4 )
% 5.64/5.99 => ( ( groups708209901874060359at_nat @ G @ A4 )
% 5.64/5.99 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( minus_minus_set_nat @ A4 @ B4 ) ) @ ( groups708209901874060359at_nat @ G @ B4 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.subset_diff
% 5.64/5.99 thf(fact_9185_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,G: real > complex,H2: real > complex] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G @ T6 )
% 5.64/5.99 = ( groups713298508707869441omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9186_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,G: int > complex,H2: int > complex] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G @ T6 )
% 5.64/5.99 = ( groups7440179247065528705omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9187_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_complex,S3: set_complex,G: complex > complex,H2: complex > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ T6 )
% 5.64/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G @ T6 )
% 5.64/5.99 = ( groups3708469109370488835omplex @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9188_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,G: real > real,H2: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G @ T6 )
% 5.64/5.99 = ( groups1681761925125756287l_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9189_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,G: int > real,H2: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ T6 )
% 5.64/5.99 = ( groups2316167850115554303t_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9190_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_complex,S3: set_complex,G: complex > real,H2: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ T6 )
% 5.64/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ T6 )
% 5.64/5.99 = ( groups766887009212190081x_real @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9191_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,G: real > rat,H2: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G @ T6 )
% 5.64/5.99 = ( groups4061424788464935467al_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9192_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,G: int > rat,H2: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ T6 )
% 5.64/5.99 = ( groups1072433553688619179nt_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9193_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_complex,S3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ T6 )
% 5.64/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ T6 )
% 5.64/5.99 = ( groups225925009352817453ex_rat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9194_prod_Omono__neutral__cong__right,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,G: real > nat,H2: real > nat] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_nat ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups4696554848551431203al_nat @ G @ T6 )
% 5.64/5.99 = ( groups4696554848551431203al_nat @ H2 @ S3 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_right
% 5.64/5.99 thf(fact_9195_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,H2: real > complex,G: real > complex] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups713298508707869441omplex @ G @ S3 )
% 5.64/5.99 = ( groups713298508707869441omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9196_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,H2: int > complex,G: int > complex] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups7440179247065528705omplex @ G @ S3 )
% 5.64/5.99 = ( groups7440179247065528705omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9197_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_complex,S3: set_complex,H2: complex > complex,G: complex > complex] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ T6 )
% 5.64/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups3708469109370488835omplex @ G @ S3 )
% 5.64/5.99 = ( groups3708469109370488835omplex @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9198_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,H2: real > real,G: real > real] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups1681761925125756287l_real @ G @ S3 )
% 5.64/5.99 = ( groups1681761925125756287l_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9199_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,H2: int > real,G: int > real] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups2316167850115554303t_real @ G @ S3 )
% 5.64/5.99 = ( groups2316167850115554303t_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9200_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_complex,S3: set_complex,H2: complex > real,G: complex > real] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ T6 )
% 5.64/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups766887009212190081x_real @ G @ S3 )
% 5.64/5.99 = ( groups766887009212190081x_real @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9201_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,H2: real > rat,G: real > rat] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups4061424788464935467al_rat @ G @ S3 )
% 5.64/5.99 = ( groups4061424788464935467al_rat @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9202_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,H2: int > rat,G: int > rat] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups1072433553688619179nt_rat @ G @ S3 )
% 5.64/5.99 = ( groups1072433553688619179nt_rat @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9203_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_complex,S3: set_complex,H2: complex > rat,G: complex > rat] :
% 5.64/5.99 ( ( finite3207457112153483333omplex @ T6 )
% 5.64/5.99 => ( ( ord_le211207098394363844omplex @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ! [X4: complex] :
% 5.64/5.99 ( ( member_complex @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups225925009352817453ex_rat @ G @ S3 )
% 5.64/5.99 = ( groups225925009352817453ex_rat @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9204_prod_Omono__neutral__cong__left,axiom,
% 5.64/5.99 ! [T6: set_real,S3: set_real,H2: real > nat,G: real > nat] :
% 5.64/5.99 ( ( finite_finite_real @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_real @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ ( minus_minus_set_real @ T6 @ S3 ) )
% 5.64/5.99 => ( ( H2 @ X4 )
% 5.64/5.99 = one_one_nat ) )
% 5.64/5.99 => ( ! [X4: real] :
% 5.64/5.99 ( ( member_real @ X4 @ S3 )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = ( H2 @ X4 ) ) )
% 5.64/5.99 => ( ( groups4696554848551431203al_nat @ G @ S3 )
% 5.64/5.99 = ( groups4696554848551431203al_nat @ H2 @ T6 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_cong_left
% 5.64/5.99 thf(fact_9205_prod_Omono__neutral__right,axiom,
% 5.64/5.99 ! [T6: set_nat,S3: set_nat,G: nat > complex] :
% 5.64/5.99 ( ( finite_finite_nat @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_complex ) )
% 5.64/5.99 => ( ( groups6464643781859351333omplex @ G @ T6 )
% 5.64/5.99 = ( groups6464643781859351333omplex @ G @ S3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_right
% 5.64/5.99 thf(fact_9206_prod_Omono__neutral__right,axiom,
% 5.64/5.99 ! [T6: set_nat,S3: set_nat,G: nat > real] :
% 5.64/5.99 ( ( finite_finite_nat @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_real ) )
% 5.64/5.99 => ( ( groups129246275422532515t_real @ G @ T6 )
% 5.64/5.99 = ( groups129246275422532515t_real @ G @ S3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_right
% 5.64/5.99 thf(fact_9207_prod_Omono__neutral__right,axiom,
% 5.64/5.99 ! [T6: set_nat,S3: set_nat,G: nat > rat] :
% 5.64/5.99 ( ( finite_finite_nat @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_rat ) )
% 5.64/5.99 => ( ( groups73079841787564623at_rat @ G @ T6 )
% 5.64/5.99 = ( groups73079841787564623at_rat @ G @ S3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_right
% 5.64/5.99 thf(fact_9208_prod_Omono__neutral__right,axiom,
% 5.64/5.99 ! [T6: set_nat,S3: set_nat,G: nat > nat] :
% 5.64/5.99 ( ( finite_finite_nat @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_nat ) )
% 5.64/5.99 => ( ( groups708209901874060359at_nat @ G @ T6 )
% 5.64/5.99 = ( groups708209901874060359at_nat @ G @ S3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_right
% 5.64/5.99 thf(fact_9209_prod_Omono__neutral__right,axiom,
% 5.64/5.99 ! [T6: set_nat,S3: set_nat,G: nat > int] :
% 5.64/5.99 ( ( finite_finite_nat @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_nat @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: nat] :
% 5.64/5.99 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_int ) )
% 5.64/5.99 => ( ( groups705719431365010083at_int @ G @ T6 )
% 5.64/5.99 = ( groups705719431365010083at_int @ G @ S3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_right
% 5.64/5.99 thf(fact_9210_prod_Omono__neutral__right,axiom,
% 5.64/5.99 ! [T6: set_int,S3: set_int,G: int > int] :
% 5.64/5.99 ( ( finite_finite_int @ T6 )
% 5.64/5.99 => ( ( ord_less_eq_set_int @ S3 @ T6 )
% 5.64/5.99 => ( ! [X4: int] :
% 5.64/5.99 ( ( member_int @ X4 @ ( minus_minus_set_int @ T6 @ S3 ) )
% 5.64/5.99 => ( ( G @ X4 )
% 5.64/5.99 = one_one_int ) )
% 5.64/5.99 => ( ( groups1705073143266064639nt_int @ G @ T6 )
% 5.64/5.99 = ( groups1705073143266064639nt_int @ G @ S3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod.mono_neutral_right
% 5.64/5.99 thf(fact_9211_sum__choose__lower,axiom,
% 5.64/5.99 ! [R2: nat,N: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K2 ) @ K2 )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N ) ) @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum_choose_lower
% 5.64/5.99 thf(fact_9212_choose__rising__sum_I1_J,axiom,
% 5.64/5.99 ! [N: nat,M: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_rising_sum(1)
% 5.64/5.99 thf(fact_9213_choose__rising__sum_I2_J,axiom,
% 5.64/5.99 ! [N: nat,M: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_rising_sum(2)
% 5.64/5.99 thf(fact_9214_atLeast1__atMost__eq__remove0,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/5.99 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % atLeast1_atMost_eq_remove0
% 5.64/5.99 thf(fact_9215_fact__eq__fact__times,axiom,
% 5.64/5.99 ! [N: nat,M: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.99 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.64/5.99 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.64/5.99 @ ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [X: nat] : X
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_eq_fact_times
% 5.64/5.99 thf(fact_9216_sum__choose__diagonal,axiom,
% 5.64/5.99 ! [M: nat,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 => ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sum_choose_diagonal
% 5.64/5.99 thf(fact_9217_vandermonde,axiom,
% 5.64/5.99 ! [M: nat,N: nat,R2: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R2 @ K2 ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ R2 ) )
% 5.64/5.99 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % vandermonde
% 5.64/5.99 thf(fact_9218_fact__div__fact,axiom,
% 5.64/5.99 ! [N: nat,M: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ N @ M )
% 5.64/5.99 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.64/5.99 = ( groups708209901874060359at_nat
% 5.64/5.99 @ ^ [X: nat] : X
% 5.64/5.99 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % fact_div_fact
% 5.64/5.99 thf(fact_9219_choose__row__sum,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_row_sum
% 5.64/5.99 thf(fact_9220_binomial,axiom,
% 5.64/5.99 ! [A: nat,B: nat,N: nat] :
% 5.64/5.99 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.64/5.99 = ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial
% 5.64/5.99 thf(fact_9221_polynomial__product__nat,axiom,
% 5.64/5.99 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X2: nat] :
% 5.64/5.99 ( ! [I3: nat] :
% 5.64/5.99 ( ( ord_less_nat @ M @ I3 )
% 5.64/5.99 => ( ( A @ I3 )
% 5.64/5.99 = zero_zero_nat ) )
% 5.64/5.99 => ( ! [J2: nat] :
% 5.64/5.99 ( ( ord_less_nat @ N @ J2 )
% 5.64/5.99 => ( ( B @ J2 )
% 5.64/5.99 = zero_zero_nat ) )
% 5.64/5.99 => ( ( times_times_nat
% 5.64/5.99 @ ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( power_power_nat @ X2 @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 @ ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) ) )
% 5.64/5.99 = ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [R5: nat] :
% 5.64/5.99 ( times_times_nat
% 5.64/5.99 @ ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ R5 ) )
% 5.64/5.99 @ ( power_power_nat @ X2 @ R5 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % polynomial_product_nat
% 5.64/5.99 thf(fact_9222_choose__square__sum,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_square_sum
% 5.64/5.99 thf(fact_9223_binomial__r__part__sum,axiom,
% 5.64/5.99 ! [M: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.64/5.99 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % binomial_r_part_sum
% 5.64/5.99 thf(fact_9224_choose__linear__sum,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( groups3542108847815614940at_nat
% 5.64/5.99 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N @ I4 ) )
% 5.64/5.99 @ ( set_ord_atMost_nat @ N ) )
% 5.64/5.99 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % choose_linear_sum
% 5.64/5.99 thf(fact_9225_of__nat__id,axiom,
% 5.64/5.99 ( semiri1316708129612266289at_nat
% 5.64/5.99 = ( ^ [N2: nat] : N2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % of_nat_id
% 5.64/5.99 thf(fact_9226_real__scaleR__def,axiom,
% 5.64/5.99 real_V1485227260804924795R_real = times_times_real ).
% 5.64/5.99
% 5.64/5.99 % real_scaleR_def
% 5.64/5.99 thf(fact_9227_prod__int__plus__eq,axiom,
% 5.64/5.99 ! [I: nat,J: nat] :
% 5.64/5.99 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.64/5.99 = ( groups1705073143266064639nt_int
% 5.64/5.99 @ ^ [X: int] : X
% 5.64/5.99 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % prod_int_plus_eq
% 5.64/5.99 thf(fact_9228_Maclaurin__sin__bound,axiom,
% 5.64/5.99 ! [X2: real,N: nat] :
% 5.64/5.99 ( ord_less_eq_real
% 5.64/5.99 @ ( abs_abs_real
% 5.64/5.99 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.64/5.99 @ ( groups6591440286371151544t_real
% 5.64/5.99 @ ^ [M2: nat] : ( times_times_real @ ( sin_coeff @ M2 ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/5.99 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.64/5.99 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Maclaurin_sin_bound
% 5.64/5.99 thf(fact_9229_complex__unimodular__polar,axiom,
% 5.64/5.99 ! [Z: complex] :
% 5.64/5.99 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.64/5.99 = one_one_real )
% 5.64/5.99 => ~ ! [T4: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/5.99 => ( ( ord_less_real @ T4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/5.99 => ( Z
% 5.64/5.99 != ( complex2 @ ( cos_real @ T4 ) @ ( sin_real @ T4 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_unimodular_polar
% 5.64/5.99 thf(fact_9230_cot__less__zero,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/5.99 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % cot_less_zero
% 5.64/5.99 thf(fact_9231_cot__npi,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.64/5.99 = zero_zero_real ) ).
% 5.64/5.99
% 5.64/5.99 % cot_npi
% 5.64/5.99 thf(fact_9232_cot__periodic,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( cot_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.64/5.99 = ( cot_real @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % cot_periodic
% 5.64/5.99 thf(fact_9233_complex__scaleR,axiom,
% 5.64/5.99 ! [R2: real,A: real,B: real] :
% 5.64/5.99 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.64/5.99 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_scaleR
% 5.64/5.99 thf(fact_9234_complex__of__real__mult__Complex,axiom,
% 5.64/5.99 ! [R2: real,X2: real,Y4: real] :
% 5.64/5.99 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X2 @ Y4 ) )
% 5.64/5.99 = ( complex2 @ ( times_times_real @ R2 @ X2 ) @ ( times_times_real @ R2 @ Y4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_of_real_mult_Complex
% 5.64/5.99 thf(fact_9235_Complex__mult__complex__of__real,axiom,
% 5.64/5.99 ! [X2: real,Y4: real,R2: real] :
% 5.64/5.99 ( ( times_times_complex @ ( complex2 @ X2 @ Y4 ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.64/5.99 = ( complex2 @ ( times_times_real @ X2 @ R2 ) @ ( times_times_real @ Y4 @ R2 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Complex_mult_complex_of_real
% 5.64/5.99 thf(fact_9236_divide__real__def,axiom,
% 5.64/5.99 ( divide_divide_real
% 5.64/5.99 = ( ^ [X: real,Y: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % divide_real_def
% 5.64/5.99 thf(fact_9237_complex__mult,axiom,
% 5.64/5.99 ! [A: real,B: real,C: real,D: real] :
% 5.64/5.99 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.64/5.99 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_mult
% 5.64/5.99 thf(fact_9238_forall__pos__mono__1,axiom,
% 5.64/5.99 ! [P: real > $o,E: real] :
% 5.64/5.99 ( ! [D3: real,E2: real] :
% 5.64/5.99 ( ( ord_less_real @ D3 @ E2 )
% 5.64/5.99 => ( ( P @ D3 )
% 5.64/5.99 => ( P @ E2 ) ) )
% 5.64/5.99 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.64/5.99 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.64/5.99 => ( P @ E ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % forall_pos_mono_1
% 5.64/5.99 thf(fact_9239_forall__pos__mono,axiom,
% 5.64/5.99 ! [P: real > $o,E: real] :
% 5.64/5.99 ( ! [D3: real,E2: real] :
% 5.64/5.99 ( ( ord_less_real @ D3 @ E2 )
% 5.64/5.99 => ( ( P @ D3 )
% 5.64/5.99 => ( P @ E2 ) ) )
% 5.64/5.99 => ( ! [N3: nat] :
% 5.64/5.99 ( ( N3 != zero_zero_nat )
% 5.64/5.99 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.64/5.99 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.64/5.99 => ( P @ E ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % forall_pos_mono
% 5.64/5.99 thf(fact_9240_real__arch__inverse,axiom,
% 5.64/5.99 ! [E: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ E )
% 5.64/5.99 = ( ? [N2: nat] :
% 5.64/5.99 ( ( N2 != zero_zero_nat )
% 5.64/5.99 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.64/5.99 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % real_arch_inverse
% 5.64/5.99 thf(fact_9241_sqrt__divide__self__eq,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( divide_divide_real @ ( sqrt @ X2 ) @ X2 )
% 5.64/5.99 = ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sqrt_divide_self_eq
% 5.64/5.99 thf(fact_9242_ln__inverse,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ln_ln_real @ ( inverse_inverse_real @ X2 ) )
% 5.64/5.99 = ( uminus_uminus_real @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % ln_inverse
% 5.64/5.99 thf(fact_9243_log__inverse,axiom,
% 5.64/5.99 ! [A: real,X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/5.99 => ( ( A != one_one_real )
% 5.64/5.99 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( log @ A @ ( inverse_inverse_real @ X2 ) )
% 5.64/5.99 = ( uminus_uminus_real @ ( log @ A @ X2 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % log_inverse
% 5.64/5.99 thf(fact_9244_complex__norm,axiom,
% 5.64/5.99 ! [X2: real,Y4: real] :
% 5.64/5.99 ( ( real_V1022390504157884413omplex @ ( complex2 @ X2 @ Y4 ) )
% 5.64/5.99 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_norm
% 5.64/5.99 thf(fact_9245_exp__plus__inverse__exp,axiom,
% 5.64/5.99 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % exp_plus_inverse_exp
% 5.64/5.99 thf(fact_9246_plus__inverse__ge__2,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % plus_inverse_ge_2
% 5.64/5.99 thf(fact_9247_real__inv__sqrt__pow2,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.99 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % real_inv_sqrt_pow2
% 5.64/5.99 thf(fact_9248_tan__cot,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.64/5.99 = ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % tan_cot
% 5.64/5.99 thf(fact_9249_real__le__x__sinh,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ord_less_eq_real @ X2 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % real_le_x_sinh
% 5.64/5.99 thf(fact_9250_real__le__abs__sinh,axiom,
% 5.64/5.99 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % real_le_abs_sinh
% 5.64/5.99 thf(fact_9251_cot__gt__zero,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.99 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % cot_gt_zero
% 5.64/5.99 thf(fact_9252_tan__cot_H,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.64/5.99 = ( cot_real @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % tan_cot'
% 5.64/5.99 thf(fact_9253_arctan__def,axiom,
% 5.64/5.99 ( arctan
% 5.64/5.99 = ( ^ [Y: real] :
% 5.64/5.99 ( the_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.64/5.99 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.99 & ( ( tan_real @ X )
% 5.64/5.99 = Y ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % arctan_def
% 5.64/5.99 thf(fact_9254_arcsin__def,axiom,
% 5.64/5.99 ( arcsin
% 5.64/5.99 = ( ^ [Y: real] :
% 5.64/5.99 ( the_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.64/5.99 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/5.99 & ( ( sin_real @ X )
% 5.64/5.99 = Y ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % arcsin_def
% 5.64/5.99 thf(fact_9255_sinh__real__less__iff,axiom,
% 5.64/5.99 ! [X2: real,Y4: real] :
% 5.64/5.99 ( ( ord_less_real @ ( sinh_real @ X2 ) @ ( sinh_real @ Y4 ) )
% 5.64/5.99 = ( ord_less_real @ X2 @ Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % sinh_real_less_iff
% 5.64/5.99 thf(fact_9256_sinh__real__pos__iff,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X2 ) )
% 5.64/5.99 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % sinh_real_pos_iff
% 5.64/5.99 thf(fact_9257_sinh__real__neg__iff,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ ( sinh_real @ X2 ) @ zero_zero_real )
% 5.64/5.99 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.64/5.99
% 5.64/5.99 % sinh_real_neg_iff
% 5.64/5.99 thf(fact_9258_divide__complex__def,axiom,
% 5.64/5.99 ( divide1717551699836669952omplex
% 5.64/5.99 = ( ^ [X: complex,Y: complex] : ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % divide_complex_def
% 5.64/5.99 thf(fact_9259_sinh__less__cosh__real,axiom,
% 5.64/5.99 ! [X2: real] : ( ord_less_real @ ( sinh_real @ X2 ) @ ( cosh_real @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % sinh_less_cosh_real
% 5.64/5.99 thf(fact_9260_complex__exp__exists,axiom,
% 5.64/5.99 ! [Z: complex] :
% 5.64/5.99 ? [A5: complex,R3: real] :
% 5.64/5.99 ( Z
% 5.64/5.99 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A5 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_exp_exists
% 5.64/5.99 thf(fact_9261_cosh__real__pos,axiom,
% 5.64/5.99 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % cosh_real_pos
% 5.64/5.99 thf(fact_9262_cosh__real__nonpos__less__iff,axiom,
% 5.64/5.99 ! [X2: real,Y4: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.64/5.99 => ( ( ord_less_eq_real @ Y4 @ zero_zero_real )
% 5.64/5.99 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y4 ) )
% 5.64/5.99 = ( ord_less_real @ Y4 @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % cosh_real_nonpos_less_iff
% 5.64/5.99 thf(fact_9263_cosh__real__nonneg__less__iff,axiom,
% 5.64/5.99 ! [X2: real,Y4: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/5.99 => ( ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y4 ) )
% 5.64/5.99 = ( ord_less_real @ X2 @ Y4 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % cosh_real_nonneg_less_iff
% 5.64/5.99 thf(fact_9264_cosh__real__strict__mono,axiom,
% 5.64/5.99 ! [X2: real,Y4: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/5.99 => ( ord_less_real @ ( cosh_real @ X2 ) @ ( cosh_real @ Y4 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % cosh_real_strict_mono
% 5.64/5.99 thf(fact_9265_complex__inverse,axiom,
% 5.64/5.99 ! [A: real,B: real] :
% 5.64/5.99 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.64/5.99 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_inverse
% 5.64/5.99 thf(fact_9266_pi__half,axiom,
% 5.64/5.99 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.99 = ( the_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.64/5.99 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.99 & ( ( cos_real @ X )
% 5.64/5.99 = zero_zero_real ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pi_half
% 5.64/5.99 thf(fact_9267_pi__def,axiom,
% 5.64/5.99 ( pi
% 5.64/5.99 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.64/5.99 @ ( the_real
% 5.64/5.99 @ ^ [X: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.64/5.99 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.64/5.99 & ( ( cos_real @ X )
% 5.64/5.99 = zero_zero_real ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % pi_def
% 5.64/5.99 thf(fact_9268_cosh__ln__real,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.99 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % cosh_ln_real
% 5.64/5.99 thf(fact_9269_sinh__ln__real,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.64/5.99 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sinh_ln_real
% 5.64/5.99 thf(fact_9270_signed__take__bit__eq__take__bit__minus,axiom,
% 5.64/5.99 ( bit_ri631733984087533419it_int
% 5.64/5.99 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % signed_take_bit_eq_take_bit_minus
% 5.64/5.99 thf(fact_9271_modulo__int__unfold,axiom,
% 5.64/5.99 ! [L: int,K: int,N: nat,M: nat] :
% 5.64/5.99 ( ( ( ( ( sgn_sgn_int @ L )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( ( sgn_sgn_int @ K )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( N = zero_zero_nat ) )
% 5.64/5.99 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.64/5.99 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( ( sgn_sgn_int @ K )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( N = zero_zero_nat ) )
% 5.64/5.99 => ( ( ( ( sgn_sgn_int @ K )
% 5.64/5.99 = ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.64/5.99 & ( ( ( sgn_sgn_int @ K )
% 5.64/5.99 != ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.99 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.64/5.99 @ ( minus_minus_int
% 5.64/5.99 @ ( semiri1314217659103216013at_int
% 5.64/5.99 @ ( times_times_nat @ N
% 5.64/5.99 @ ( zero_n2687167440665602831ol_nat
% 5.64/5.99 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.64/5.99 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % modulo_int_unfold
% 5.64/5.99 thf(fact_9272_powr__int,axiom,
% 5.64/5.99 ! [X2: real,I: int] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.64/5.99 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.64/5.99 = ( power_power_real @ X2 @ ( nat2 @ I ) ) ) )
% 5.64/5.99 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.64/5.99 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I ) )
% 5.64/5.99 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % powr_int
% 5.64/5.99 thf(fact_9273_nat__numeral,axiom,
% 5.64/5.99 ! [K: num] :
% 5.64/5.99 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.64/5.99 = ( numeral_numeral_nat @ K ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_numeral
% 5.64/5.99 thf(fact_9274_nat__1,axiom,
% 5.64/5.99 ( ( nat2 @ one_one_int )
% 5.64/5.99 = ( suc @ zero_zero_nat ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_1
% 5.64/5.99 thf(fact_9275_zless__nat__conj,axiom,
% 5.64/5.99 ! [W: int,Z: int] :
% 5.64/5.99 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.99 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % zless_nat_conj
% 5.64/5.99 thf(fact_9276_dvd__mult__sgn__iff,axiom,
% 5.64/5.99 ! [L: int,K: int,R2: int] :
% 5.64/5.99 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.64/5.99 = ( ( dvd_dvd_int @ L @ K )
% 5.64/5.99 | ( R2 = zero_zero_int ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % dvd_mult_sgn_iff
% 5.64/5.99 thf(fact_9277_dvd__sgn__mult__iff,axiom,
% 5.64/5.99 ! [L: int,R2: int,K: int] :
% 5.64/5.99 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.64/5.99 = ( ( dvd_dvd_int @ L @ K )
% 5.64/5.99 | ( R2 = zero_zero_int ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % dvd_sgn_mult_iff
% 5.64/5.99 thf(fact_9278_mult__sgn__dvd__iff,axiom,
% 5.64/5.99 ! [L: int,R2: int,K: int] :
% 5.64/5.99 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.64/5.99 = ( ( dvd_dvd_int @ L @ K )
% 5.64/5.99 & ( ( R2 = zero_zero_int )
% 5.64/5.99 => ( K = zero_zero_int ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % mult_sgn_dvd_iff
% 5.64/5.99 thf(fact_9279_sgn__mult__dvd__iff,axiom,
% 5.64/5.99 ! [R2: int,L: int,K: int] :
% 5.64/5.99 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 5.64/5.99 = ( ( dvd_dvd_int @ L @ K )
% 5.64/5.99 & ( ( R2 = zero_zero_int )
% 5.64/5.99 => ( K = zero_zero_int ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % sgn_mult_dvd_iff
% 5.64/5.99 thf(fact_9280_signed__take__bit__negative__iff,axiom,
% 5.64/5.99 ! [N: nat,K: int] :
% 5.64/5.99 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.64/5.99 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % signed_take_bit_negative_iff
% 5.64/5.99 thf(fact_9281_zero__less__nat__eq,axiom,
% 5.64/5.99 ! [Z: int] :
% 5.64/5.99 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.64/5.99
% 5.64/5.99 % zero_less_nat_eq
% 5.64/5.99 thf(fact_9282_diff__nat__numeral,axiom,
% 5.64/5.99 ! [V: num,V3: num] :
% 5.64/5.99 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.64/5.99 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % diff_nat_numeral
% 5.64/5.99 thf(fact_9283_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.64/5.99 ! [W: num,N: nat] :
% 5.64/5.99 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.64/5.99 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_minus_numeral_Bit0_Suc_iff
% 5.64/5.99 thf(fact_9284_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.64/5.99 ! [W: num,N: nat] :
% 5.64/5.99 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.64/5.99 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_minus_numeral_Bit1_Suc_iff
% 5.64/5.99 thf(fact_9285_numeral__power__eq__nat__cancel__iff,axiom,
% 5.64/5.99 ! [X2: num,N: nat,Y4: int] :
% 5.64/5.99 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N )
% 5.64/5.99 = ( nat2 @ Y4 ) )
% 5.64/5.99 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N )
% 5.64/5.99 = Y4 ) ) ).
% 5.64/5.99
% 5.64/5.99 % numeral_power_eq_nat_cancel_iff
% 5.64/5.99 thf(fact_9286_nat__eq__numeral__power__cancel__iff,axiom,
% 5.64/5.99 ! [Y4: int,X2: num,N: nat] :
% 5.64/5.99 ( ( ( nat2 @ Y4 )
% 5.64/5.99 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.64/5.99 = ( Y4
% 5.64/5.99 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_eq_numeral_power_cancel_iff
% 5.64/5.99 thf(fact_9287_nat__ceiling__le__eq,axiom,
% 5.64/5.99 ! [X2: real,A: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A )
% 5.64/5.99 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_ceiling_le_eq
% 5.64/5.99 thf(fact_9288_one__less__nat__eq,axiom,
% 5.64/5.99 ! [Z: int] :
% 5.64/5.99 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.64/5.99
% 5.64/5.99 % one_less_nat_eq
% 5.64/5.99 thf(fact_9289_bit__minus__numeral__int_I1_J,axiom,
% 5.64/5.99 ! [W: num,N: num] :
% 5.64/5.99 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.99 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_minus_numeral_int(1)
% 5.64/5.99 thf(fact_9290_bit__minus__numeral__int_I2_J,axiom,
% 5.64/5.99 ! [W: num,N: num] :
% 5.64/5.99 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.64/5.99 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_minus_numeral_int(2)
% 5.64/5.99 thf(fact_9291_nat__numeral__diff__1,axiom,
% 5.64/5.99 ! [V: num] :
% 5.64/5.99 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.64/5.99 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_numeral_diff_1
% 5.64/5.99 thf(fact_9292_numeral__power__less__nat__cancel__iff,axiom,
% 5.64/5.99 ! [X2: num,N: nat,A: int] :
% 5.64/5.99 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.64/5.99 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.99
% 5.64/5.99 % numeral_power_less_nat_cancel_iff
% 5.64/5.99 thf(fact_9293_nat__less__numeral__power__cancel__iff,axiom,
% 5.64/5.99 ! [A: int,X2: num,N: nat] :
% 5.64/5.99 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.64/5.99 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_less_numeral_power_cancel_iff
% 5.64/5.99 thf(fact_9294_nat__le__numeral__power__cancel__iff,axiom,
% 5.64/5.99 ! [A: int,X2: num,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) )
% 5.64/5.99 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_le_numeral_power_cancel_iff
% 5.64/5.99 thf(fact_9295_numeral__power__le__nat__cancel__iff,axiom,
% 5.64/5.99 ! [X2: num,N: nat,A: int] :
% 5.64/5.99 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N ) @ ( nat2 @ A ) )
% 5.64/5.99 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N ) @ A ) ) ).
% 5.64/5.99
% 5.64/5.99 % numeral_power_le_nat_cancel_iff
% 5.64/5.99 thf(fact_9296_nat__zero__as__int,axiom,
% 5.64/5.99 ( zero_zero_nat
% 5.64/5.99 = ( nat2 @ zero_zero_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_zero_as_int
% 5.64/5.99 thf(fact_9297_nat__numeral__as__int,axiom,
% 5.64/5.99 ( numeral_numeral_nat
% 5.64/5.99 = ( ^ [I4: num] : ( nat2 @ ( numeral_numeral_int @ I4 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_numeral_as_int
% 5.64/5.99 thf(fact_9298_nat__mono,axiom,
% 5.64/5.99 ! [X2: int,Y4: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ X2 @ Y4 )
% 5.64/5.99 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y4 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_mono
% 5.64/5.99 thf(fact_9299_int__sgnE,axiom,
% 5.64/5.99 ! [K: int] :
% 5.64/5.99 ~ ! [N3: nat,L4: int] :
% 5.64/5.99 ( K
% 5.64/5.99 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % int_sgnE
% 5.64/5.99 thf(fact_9300_nat__one__as__int,axiom,
% 5.64/5.99 ( one_one_nat
% 5.64/5.99 = ( nat2 @ one_one_int ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_one_as_int
% 5.64/5.99 thf(fact_9301_div__eq__sgn__abs,axiom,
% 5.64/5.99 ! [K: int,L: int] :
% 5.64/5.99 ( ( ( sgn_sgn_int @ K )
% 5.64/5.99 = ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( divide_divide_int @ K @ L )
% 5.64/5.99 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % div_eq_sgn_abs
% 5.64/5.99 thf(fact_9302_nat__mono__iff,axiom,
% 5.64/5.99 ! [Z: int,W: int] :
% 5.64/5.99 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.64/5.99 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_mono_iff
% 5.64/5.99 thf(fact_9303_zless__nat__eq__int__zless,axiom,
% 5.64/5.99 ! [M: nat,Z: int] :
% 5.64/5.99 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.64/5.99
% 5.64/5.99 % zless_nat_eq_int_zless
% 5.64/5.99 thf(fact_9304_nat__le__iff,axiom,
% 5.64/5.99 ! [X2: int,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N )
% 5.64/5.99 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_le_iff
% 5.64/5.99 thf(fact_9305_nat__int__add,axiom,
% 5.64/5.99 ! [A: nat,B: nat] :
% 5.64/5.99 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.64/5.99 = ( plus_plus_nat @ A @ B ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_int_add
% 5.64/5.99 thf(fact_9306_int__minus,axiom,
% 5.64/5.99 ! [N: nat,M: nat] :
% 5.64/5.99 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.64/5.99 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % int_minus
% 5.64/5.99 thf(fact_9307_nat__abs__mult__distrib,axiom,
% 5.64/5.99 ! [W: int,Z: int] :
% 5.64/5.99 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.64/5.99 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_abs_mult_distrib
% 5.64/5.99 thf(fact_9308_nat__plus__as__int,axiom,
% 5.64/5.99 ( plus_plus_nat
% 5.64/5.99 = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_plus_as_int
% 5.64/5.99 thf(fact_9309_nat__times__as__int,axiom,
% 5.64/5.99 ( times_times_nat
% 5.64/5.99 = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_times_as_int
% 5.64/5.99 thf(fact_9310_nat__minus__as__int,axiom,
% 5.64/5.99 ( minus_minus_nat
% 5.64/5.99 = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_minus_as_int
% 5.64/5.99 thf(fact_9311_nat__div__as__int,axiom,
% 5.64/5.99 ( divide_divide_nat
% 5.64/5.99 = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_div_as_int
% 5.64/5.99 thf(fact_9312_nat__mod__as__int,axiom,
% 5.64/5.99 ( modulo_modulo_nat
% 5.64/5.99 = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_mod_as_int
% 5.64/5.99 thf(fact_9313_zsgn__def,axiom,
% 5.64/5.99 ( sgn_sgn_int
% 5.64/5.99 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % zsgn_def
% 5.64/5.99 thf(fact_9314_nat__less__eq__zless,axiom,
% 5.64/5.99 ! [W: int,Z: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.64/5.99 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_less_eq_zless
% 5.64/5.99 thf(fact_9315_nat__le__eq__zle,axiom,
% 5.64/5.99 ! [W: int,Z: int] :
% 5.64/5.99 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.64/5.99 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.64/5.99 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.64/5.99 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_le_eq_zle
% 5.64/5.99 thf(fact_9316_split__nat,axiom,
% 5.64/5.99 ! [P: nat > $o,I: int] :
% 5.64/5.99 ( ( P @ ( nat2 @ I ) )
% 5.64/5.99 = ( ! [N2: nat] :
% 5.64/5.99 ( ( I
% 5.64/5.99 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.64/5.99 => ( P @ N2 ) )
% 5.64/5.99 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.64/5.99 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % split_nat
% 5.64/5.99 thf(fact_9317_le__nat__iff,axiom,
% 5.64/5.99 ! [K: int,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.99 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.64/5.99 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % le_nat_iff
% 5.64/5.99 thf(fact_9318_nat__add__distrib,axiom,
% 5.64/5.99 ! [Z: int,Z7: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.99 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.64/5.99 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.64/5.99 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_add_distrib
% 5.64/5.99 thf(fact_9319_div__sgn__abs__cancel,axiom,
% 5.64/5.99 ! [V: int,K: int,L: int] :
% 5.64/5.99 ( ( V != zero_zero_int )
% 5.64/5.99 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 5.64/5.99 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % div_sgn_abs_cancel
% 5.64/5.99 thf(fact_9320_bit__imp__take__bit__positive,axiom,
% 5.64/5.99 ! [N: nat,M: nat,K: int] :
% 5.64/5.99 ( ( ord_less_nat @ N @ M )
% 5.64/5.99 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.64/5.99 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_imp_take_bit_positive
% 5.64/5.99 thf(fact_9321_Suc__as__int,axiom,
% 5.64/5.99 ( suc
% 5.64/5.99 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Suc_as_int
% 5.64/5.99 thf(fact_9322_nat__mult__distrib,axiom,
% 5.64/5.99 ! [Z: int,Z7: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.99 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.64/5.99 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_mult_distrib
% 5.64/5.99 thf(fact_9323_nat__abs__triangle__ineq,axiom,
% 5.64/5.99 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_abs_triangle_ineq
% 5.64/5.99 thf(fact_9324_nat__div__distrib_H,axiom,
% 5.64/5.99 ! [Y4: int,X2: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Y4 )
% 5.64/5.99 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y4 ) )
% 5.64/5.99 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y4 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_div_distrib'
% 5.64/5.99 thf(fact_9325_nat__div__distrib,axiom,
% 5.64/5.99 ! [X2: int,Y4: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/5.99 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y4 ) )
% 5.64/5.99 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y4 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_div_distrib
% 5.64/5.99 thf(fact_9326_div__dvd__sgn__abs,axiom,
% 5.64/5.99 ! [L: int,K: int] :
% 5.64/5.99 ( ( dvd_dvd_int @ L @ K )
% 5.64/5.99 => ( ( divide_divide_int @ K @ L )
% 5.64/5.99 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % div_dvd_sgn_abs
% 5.64/5.99 thf(fact_9327_bit__concat__bit__iff,axiom,
% 5.64/5.99 ! [M: nat,K: int,L: int,N: nat] :
% 5.64/5.99 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N )
% 5.64/5.99 = ( ( ( ord_less_nat @ N @ M )
% 5.64/5.99 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.64/5.99 | ( ( ord_less_eq_nat @ M @ N )
% 5.64/5.99 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_concat_bit_iff
% 5.64/5.99 thf(fact_9328_nat__power__eq,axiom,
% 5.64/5.99 ! [Z: int,N: nat] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.99 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.64/5.99 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_power_eq
% 5.64/5.99 thf(fact_9329_div__abs__eq__div__nat,axiom,
% 5.64/5.99 ! [K: int,L: int] :
% 5.64/5.99 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.64/5.99 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % div_abs_eq_div_nat
% 5.64/5.99 thf(fact_9330_floor__eq3,axiom,
% 5.64/5.99 ! [N: nat,X2: real] :
% 5.64/5.99 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.64/5.99 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.99 = N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_eq3
% 5.64/5.99 thf(fact_9331_le__nat__floor,axiom,
% 5.64/5.99 ! [X2: nat,A: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A )
% 5.64/5.99 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % le_nat_floor
% 5.64/5.99 thf(fact_9332_divide__int__def,axiom,
% 5.64/5.99 ( divide_divide_int
% 5.64/5.99 = ( ^ [K2: int,L2: int] :
% 5.64/5.99 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.64/5.99 @ ( if_int
% 5.64/5.99 @ ( ( sgn_sgn_int @ K2 )
% 5.64/5.99 = ( sgn_sgn_int @ L2 ) )
% 5.64/5.99 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.64/5.99 @ ( uminus_uminus_int
% 5.64/5.99 @ ( semiri1314217659103216013at_int
% 5.64/5.99 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.64/5.99 @ ( zero_n2687167440665602831ol_nat
% 5.64/5.99 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % divide_int_def
% 5.64/5.99 thf(fact_9333_modulo__int__def,axiom,
% 5.64/5.99 ( modulo_modulo_int
% 5.64/5.99 = ( ^ [K2: int,L2: int] :
% 5.64/5.99 ( if_int @ ( L2 = zero_zero_int ) @ K2
% 5.64/5.99 @ ( if_int
% 5.64/5.99 @ ( ( sgn_sgn_int @ K2 )
% 5.64/5.99 = ( sgn_sgn_int @ L2 ) )
% 5.64/5.99 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.64/5.99 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.64/5.99 @ ( minus_minus_int
% 5.64/5.99 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.64/5.99 @ ( zero_n2684676970156552555ol_int
% 5.64/5.99 @ ~ ( dvd_dvd_int @ L2 @ K2 ) ) )
% 5.64/5.99 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % modulo_int_def
% 5.64/5.99 thf(fact_9334_nat__2,axiom,
% 5.64/5.99 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/5.99 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_2
% 5.64/5.99 thf(fact_9335_int__bit__bound,axiom,
% 5.64/5.99 ! [K: int] :
% 5.64/5.99 ~ ! [N3: nat] :
% 5.64/5.99 ( ! [M5: nat] :
% 5.64/5.99 ( ( ord_less_eq_nat @ N3 @ M5 )
% 5.64/5.99 => ( ( bit_se1146084159140164899it_int @ K @ M5 )
% 5.64/5.99 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.64/5.99 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.64/5.99 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.64/5.99 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % int_bit_bound
% 5.64/5.99 thf(fact_9336_Suc__nat__eq__nat__zadd1,axiom,
% 5.64/5.99 ! [Z: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.64/5.99 => ( ( suc @ ( nat2 @ Z ) )
% 5.64/5.99 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % Suc_nat_eq_nat_zadd1
% 5.64/5.99 thf(fact_9337_nat__less__iff,axiom,
% 5.64/5.99 ! [W: int,M: nat] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.64/5.99 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.64/5.99 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_less_iff
% 5.64/5.99 thf(fact_9338_nat__mult__distrib__neg,axiom,
% 5.64/5.99 ! [Z: int,Z7: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.64/5.99 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.64/5.99 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_mult_distrib_neg
% 5.64/5.99 thf(fact_9339_nat__abs__int__diff,axiom,
% 5.64/5.99 ! [A: nat,B: nat] :
% 5.64/5.99 ( ( ( ord_less_eq_nat @ A @ B )
% 5.64/5.99 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.64/5.99 = ( minus_minus_nat @ B @ A ) ) )
% 5.64/5.99 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.64/5.99 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.64/5.99 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % nat_abs_int_diff
% 5.64/5.99 thf(fact_9340_floor__eq4,axiom,
% 5.64/5.99 ! [N: nat,X2: real] :
% 5.64/5.99 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X2 )
% 5.64/5.99 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.64/5.99 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.64/5.99 = N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_eq4
% 5.64/5.99 thf(fact_9341_diff__nat__eq__if,axiom,
% 5.64/5.99 ! [Z7: int,Z: int] :
% 5.64/5.99 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.64/5.99 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.64/5.99 = ( nat2 @ Z ) ) )
% 5.64/5.99 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.64/5.99 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.64/5.99 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % diff_nat_eq_if
% 5.64/5.99 thf(fact_9342_bit__int__def,axiom,
% 5.64/5.99 ( bit_se1146084159140164899it_int
% 5.64/5.99 = ( ^ [K2: int,N2: nat] :
% 5.64/5.99 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % bit_int_def
% 5.64/5.99 thf(fact_9343_eucl__rel__int__remainderI,axiom,
% 5.64/5.99 ! [R2: int,L: int,K: int,Q3: int] :
% 5.64/5.99 ( ( ( sgn_sgn_int @ R2 )
% 5.64/5.99 = ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 5.64/5.99 => ( ( K
% 5.64/5.99 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R2 ) )
% 5.64/5.99 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % eucl_rel_int_remainderI
% 5.64/5.99 thf(fact_9344_eucl__rel__int_Osimps,axiom,
% 5.64/5.99 ( eucl_rel_int
% 5.64/5.99 = ( ^ [A12: int,A23: int,A32: product_prod_int_int] :
% 5.64/5.99 ( ? [K2: int] :
% 5.64/5.99 ( ( A12 = K2 )
% 5.64/5.99 & ( A23 = zero_zero_int )
% 5.64/5.99 & ( A32
% 5.64/5.99 = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 5.64/5.99 | ? [L2: int,K2: int,Q4: int] :
% 5.64/5.99 ( ( A12 = K2 )
% 5.64/5.99 & ( A23 = L2 )
% 5.64/5.99 & ( A32
% 5.64/5.99 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.64/5.99 & ( L2 != zero_zero_int )
% 5.64/5.99 & ( K2
% 5.64/5.99 = ( times_times_int @ Q4 @ L2 ) ) )
% 5.64/5.99 | ? [R5: int,L2: int,K2: int,Q4: int] :
% 5.64/5.99 ( ( A12 = K2 )
% 5.64/5.99 & ( A23 = L2 )
% 5.64/5.99 & ( A32
% 5.64/5.99 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.64/5.99 & ( ( sgn_sgn_int @ R5 )
% 5.64/5.99 = ( sgn_sgn_int @ L2 ) )
% 5.64/5.99 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.64/5.99 & ( K2
% 5.64/5.99 = ( plus_plus_int @ ( times_times_int @ Q4 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % eucl_rel_int.simps
% 5.64/5.99 thf(fact_9345_eucl__rel__int_Ocases,axiom,
% 5.64/5.99 ! [A1: int,A22: int,A33: product_prod_int_int] :
% 5.64/5.99 ( ( eucl_rel_int @ A1 @ A22 @ A33 )
% 5.64/5.99 => ( ( ( A22 = zero_zero_int )
% 5.64/5.99 => ( A33
% 5.64/5.99 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.64/5.99 => ( ! [Q2: int] :
% 5.64/5.99 ( ( A33
% 5.64/5.99 = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 5.64/5.99 => ( ( A22 != zero_zero_int )
% 5.64/5.99 => ( A1
% 5.64/5.99 != ( times_times_int @ Q2 @ A22 ) ) ) )
% 5.64/5.99 => ~ ! [R3: int,Q2: int] :
% 5.64/5.99 ( ( A33
% 5.64/5.99 = ( product_Pair_int_int @ Q2 @ R3 ) )
% 5.64/5.99 => ( ( ( sgn_sgn_int @ R3 )
% 5.64/5.99 = ( sgn_sgn_int @ A22 ) )
% 5.64/5.99 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A22 ) )
% 5.64/5.99 => ( A1
% 5.64/5.99 != ( plus_plus_int @ ( times_times_int @ Q2 @ A22 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % eucl_rel_int.cases
% 5.64/5.99 thf(fact_9346_div__noneq__sgn__abs,axiom,
% 5.64/5.99 ! [L: int,K: int] :
% 5.64/5.99 ( ( L != zero_zero_int )
% 5.64/5.99 => ( ( ( sgn_sgn_int @ K )
% 5.64/5.99 != ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( divide_divide_int @ K @ L )
% 5.64/5.99 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.64/5.99 @ ( zero_n2684676970156552555ol_int
% 5.64/5.99 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % div_noneq_sgn_abs
% 5.64/5.99 thf(fact_9347_floor__real__def,axiom,
% 5.64/5.99 ( archim6058952711729229775r_real
% 5.64/5.99 = ( ^ [X: real] :
% 5.64/5.99 ( the_int
% 5.64/5.99 @ ^ [Z4: int] :
% 5.64/5.99 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z4 ) @ X )
% 5.64/5.99 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % floor_real_def
% 5.64/5.99 thf(fact_9348_even__nat__iff,axiom,
% 5.64/5.99 ! [K: int] :
% 5.64/5.99 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.64/5.99 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.64/5.99 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % even_nat_iff
% 5.64/5.99 thf(fact_9349_set__bit__eq,axiom,
% 5.64/5.99 ( bit_se7879613467334960850it_int
% 5.64/5.99 = ( ^ [N2: nat,K2: int] :
% 5.64/5.99 ( plus_plus_int @ K2
% 5.64/5.99 @ ( times_times_int
% 5.64/5.99 @ ( zero_n2684676970156552555ol_int
% 5.64/5.99 @ ~ ( bit_se1146084159140164899it_int @ K2 @ N2 ) )
% 5.64/5.99 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % set_bit_eq
% 5.64/5.99 thf(fact_9350_unset__bit__eq,axiom,
% 5.64/5.99 ( bit_se4203085406695923979it_int
% 5.64/5.99 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % unset_bit_eq
% 5.64/5.99 thf(fact_9351_take__bit__Suc__from__most,axiom,
% 5.64/5.99 ! [N: nat,K: int] :
% 5.64/5.99 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.64/5.99 = ( 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 ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % take_bit_Suc_from_most
% 5.64/5.99 thf(fact_9352_powr__real__of__int,axiom,
% 5.64/5.99 ! [X2: real,N: int] :
% 5.64/5.99 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/5.99 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.64/5.99 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.64/5.99 = ( power_power_real @ X2 @ ( nat2 @ N ) ) ) )
% 5.64/5.99 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.64/5.99 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.64/5.99 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % powr_real_of_int
% 5.64/5.99 thf(fact_9353_divide__int__unfold,axiom,
% 5.64/5.99 ! [L: int,K: int,N: nat,M: nat] :
% 5.64/5.99 ( ( ( ( ( sgn_sgn_int @ L )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( ( sgn_sgn_int @ K )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( N = zero_zero_nat ) )
% 5.64/5.99 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.99 = zero_zero_int ) )
% 5.64/5.99 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( ( sgn_sgn_int @ K )
% 5.64/5.99 = zero_zero_int )
% 5.64/5.99 | ( N = zero_zero_nat ) )
% 5.64/5.99 => ( ( ( ( sgn_sgn_int @ K )
% 5.64/5.99 = ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.99 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.64/5.99 & ( ( ( sgn_sgn_int @ K )
% 5.64/5.99 != ( sgn_sgn_int @ L ) )
% 5.64/5.99 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.64/5.99 = ( uminus_uminus_int
% 5.64/5.99 @ ( semiri1314217659103216013at_int
% 5.64/5.99 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.64/5.99 @ ( zero_n2687167440665602831ol_nat
% 5.64/5.99 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % divide_int_unfold
% 5.64/5.99 thf(fact_9354_exp__two__pi__i_H,axiom,
% 5.64/5.99 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.64/5.99 = one_one_complex ) ).
% 5.64/5.99
% 5.64/5.99 % exp_two_pi_i'
% 5.64/5.99 thf(fact_9355_exp__two__pi__i,axiom,
% 5.64/5.99 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.64/5.99 = one_one_complex ) ).
% 5.64/5.99
% 5.64/5.99 % exp_two_pi_i
% 5.64/5.99 thf(fact_9356_arctan__inverse,axiom,
% 5.64/5.99 ! [X2: real] :
% 5.64/5.99 ( ( X2 != zero_zero_real )
% 5.64/5.99 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X2 ) )
% 5.64/5.99 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X2 ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % arctan_inverse
% 5.64/5.99 thf(fact_9357_complex__i__mult__minus,axiom,
% 5.64/5.99 ! [X2: complex] :
% 5.64/5.99 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X2 ) )
% 5.64/5.99 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % complex_i_mult_minus
% 5.64/5.99 thf(fact_9358_divide__i,axiom,
% 5.64/5.99 ! [X2: complex] :
% 5.64/5.99 ( ( divide1717551699836669952omplex @ X2 @ imaginary_unit )
% 5.64/5.99 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X2 ) ) ).
% 5.64/5.99
% 5.64/5.99 % divide_i
% 5.64/5.99 thf(fact_9359_i__squared,axiom,
% 5.64/5.99 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.64/5.99 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % i_squared
% 5.64/5.99 thf(fact_9360_divide__numeral__i,axiom,
% 5.64/5.99 ! [Z: complex,N: num] :
% 5.64/5.99 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.64/5.99 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % divide_numeral_i
% 5.64/5.99 thf(fact_9361_power2__i,axiom,
% 5.64/5.99 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/5.99 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % power2_i
% 5.64/5.99 thf(fact_9362_exp__pi__i_H,axiom,
% 5.64/5.99 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.64/5.99 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % exp_pi_i'
% 5.64/5.99 thf(fact_9363_exp__pi__i,axiom,
% 5.64/5.99 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.64/5.99 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.64/5.99
% 5.64/5.99 % exp_pi_i
% 5.64/5.99 thf(fact_9364_i__even__power,axiom,
% 5.64/5.99 ! [N: nat] :
% 5.64/5.99 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/5.99 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.64/5.99
% 5.64/5.99 % i_even_power
% 5.64/5.99 thf(fact_9365_i__times__eq__iff,axiom,
% 5.64/5.99 ! [W: complex,Z: complex] :
% 5.64/5.99 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.64/5.99 = Z )
% 5.64/5.99 = ( W
% 5.64/5.99 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.64/5.99
% 5.64/5.99 % i_times_eq_iff
% 5.64/5.99 thf(fact_9366_bit__Suc__0__iff,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/6.00 = ( N = zero_zero_nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % bit_Suc_0_iff
% 5.64/6.00 thf(fact_9367_not__bit__Suc__0__Suc,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % not_bit_Suc_0_Suc
% 5.64/6.00 thf(fact_9368_real__sgn__eq,axiom,
% 5.64/6.00 ( sgn_sgn_real
% 5.64/6.00 = ( ^ [X: real] : ( divide_divide_real @ X @ ( abs_abs_real @ X ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_sgn_eq
% 5.64/6.00 thf(fact_9369_not__bit__Suc__0__numeral,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % not_bit_Suc_0_numeral
% 5.64/6.00 thf(fact_9370_sgn__eq,axiom,
% 5.64/6.00 ( sgn_sgn_complex
% 5.64/6.00 = ( ^ [Z4: complex] : ( divide1717551699836669952omplex @ Z4 @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ Z4 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_eq
% 5.64/6.00 thf(fact_9371_Complex__mult__i,axiom,
% 5.64/6.00 ! [A: real,B: real] :
% 5.64/6.00 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.64/6.00 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.64/6.00
% 5.64/6.00 % Complex_mult_i
% 5.64/6.00 thf(fact_9372_i__mult__Complex,axiom,
% 5.64/6.00 ! [A: real,B: real] :
% 5.64/6.00 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.64/6.00 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.64/6.00
% 5.64/6.00 % i_mult_Complex
% 5.64/6.00 thf(fact_9373_sgn__real__def,axiom,
% 5.64/6.00 ( sgn_sgn_real
% 5.64/6.00 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_real_def
% 5.64/6.00 thf(fact_9374_Complex__eq,axiom,
% 5.64/6.00 ( complex2
% 5.64/6.00 = ( ^ [A3: real,B3: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A3 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Complex_eq
% 5.64/6.00 thf(fact_9375_sgn__power__injE,axiom,
% 5.64/6.00 ! [A: real,N: nat,X2: real,B: real] :
% 5.64/6.00 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.64/6.00 = X2 )
% 5.64/6.00 => ( ( X2
% 5.64/6.00 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.64/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( A = B ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_power_injE
% 5.64/6.00 thf(fact_9376_i__complex__of__real,axiom,
% 5.64/6.00 ! [R2: real] :
% 5.64/6.00 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.64/6.00 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % i_complex_of_real
% 5.64/6.00 thf(fact_9377_complex__of__real__i,axiom,
% 5.64/6.00 ! [R2: real] :
% 5.64/6.00 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.64/6.00 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_of_real_i
% 5.64/6.00 thf(fact_9378_complex__split__polar,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ? [R3: real,A5: real] :
% 5.64/6.00 ( Z
% 5.64/6.00 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_split_polar
% 5.64/6.00 thf(fact_9379_bit__nat__def,axiom,
% 5.64/6.00 ( bit_se1148574629649215175it_nat
% 5.64/6.00 = ( ^ [M2: nat,N2: nat] :
% 5.64/6.00 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bit_nat_def
% 5.64/6.00 thf(fact_9380_cmod__unit__one,axiom,
% 5.64/6.00 ! [A: real] :
% 5.64/6.00 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.64/6.00 = one_one_real ) ).
% 5.64/6.00
% 5.64/6.00 % cmod_unit_one
% 5.64/6.00 thf(fact_9381_cmod__complex__polar,axiom,
% 5.64/6.00 ! [R2: real,A: real] :
% 5.64/6.00 ( ( 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 ) ) ) ) ) )
% 5.64/6.00 = ( abs_abs_real @ R2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % cmod_complex_polar
% 5.64/6.00 thf(fact_9382_csqrt__ii,axiom,
% 5.64/6.00 ( ( csqrt @ imaginary_unit )
% 5.64/6.00 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt_ii
% 5.64/6.00 thf(fact_9383_floor__rat__def,axiom,
% 5.64/6.00 ( archim3151403230148437115or_rat
% 5.64/6.00 = ( ^ [X: rat] :
% 5.64/6.00 ( the_int
% 5.64/6.00 @ ^ [Z4: int] :
% 5.64/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z4 ) @ X )
% 5.64/6.00 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z4 @ one_one_int ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % floor_rat_def
% 5.64/6.00 thf(fact_9384_Arg__minus__ii,axiom,
% 5.64/6.00 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.64/6.00 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Arg_minus_ii
% 5.64/6.00 thf(fact_9385_Arg__ii,axiom,
% 5.64/6.00 ( ( arg @ imaginary_unit )
% 5.64/6.00 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Arg_ii
% 5.64/6.00 thf(fact_9386_power2__csqrt,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/6.00 = Z ) ).
% 5.64/6.00
% 5.64/6.00 % power2_csqrt
% 5.64/6.00 thf(fact_9387_sgn__rat__def,axiom,
% 5.64/6.00 ( sgn_sgn_rat
% 5.64/6.00 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_rat_def
% 5.64/6.00 thf(fact_9388_abs__rat__def,axiom,
% 5.64/6.00 ( abs_abs_rat
% 5.64/6.00 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % abs_rat_def
% 5.64/6.00 thf(fact_9389_less__eq__rat__def,axiom,
% 5.64/6.00 ( ord_less_eq_rat
% 5.64/6.00 = ( ^ [X: rat,Y: rat] :
% 5.64/6.00 ( ( ord_less_rat @ X @ Y )
% 5.64/6.00 | ( X = Y ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_eq_rat_def
% 5.64/6.00 thf(fact_9390_obtain__pos__sum,axiom,
% 5.64/6.00 ! [R2: rat] :
% 5.64/6.00 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.64/6.00 => ~ ! [S: rat] :
% 5.64/6.00 ( ( ord_less_rat @ zero_zero_rat @ S )
% 5.64/6.00 => ! [T4: rat] :
% 5.64/6.00 ( ( ord_less_rat @ zero_zero_rat @ T4 )
% 5.64/6.00 => ( R2
% 5.64/6.00 != ( plus_plus_rat @ S @ T4 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % obtain_pos_sum
% 5.64/6.00 thf(fact_9391_Arg__bounded,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.64/6.00 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.64/6.00
% 5.64/6.00 % Arg_bounded
% 5.64/6.00 thf(fact_9392_cis__minus__pi__half,axiom,
% 5.64/6.00 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/6.00 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.64/6.00
% 5.64/6.00 % cis_minus_pi_half
% 5.64/6.00 thf(fact_9393_Arg__correct,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( Z != zero_zero_complex )
% 5.64/6.00 => ( ( ( sgn_sgn_complex @ Z )
% 5.64/6.00 = ( cis @ ( arg @ Z ) ) )
% 5.64/6.00 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.64/6.00 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Arg_correct
% 5.64/6.00 thf(fact_9394_setceilmax,axiom,
% 5.64/6.00 ! [S2: vEBT_VEBT,M: nat,Listy: list_VEBT_VEBT,N: nat] :
% 5.64/6.00 ( ( vEBT_invar_vebt @ S2 @ M )
% 5.64/6.00 => ( ! [X4: vEBT_VEBT] :
% 5.64/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.64/6.00 => ( vEBT_invar_vebt @ X4 @ N ) )
% 5.64/6.00 => ( ( M
% 5.64/6.00 = ( suc @ N ) )
% 5.64/6.00 => ( ! [X4: vEBT_VEBT] :
% 5.64/6.00 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Listy ) )
% 5.64/6.00 => ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ X4 ) )
% 5.64/6.00 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.64/6.00 => ( ( ( semiri1314217659103216013at_int @ ( vEBT_VEBT_height @ S2 ) )
% 5.64/6.00 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) )
% 5.64/6.00 => ( ( semiri1314217659103216013at_int @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ S2 @ ( set_VEBT_VEBT2 @ Listy ) ) ) ) )
% 5.64/6.00 = ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % setceilmax
% 5.64/6.00 thf(fact_9395_rat__inverse__code,axiom,
% 5.64/6.00 ! [P2: rat] :
% 5.64/6.00 ( ( quotient_of @ ( inverse_inverse_rat @ P2 ) )
% 5.64/6.00 = ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B3 ) @ ( abs_abs_int @ A3 ) ) )
% 5.64/6.00 @ ( quotient_of @ P2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_inverse_code
% 5.64/6.00 thf(fact_9396_height__compose__list,axiom,
% 5.64/6.00 ! [T: vEBT_VEBT,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/6.00 ( ( member_VEBT_VEBT @ T @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/6.00 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ T ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % height_compose_list
% 5.64/6.00 thf(fact_9397_max__ins__scaled,axiom,
% 5.64/6.00 ! [N: nat,X14: vEBT_VEBT,M: nat,X13: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ X14 ) ) @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ ( lattic8265883725875713057ax_nat @ ( insert_nat @ ( vEBT_VEBT_height @ X14 ) @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % max_ins_scaled
% 5.64/6.00 thf(fact_9398_height__i__max,axiom,
% 5.64/6.00 ! [I: nat,X13: list_VEBT_VEBT,Foo: nat] :
% 5.64/6.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.64/6.00 => ( ord_less_eq_nat @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) @ ( ord_max_nat @ Foo @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % height_i_max
% 5.64/6.00 thf(fact_9399_max__idx__list,axiom,
% 5.64/6.00 ! [I: nat,X13: list_VEBT_VEBT,N: nat,X14: vEBT_VEBT] :
% 5.64/6.00 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ X13 ) )
% 5.64/6.00 => ( ord_less_eq_nat @ ( times_times_nat @ N @ ( vEBT_VEBT_height @ ( nth_VEBT_VEBT @ X13 @ I ) ) ) @ ( suc @ ( suc @ ( times_times_nat @ N @ ( ord_max_nat @ ( vEBT_VEBT_height @ X14 ) @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( set_VEBT_VEBT2 @ X13 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % max_idx_list
% 5.64/6.00 thf(fact_9400_cis__pi__half,axiom,
% 5.64/6.00 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = imaginary_unit ) ).
% 5.64/6.00
% 5.64/6.00 % cis_pi_half
% 5.64/6.00 thf(fact_9401_cis__2pi,axiom,
% 5.64/6.00 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.64/6.00 = one_one_complex ) ).
% 5.64/6.00
% 5.64/6.00 % cis_2pi
% 5.64/6.00 thf(fact_9402_divide__rat__def,axiom,
% 5.64/6.00 ( divide_divide_rat
% 5.64/6.00 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divide_rat_def
% 5.64/6.00 thf(fact_9403_cis__mult,axiom,
% 5.64/6.00 ! [A: real,B: real] :
% 5.64/6.00 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.64/6.00 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cis_mult
% 5.64/6.00 thf(fact_9404_cis__divide,axiom,
% 5.64/6.00 ! [A: real,B: real] :
% 5.64/6.00 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.64/6.00 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cis_divide
% 5.64/6.00 thf(fact_9405_quotient__of__div,axiom,
% 5.64/6.00 ! [R2: rat,N: int,D: int] :
% 5.64/6.00 ( ( ( quotient_of @ R2 )
% 5.64/6.00 = ( product_Pair_int_int @ N @ D ) )
% 5.64/6.00 => ( R2
% 5.64/6.00 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % quotient_of_div
% 5.64/6.00 thf(fact_9406_VEBT__internal_Oheight_Osimps_I2_J,axiom,
% 5.64/6.00 ! [Uu2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.64/6.00 ( ( vEBT_VEBT_height @ ( vEBT_Node @ Uu2 @ Deg @ TreeList @ Summary ) )
% 5.64/6.00 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary @ ( set_VEBT_VEBT2 @ TreeList ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.height.simps(2)
% 5.64/6.00 thf(fact_9407_rat__floor__code,axiom,
% 5.64/6.00 ( archim3151403230148437115or_rat
% 5.64/6.00 = ( ^ [P5: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P5 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_floor_code
% 5.64/6.00 thf(fact_9408_quotient__of__denom__pos,axiom,
% 5.64/6.00 ! [R2: rat,P2: int,Q3: int] :
% 5.64/6.00 ( ( ( quotient_of @ R2 )
% 5.64/6.00 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.64/6.00 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.64/6.00
% 5.64/6.00 % quotient_of_denom_pos
% 5.64/6.00 thf(fact_9409_DeMoivre,axiom,
% 5.64/6.00 ! [A: real,N: nat] :
% 5.64/6.00 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.64/6.00 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DeMoivre
% 5.64/6.00 thf(fact_9410_VEBT__internal_Oheight_Oelims,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT,Y4: nat] :
% 5.64/6.00 ( ( ( vEBT_VEBT_height @ X2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ? [A5: $o,B5: $o] :
% 5.64/6.00 ( X2
% 5.64/6.00 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/6.00 => ( Y4 != zero_zero_nat ) )
% 5.64/6.00 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.height.elims
% 5.64/6.00 thf(fact_9411_divide__nat__def,axiom,
% 5.64/6.00 ( divide_divide_nat
% 5.64/6.00 = ( ^ [M2: nat,N2: nat] :
% 5.64/6.00 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.64/6.00 @ ( lattic8265883725875713057ax_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N2 ) @ M2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divide_nat_def
% 5.64/6.00 thf(fact_9412_cis__conv__exp,axiom,
% 5.64/6.00 ( cis
% 5.64/6.00 = ( ^ [B3: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B3 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cis_conv_exp
% 5.64/6.00 thf(fact_9413_rat__less__code,axiom,
% 5.64/6.00 ( ord_less_rat
% 5.64/6.00 = ( ^ [P5: rat,Q4: rat] :
% 5.64/6.00 ( produc4947309494688390418_int_o
% 5.64/6.00 @ ^ [A3: int,C2: int] :
% 5.64/6.00 ( produc4947309494688390418_int_o
% 5.64/6.00 @ ^ [B3: int,D2: int] : ( ord_less_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.64/6.00 @ ( quotient_of @ Q4 ) )
% 5.64/6.00 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_less_code
% 5.64/6.00 thf(fact_9414_rat__less__eq__code,axiom,
% 5.64/6.00 ( ord_less_eq_rat
% 5.64/6.00 = ( ^ [P5: rat,Q4: rat] :
% 5.64/6.00 ( produc4947309494688390418_int_o
% 5.64/6.00 @ ^ [A3: int,C2: int] :
% 5.64/6.00 ( produc4947309494688390418_int_o
% 5.64/6.00 @ ^ [B3: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C2 @ B3 ) )
% 5.64/6.00 @ ( quotient_of @ Q4 ) )
% 5.64/6.00 @ ( quotient_of @ P5 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_less_eq_code
% 5.64/6.00 thf(fact_9415_cis__Arg__unique,axiom,
% 5.64/6.00 ! [Z: complex,X2: real] :
% 5.64/6.00 ( ( ( sgn_sgn_complex @ Z )
% 5.64/6.00 = ( cis @ X2 ) )
% 5.64/6.00 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X2 )
% 5.64/6.00 => ( ( ord_less_eq_real @ X2 @ pi )
% 5.64/6.00 => ( ( arg @ Z )
% 5.64/6.00 = X2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cis_Arg_unique
% 5.64/6.00 thf(fact_9416_bij__betw__roots__unity,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( bij_betw_nat_complex
% 5.64/6.00 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.64/6.00 @ ( set_ord_lessThan_nat @ N )
% 5.64/6.00 @ ( collect_complex
% 5.64/6.00 @ ^ [Z4: complex] :
% 5.64/6.00 ( ( power_power_complex @ Z4 @ N )
% 5.64/6.00 = one_one_complex ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bij_betw_roots_unity
% 5.64/6.00 thf(fact_9417_rat__plus__code,axiom,
% 5.64/6.00 ! [P2: rat,Q3: rat] :
% 5.64/6.00 ( ( quotient_of @ ( plus_plus_rat @ P2 @ Q3 ) )
% 5.64/6.00 = ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [A3: int,C2: int] :
% 5.64/6.00 ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B3 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.64/6.00 @ ( quotient_of @ Q3 ) )
% 5.64/6.00 @ ( quotient_of @ P2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_plus_code
% 5.64/6.00 thf(fact_9418_Arg__def,axiom,
% 5.64/6.00 ( arg
% 5.64/6.00 = ( ^ [Z4: complex] :
% 5.64/6.00 ( if_real @ ( Z4 = zero_zero_complex ) @ zero_zero_real
% 5.64/6.00 @ ( fChoice_real
% 5.64/6.00 @ ^ [A3: real] :
% 5.64/6.00 ( ( ( sgn_sgn_complex @ Z4 )
% 5.64/6.00 = ( cis @ A3 ) )
% 5.64/6.00 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.64/6.00 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Arg_def
% 5.64/6.00 thf(fact_9419_image__Suc__atLeastAtMost,axiom,
% 5.64/6.00 ! [I: nat,J: nat] :
% 5.64/6.00 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.64/6.00 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % image_Suc_atLeastAtMost
% 5.64/6.00 thf(fact_9420_normalize__negative,axiom,
% 5.64/6.00 ! [Q3: int,P2: int] :
% 5.64/6.00 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 5.64/6.00 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.64/6.00 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % normalize_negative
% 5.64/6.00 thf(fact_9421_zero__notin__Suc__image,axiom,
% 5.64/6.00 ! [A4: set_nat] :
% 5.64/6.00 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 5.64/6.00
% 5.64/6.00 % zero_notin_Suc_image
% 5.64/6.00 thf(fact_9422_image__Suc__lessThan,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.00 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % image_Suc_lessThan
% 5.64/6.00 thf(fact_9423_image__Suc__atMost,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.64/6.00 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % image_Suc_atMost
% 5.64/6.00 thf(fact_9424_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.64/6.00 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeast0_atMost_Suc_eq_insert_0
% 5.64/6.00 thf(fact_9425_lessThan__Suc__eq__insert__0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.64/6.00 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % lessThan_Suc_eq_insert_0
% 5.64/6.00 thf(fact_9426_atMost__Suc__eq__insert__0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.64/6.00 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atMost_Suc_eq_insert_0
% 5.64/6.00 thf(fact_9427_normalize__denom__pos,axiom,
% 5.64/6.00 ! [R2: product_prod_int_int,P2: int,Q3: int] :
% 5.64/6.00 ( ( ( normalize @ R2 )
% 5.64/6.00 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.64/6.00 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.64/6.00
% 5.64/6.00 % normalize_denom_pos
% 5.64/6.00 thf(fact_9428_normalize__crossproduct,axiom,
% 5.64/6.00 ! [Q3: int,S2: int,P2: int,R2: int] :
% 5.64/6.00 ( ( Q3 != zero_zero_int )
% 5.64/6.00 => ( ( S2 != zero_zero_int )
% 5.64/6.00 => ( ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.64/6.00 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 5.64/6.00 => ( ( times_times_int @ P2 @ S2 )
% 5.64/6.00 = ( times_times_int @ R2 @ Q3 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % normalize_crossproduct
% 5.64/6.00 thf(fact_9429_rat__divide__code,axiom,
% 5.64/6.00 ! [P2: rat,Q3: rat] :
% 5.64/6.00 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q3 ) )
% 5.64/6.00 = ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [A3: int,C2: int] :
% 5.64/6.00 ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C2 @ B3 ) ) )
% 5.64/6.00 @ ( quotient_of @ Q3 ) )
% 5.64/6.00 @ ( quotient_of @ P2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_divide_code
% 5.64/6.00 thf(fact_9430_rat__times__code,axiom,
% 5.64/6.00 ! [P2: rat,Q3: rat] :
% 5.64/6.00 ( ( quotient_of @ ( times_times_rat @ P2 @ Q3 ) )
% 5.64/6.00 = ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [A3: int,C2: int] :
% 5.64/6.00 ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B3 ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.64/6.00 @ ( quotient_of @ Q3 ) )
% 5.64/6.00 @ ( quotient_of @ P2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_times_code
% 5.64/6.00 thf(fact_9431_rat__minus__code,axiom,
% 5.64/6.00 ! [P2: rat,Q3: rat] :
% 5.64/6.00 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q3 ) )
% 5.64/6.00 = ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [A3: int,C2: int] :
% 5.64/6.00 ( produc4245557441103728435nt_int
% 5.64/6.00 @ ^ [B3: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B3 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.64/6.00 @ ( quotient_of @ Q3 ) )
% 5.64/6.00 @ ( quotient_of @ P2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_minus_code
% 5.64/6.00 thf(fact_9432_Frct__code__post_I5_J,axiom,
% 5.64/6.00 ! [K: num] :
% 5.64/6.00 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.64/6.00 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Frct_code_post(5)
% 5.64/6.00 thf(fact_9433_cis__multiple__2pi,axiom,
% 5.64/6.00 ! [N: real] :
% 5.64/6.00 ( ( member_real @ N @ ring_1_Ints_real )
% 5.64/6.00 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.64/6.00 = one_one_complex ) ) ).
% 5.64/6.00
% 5.64/6.00 % cis_multiple_2pi
% 5.64/6.00 thf(fact_9434_VEBT__internal_Oheight_Opelims,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT,Y4: nat] :
% 5.64/6.00 ( ( ( vEBT_VEBT_height @ X2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ X2 )
% 5.64/6.00 => ( ! [A5: $o,B5: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/6.00 => ( ( Y4 = zero_zero_nat )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.64/6.00 => ~ ! [Uu: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.00 => ( ( Y4
% 5.64/6.00 = ( plus_plus_nat @ one_one_nat @ ( lattic8265883725875713057ax_nat @ ( image_VEBT_VEBT_nat @ vEBT_VEBT_height @ ( insert_VEBT_VEBT @ Summary2 @ ( set_VEBT_VEBT2 @ TreeList2 ) ) ) ) ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_VEBT_height_rel @ ( vEBT_Node @ Uu @ Deg2 @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.height.pelims
% 5.64/6.00 thf(fact_9435_xor__Suc__0__eq,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/6.00 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/6.00 @ ( zero_n2687167440665602831ol_nat
% 5.64/6.00 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_Suc_0_eq
% 5.64/6.00 thf(fact_9436_bij__betw__Suc,axiom,
% 5.64/6.00 ! [M7: set_nat,N5: set_nat] :
% 5.64/6.00 ( ( bij_betw_nat_nat @ suc @ M7 @ N5 )
% 5.64/6.00 = ( ( image_nat_nat @ suc @ M7 )
% 5.64/6.00 = N5 ) ) ).
% 5.64/6.00
% 5.64/6.00 % bij_betw_Suc
% 5.64/6.00 thf(fact_9437_xor__nat__numerals_I1_J,axiom,
% 5.64/6.00 ! [Y4: num] :
% 5.64/6.00 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) )
% 5.64/6.00 = ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_nat_numerals(1)
% 5.64/6.00 thf(fact_9438_xor__nat__numerals_I2_J,axiom,
% 5.64/6.00 ! [Y4: num] :
% 5.64/6.00 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y4 ) ) )
% 5.64/6.00 = ( numeral_numeral_nat @ ( bit0 @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_nat_numerals(2)
% 5.64/6.00 thf(fact_9439_xor__nat__numerals_I3_J,axiom,
% 5.64/6.00 ! [X2: num] :
% 5.64/6.00 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.64/6.00 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_nat_numerals(3)
% 5.64/6.00 thf(fact_9440_xor__nat__numerals_I4_J,axiom,
% 5.64/6.00 ! [X2: num] :
% 5.64/6.00 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.64/6.00 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_nat_numerals(4)
% 5.64/6.00 thf(fact_9441_sin__times__pi__eq__0,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( ( sin_real @ ( times_times_real @ X2 @ pi ) )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % sin_times_pi_eq_0
% 5.64/6.00 thf(fact_9442_Frct__code__post_I6_J,axiom,
% 5.64/6.00 ! [K: num,L: num] :
% 5.64/6.00 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.64/6.00 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Frct_code_post(6)
% 5.64/6.00 thf(fact_9443_sin__integer__2pi,axiom,
% 5.64/6.00 ! [N: real] :
% 5.64/6.00 ( ( member_real @ N @ ring_1_Ints_real )
% 5.64/6.00 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.64/6.00 = zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % sin_integer_2pi
% 5.64/6.00 thf(fact_9444_cos__integer__2pi,axiom,
% 5.64/6.00 ! [N: real] :
% 5.64/6.00 ( ( member_real @ N @ ring_1_Ints_real )
% 5.64/6.00 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.64/6.00 = one_one_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % cos_integer_2pi
% 5.64/6.00 thf(fact_9445_xor__nat__unfold,axiom,
% 5.64/6.00 ( bit_se6528837805403552850or_nat
% 5.64/6.00 = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M2 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_nat_unfold
% 5.64/6.00 thf(fact_9446_xor__nat__rec,axiom,
% 5.64/6.00 ( bit_se6528837805403552850or_nat
% 5.64/6.00 = ( ^ [M2: nat,N2: nat] :
% 5.64/6.00 ( plus_plus_nat
% 5.64/6.00 @ ( zero_n2687167440665602831ol_nat
% 5.64/6.00 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 5.64/6.00 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.64/6.00 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_nat_rec
% 5.64/6.00 thf(fact_9447_Suc__0__xor__eq,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/6.00 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/6.00 @ ( zero_n2687167440665602831ol_nat
% 5.64/6.00 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Suc_0_xor_eq
% 5.64/6.00 thf(fact_9448_vebt__maxt_Opelims,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT,Y4: option_nat] :
% 5.64/6.00 ( ( ( vEBT_vebt_maxt @ X2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X2 )
% 5.64/6.00 => ( ! [A5: $o,B5: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/6.00 => ( ( ( B5
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( some_nat @ one_one_nat ) ) )
% 5.64/6.00 & ( ~ B5
% 5.64/6.00 => ( ( A5
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/6.00 & ( ~ A5
% 5.64/6.00 => ( Y4 = none_nat ) ) ) ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.64/6.00 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/6.00 => ( ( Y4 = none_nat )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 5.64/6.00 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.64/6.00 => ( ( Y4
% 5.64/6.00 = ( some_nat @ Ma2 ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % vebt_maxt.pelims
% 5.64/6.00 thf(fact_9449_vebt__mint_Opelims,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT,Y4: option_nat] :
% 5.64/6.00 ( ( ( vEBT_vebt_mint @ X2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X2 )
% 5.64/6.00 => ( ! [A5: $o,B5: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.64/6.00 => ( ( ( A5
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( some_nat @ zero_zero_nat ) ) )
% 5.64/6.00 & ( ~ A5
% 5.64/6.00 => ( ( B5
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( some_nat @ one_one_nat ) ) )
% 5.64/6.00 & ( ~ B5
% 5.64/6.00 => ( Y4 = none_nat ) ) ) ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.64/6.00 => ( ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.64/6.00 => ( ( Y4 = none_nat )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) ) ) )
% 5.64/6.00 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.64/6.00 => ( ( Y4
% 5.64/6.00 = ( some_nat @ Mi2 ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % vebt_mint.pelims
% 5.64/6.00 thf(fact_9450_bij__betw__nth__root__unity,axiom,
% 5.64/6.00 ! [C: complex,N: nat] :
% 5.64/6.00 ( ( C != zero_zero_complex )
% 5.64/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.64/6.00 @ ( collect_complex
% 5.64/6.00 @ ^ [Z4: complex] :
% 5.64/6.00 ( ( power_power_complex @ Z4 @ N )
% 5.64/6.00 = one_one_complex ) )
% 5.64/6.00 @ ( collect_complex
% 5.64/6.00 @ ^ [Z4: complex] :
% 5.64/6.00 ( ( power_power_complex @ Z4 @ N )
% 5.64/6.00 = C ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bij_betw_nth_root_unity
% 5.64/6.00 thf(fact_9451_xor__negative__int__iff,axiom,
% 5.64/6.00 ! [K: int,L: int] :
% 5.64/6.00 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.64/6.00 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.64/6.00 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_negative_int_iff
% 5.64/6.00 thf(fact_9452_real__root__Suc__0,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.64/6.00 = X2 ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_Suc_0
% 5.64/6.00 thf(fact_9453_real__root__eq__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ( root @ N @ X2 )
% 5.64/6.00 = ( root @ N @ Y4 ) )
% 5.64/6.00 = ( X2 = Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_eq_iff
% 5.64/6.00 thf(fact_9454_real__root__eq__0__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ( root @ N @ X2 )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 = ( X2 = zero_zero_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_eq_0_iff
% 5.64/6.00 thf(fact_9455_real__root__less__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y4 ) )
% 5.64/6.00 = ( ord_less_real @ X2 @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_less_iff
% 5.64/6.00 thf(fact_9456_real__root__le__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y4 ) )
% 5.64/6.00 = ( ord_less_eq_real @ X2 @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_le_iff
% 5.64/6.00 thf(fact_9457_real__root__eq__1__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ( root @ N @ X2 )
% 5.64/6.00 = one_one_real )
% 5.64/6.00 = ( X2 = one_one_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_eq_1_iff
% 5.64/6.00 thf(fact_9458_real__root__one,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( root @ N @ one_one_real )
% 5.64/6.00 = one_one_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_one
% 5.64/6.00 thf(fact_9459_real__root__lt__0__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.64/6.00 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_lt_0_iff
% 5.64/6.00 thf(fact_9460_real__root__gt__0__iff,axiom,
% 5.64/6.00 ! [N: nat,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y4 ) )
% 5.64/6.00 = ( ord_less_real @ zero_zero_real @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_gt_0_iff
% 5.64/6.00 thf(fact_9461_real__root__le__0__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ zero_zero_real )
% 5.64/6.00 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_le_0_iff
% 5.64/6.00 thf(fact_9462_real__root__ge__0__iff,axiom,
% 5.64/6.00 ! [N: nat,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y4 ) )
% 5.64/6.00 = ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_ge_0_iff
% 5.64/6.00 thf(fact_9463_real__root__lt__1__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.64/6.00 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_lt_1_iff
% 5.64/6.00 thf(fact_9464_real__root__gt__1__iff,axiom,
% 5.64/6.00 ! [N: nat,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y4 ) )
% 5.64/6.00 = ( ord_less_real @ one_one_real @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_gt_1_iff
% 5.64/6.00 thf(fact_9465_real__root__ge__1__iff,axiom,
% 5.64/6.00 ! [N: nat,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y4 ) )
% 5.64/6.00 = ( ord_less_eq_real @ one_one_real @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_ge_1_iff
% 5.64/6.00 thf(fact_9466_real__root__le__1__iff,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ ( root @ N @ X2 ) @ one_one_real )
% 5.64/6.00 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_le_1_iff
% 5.64/6.00 thf(fact_9467_real__root__pow__pos2,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.64/6.00 = X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_pow_pos2
% 5.64/6.00 thf(fact_9468_real__root__divide,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( root @ N @ ( divide_divide_real @ X2 @ Y4 ) )
% 5.64/6.00 = ( divide_divide_real @ ( root @ N @ X2 ) @ ( root @ N @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_divide
% 5.64/6.00 thf(fact_9469_real__root__mult__exp,axiom,
% 5.64/6.00 ! [M: nat,N: nat,X2: real] :
% 5.64/6.00 ( ( root @ ( times_times_nat @ M @ N ) @ X2 )
% 5.64/6.00 = ( root @ M @ ( root @ N @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_mult_exp
% 5.64/6.00 thf(fact_9470_real__root__mult,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( root @ N @ ( times_times_real @ X2 @ Y4 ) )
% 5.64/6.00 = ( times_times_real @ ( root @ N @ X2 ) @ ( root @ N @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_mult
% 5.64/6.00 thf(fact_9471_real__root__less__mono,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ X2 @ Y4 )
% 5.64/6.00 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_less_mono
% 5.64/6.00 thf(fact_9472_real__root__le__mono,axiom,
% 5.64/6.00 ! [N: nat,X2: real,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ X2 @ Y4 )
% 5.64/6.00 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_le_mono
% 5.64/6.00 thf(fact_9473_real__root__power,axiom,
% 5.64/6.00 ! [N: nat,X2: real,K: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( root @ N @ ( power_power_real @ X2 @ K ) )
% 5.64/6.00 = ( power_power_real @ ( root @ N @ X2 ) @ K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_power
% 5.64/6.00 thf(fact_9474_real__root__abs,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( root @ N @ ( abs_abs_real @ X2 ) )
% 5.64/6.00 = ( abs_abs_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_abs
% 5.64/6.00 thf(fact_9475_sgn__root,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( sgn_sgn_real @ ( root @ N @ X2 ) )
% 5.64/6.00 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_root
% 5.64/6.00 thf(fact_9476_real__root__gt__zero,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_gt_zero
% 5.64/6.00 thf(fact_9477_real__root__strict__decreasing,axiom,
% 5.64/6.00 ! [N: nat,N5: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_nat @ N @ N5 )
% 5.64/6.00 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/6.00 => ( ord_less_real @ ( root @ N5 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_strict_decreasing
% 5.64/6.00 thf(fact_9478_sqrt__def,axiom,
% 5.64/6.00 ( sqrt
% 5.64/6.00 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sqrt_def
% 5.64/6.00 thf(fact_9479_root__abs__power,axiom,
% 5.64/6.00 ! [N: nat,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y4 @ N ) ) )
% 5.64/6.00 = ( abs_abs_real @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % root_abs_power
% 5.64/6.00 thf(fact_9480_real__root__pos__pos,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_pos_pos
% 5.64/6.00 thf(fact_9481_real__root__strict__increasing,axiom,
% 5.64/6.00 ! [N: nat,N5: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_nat @ N @ N5 )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.00 => ( ord_less_real @ ( root @ N @ X2 ) @ ( root @ N5 @ X2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_strict_increasing
% 5.64/6.00 thf(fact_9482_real__root__decreasing,axiom,
% 5.64/6.00 ! [N: nat,N5: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/6.00 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.64/6.00 => ( ord_less_eq_real @ ( root @ N5 @ X2 ) @ ( root @ N @ X2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_decreasing
% 5.64/6.00 thf(fact_9483_real__root__pow__pos,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.64/6.00 = X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_pow_pos
% 5.64/6.00 thf(fact_9484_real__root__power__cancel,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.64/6.00 = X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_power_cancel
% 5.64/6.00 thf(fact_9485_real__root__pos__unique,axiom,
% 5.64/6.00 ! [N: nat,Y4: real,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.64/6.00 => ( ( ( power_power_real @ Y4 @ N )
% 5.64/6.00 = X2 )
% 5.64/6.00 => ( ( root @ N @ X2 )
% 5.64/6.00 = Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_pos_unique
% 5.64/6.00 thf(fact_9486_odd__real__root__power__cancel,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.00 => ( ( root @ N @ ( power_power_real @ X2 @ N ) )
% 5.64/6.00 = X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % odd_real_root_power_cancel
% 5.64/6.00 thf(fact_9487_odd__real__root__unique,axiom,
% 5.64/6.00 ! [N: nat,Y4: real,X2: real] :
% 5.64/6.00 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.00 => ( ( ( power_power_real @ Y4 @ N )
% 5.64/6.00 = X2 )
% 5.64/6.00 => ( ( root @ N @ X2 )
% 5.64/6.00 = Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % odd_real_root_unique
% 5.64/6.00 thf(fact_9488_odd__real__root__pow,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.00 => ( ( power_power_real @ ( root @ N @ X2 ) @ N )
% 5.64/6.00 = X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % odd_real_root_pow
% 5.64/6.00 thf(fact_9489_real__root__increasing,axiom,
% 5.64/6.00 ! [N: nat,N5: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.64/6.00 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.64/6.00 => ( ord_less_eq_real @ ( root @ N @ X2 ) @ ( root @ N5 @ X2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_root_increasing
% 5.64/6.00 thf(fact_9490_sgn__power__root,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X2 ) ) @ N ) )
% 5.64/6.00 = X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_power_root
% 5.64/6.00 thf(fact_9491_root__sgn__power,axiom,
% 5.64/6.00 ! [N: nat,Y4: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) ) )
% 5.64/6.00 = Y4 ) ) ).
% 5.64/6.00
% 5.64/6.00 % root_sgn_power
% 5.64/6.00 thf(fact_9492_log__root,axiom,
% 5.64/6.00 ! [N: nat,A: real,B: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.64/6.00 => ( ( log @ B @ ( root @ N @ A ) )
% 5.64/6.00 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % log_root
% 5.64/6.00 thf(fact_9493_log__base__root,axiom,
% 5.64/6.00 ! [N: nat,B: real,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/6.00 => ( ( log @ ( root @ N @ B ) @ X2 )
% 5.64/6.00 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % log_base_root
% 5.64/6.00 thf(fact_9494_ln__root,axiom,
% 5.64/6.00 ! [N: nat,B: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.64/6.00 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.64/6.00 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % ln_root
% 5.64/6.00 thf(fact_9495_XOR__upper,axiom,
% 5.64/6.00 ! [X2: int,N: nat,Y4: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.64/6.00 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/6.00 => ( ( ord_less_int @ Y4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.64/6.00 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y4 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % XOR_upper
% 5.64/6.00 thf(fact_9496_split__root,axiom,
% 5.64/6.00 ! [P: real > $o,N: nat,X2: real] :
% 5.64/6.00 ( ( P @ ( root @ N @ X2 ) )
% 5.64/6.00 = ( ( ( N = zero_zero_nat )
% 5.64/6.00 => ( P @ zero_zero_real ) )
% 5.64/6.00 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ! [Y: real] :
% 5.64/6.00 ( ( ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.64/6.00 = X2 )
% 5.64/6.00 => ( P @ Y ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % split_root
% 5.64/6.00 thf(fact_9497_root__powr__inverse,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( ( root @ N @ X2 )
% 5.64/6.00 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % root_powr_inverse
% 5.64/6.00 thf(fact_9498_xor__int__rec,axiom,
% 5.64/6.00 ( bit_se6526347334894502574or_int
% 5.64/6.00 = ( ^ [K2: int,L2: int] :
% 5.64/6.00 ( plus_plus_int
% 5.64/6.00 @ ( zero_n2684676970156552555ol_int
% 5.64/6.00 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 5.64/6.00 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.64/6.00 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_int_rec
% 5.64/6.00 thf(fact_9499_xor__int__unfold,axiom,
% 5.64/6.00 ( bit_se6526347334894502574or_int
% 5.64/6.00 = ( ^ [K2: int,L2: int] :
% 5.64/6.00 ( if_int
% 5.64/6.00 @ ( K2
% 5.64/6.00 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/6.00 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.64/6.00 @ ( if_int
% 5.64/6.00 @ ( L2
% 5.64/6.00 = ( uminus_uminus_int @ one_one_int ) )
% 5.64/6.00 @ ( bit_ri7919022796975470100ot_int @ K2 )
% 5.64/6.00 @ ( if_int @ ( K2 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_int_unfold
% 5.64/6.00 thf(fact_9500_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT,Y4: $o] :
% 5.64/6.00 ( ( ( vEBT_VEBT_minNull @ X2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.64/6.00 => ( ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ $false @ $false ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.64/6.00 => ( ! [Uv: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ $true @ Uv ) )
% 5.64/6.00 => ( ~ Y4
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) ) )
% 5.64/6.00 => ( ! [Uu: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ Uu @ $true ) )
% 5.64/6.00 => ( ~ Y4
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) ) )
% 5.64/6.00 => ( ! [Uw: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) ) ) )
% 5.64/6.00 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.64/6.00 => ( ~ Y4
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.minNull.pelims(1)
% 5.64/6.00 thf(fact_9501_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT] :
% 5.64/6.00 ( ( vEBT_VEBT_minNull @ X2 )
% 5.64/6.00 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.64/6.00 => ( ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ $false @ $false ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.64/6.00 => ~ ! [Uw: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.minNull.pelims(2)
% 5.64/6.00 thf(fact_9502_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.64/6.00 ! [X2: vEBT_VEBT] :
% 5.64/6.00 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 5.64/6.00 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X2 )
% 5.64/6.00 => ( ! [Uv: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ $true @ Uv ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv ) ) )
% 5.64/6.00 => ( ! [Uu: $o] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Leaf @ Uu @ $true ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu @ $true ) ) )
% 5.64/6.00 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.64/6.00 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.minNull.pelims(3)
% 5.64/6.00 thf(fact_9503_not__negative__int__iff,axiom,
% 5.64/6.00 ! [K: int] :
% 5.64/6.00 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.64/6.00 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.64/6.00
% 5.64/6.00 % not_negative_int_iff
% 5.64/6.00 thf(fact_9504_not__nonnegative__int__iff,axiom,
% 5.64/6.00 ! [K: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.64/6.00 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % not_nonnegative_int_iff
% 5.64/6.00 thf(fact_9505_not__int__div__2,axiom,
% 5.64/6.00 ! [K: int] :
% 5.64/6.00 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/6.00 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % not_int_div_2
% 5.64/6.00 thf(fact_9506_even__not__iff__int,axiom,
% 5.64/6.00 ! [K: int] :
% 5.64/6.00 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.64/6.00 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % even_not_iff_int
% 5.64/6.00 thf(fact_9507_and__not__numerals_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = one_one_int ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(2)
% 5.64/6.00 thf(fact_9508_and__not__numerals_I4_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.64/6.00 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(4)
% 5.64/6.00 thf(fact_9509_or__not__numerals_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(2)
% 5.64/6.00 thf(fact_9510_or__not__numerals_I4_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.64/6.00 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(4)
% 5.64/6.00 thf(fact_9511_and__not__numerals_I5_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(5)
% 5.64/6.00 thf(fact_9512_and__not__numerals_I7_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.64/6.00 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(7)
% 5.64/6.00 thf(fact_9513_or__not__numerals_I3_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/6.00 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(3)
% 5.64/6.00 thf(fact_9514_and__not__numerals_I9_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/6.00 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(9)
% 5.64/6.00 thf(fact_9515_and__not__numerals_I6_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/6.00 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(6)
% 5.64/6.00 thf(fact_9516_or__not__numerals_I6_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/6.00 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(6)
% 5.64/6.00 thf(fact_9517_or__not__numerals_I5_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = ( 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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(5)
% 5.64/6.00 thf(fact_9518_and__not__numerals_I8_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = ( 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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_numerals(8)
% 5.64/6.00 thf(fact_9519_or__not__numerals_I9_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/6.00 = ( 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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(9)
% 5.64/6.00 thf(fact_9520_or__not__numerals_I8_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = ( 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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % or_not_numerals(8)
% 5.64/6.00 thf(fact_9521_not__int__rec,axiom,
% 5.64/6.00 ( bit_ri7919022796975470100ot_int
% 5.64/6.00 = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % not_int_rec
% 5.64/6.00 thf(fact_9522_horner__sum__of__bool__2__less,axiom,
% 5.64/6.00 ! [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 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % horner_sum_of_bool_2_less
% 5.64/6.00 thf(fact_9523_push__bit__negative__int__iff,axiom,
% 5.64/6.00 ! [N: nat,K: int] :
% 5.64/6.00 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.64/6.00 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % push_bit_negative_int_iff
% 5.64/6.00 thf(fact_9524_push__bit__of__Suc__0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/6.00 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % push_bit_of_Suc_0
% 5.64/6.00 thf(fact_9525_set__bit__nat__def,axiom,
% 5.64/6.00 ( bit_se7882103937844011126it_nat
% 5.64/6.00 = ( ^ [M2: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % set_bit_nat_def
% 5.64/6.00 thf(fact_9526_flip__bit__nat__def,axiom,
% 5.64/6.00 ( bit_se2161824704523386999it_nat
% 5.64/6.00 = ( ^ [M2: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % flip_bit_nat_def
% 5.64/6.00 thf(fact_9527_bit__push__bit__iff__int,axiom,
% 5.64/6.00 ! [M: nat,K: int,N: nat] :
% 5.64/6.00 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.64/6.00 = ( ( ord_less_eq_nat @ M @ N )
% 5.64/6.00 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bit_push_bit_iff_int
% 5.64/6.00 thf(fact_9528_bit__push__bit__iff__nat,axiom,
% 5.64/6.00 ! [M: nat,Q3: nat,N: nat] :
% 5.64/6.00 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N )
% 5.64/6.00 = ( ( ord_less_eq_nat @ M @ N )
% 5.64/6.00 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bit_push_bit_iff_nat
% 5.64/6.00 thf(fact_9529_push__bit__int__def,axiom,
% 5.64/6.00 ( bit_se545348938243370406it_int
% 5.64/6.00 = ( ^ [N2: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % push_bit_int_def
% 5.64/6.00 thf(fact_9530_push__bit__nat__def,axiom,
% 5.64/6.00 ( bit_se547839408752420682it_nat
% 5.64/6.00 = ( ^ [N2: nat,M2: nat] : ( times_times_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % push_bit_nat_def
% 5.64/6.00 thf(fact_9531_push__bit__minus__one,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.64/6.00 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % push_bit_minus_one
% 5.64/6.00 thf(fact_9532_Sum__Ico__nat,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( groups3542108847815614940at_nat
% 5.64/6.00 @ ^ [X: nat] : X
% 5.64/6.00 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.64/6.00 = ( 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 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Sum_Ico_nat
% 5.64/6.00 thf(fact_9533_Cauchy__iff2,axiom,
% 5.64/6.00 ( topolo4055970368930404560y_real
% 5.64/6.00 = ( ^ [X5: nat > real] :
% 5.64/6.00 ! [J3: nat] :
% 5.64/6.00 ? [M8: nat] :
% 5.64/6.00 ! [M2: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ M8 @ M2 )
% 5.64/6.00 => ! [N2: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.64/6.00 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X5 @ M2 ) @ ( X5 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Cauchy_iff2
% 5.64/6.00 thf(fact_9534_VEBT_Osize_I3_J,axiom,
% 5.64/6.00 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.64/6.00 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.64/6.00 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT.size(3)
% 5.64/6.00 thf(fact_9535_sum__power2,axiom,
% 5.64/6.00 ! [K: nat] :
% 5.64/6.00 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.64/6.00 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % sum_power2
% 5.64/6.00 thf(fact_9536_image__Suc__atLeastLessThan,axiom,
% 5.64/6.00 ! [I: nat,J: nat] :
% 5.64/6.00 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.64/6.00 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % image_Suc_atLeastLessThan
% 5.64/6.00 thf(fact_9537_atLeastLessThan__singleton,axiom,
% 5.64/6.00 ! [M: nat] :
% 5.64/6.00 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.64/6.00 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeastLessThan_singleton
% 5.64/6.00 thf(fact_9538_ex__nat__less__eq,axiom,
% 5.64/6.00 ! [N: nat,P: nat > $o] :
% 5.64/6.00 ( ( ? [M2: nat] :
% 5.64/6.00 ( ( ord_less_nat @ M2 @ N )
% 5.64/6.00 & ( P @ M2 ) ) )
% 5.64/6.00 = ( ? [X: nat] :
% 5.64/6.00 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.64/6.00 & ( P @ X ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % ex_nat_less_eq
% 5.64/6.00 thf(fact_9539_all__nat__less__eq,axiom,
% 5.64/6.00 ! [N: nat,P: nat > $o] :
% 5.64/6.00 ( ( ! [M2: nat] :
% 5.64/6.00 ( ( ord_less_nat @ M2 @ N )
% 5.64/6.00 => ( P @ M2 ) ) )
% 5.64/6.00 = ( ! [X: nat] :
% 5.64/6.00 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.64/6.00 => ( P @ X ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % all_nat_less_eq
% 5.64/6.00 thf(fact_9540_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.64/6.00 ! [L: nat,U: nat] :
% 5.64/6.00 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.64/6.00 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeastLessThanSuc_atLeastAtMost
% 5.64/6.00 thf(fact_9541_atLeast0__lessThan__Suc,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.64/6.00 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeast0_lessThan_Suc
% 5.64/6.00 thf(fact_9542_atLeastLessThanSuc,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ( ord_less_eq_nat @ M @ N )
% 5.64/6.00 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.64/6.00 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.64/6.00 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.64/6.00 = bot_bot_set_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeastLessThanSuc
% 5.64/6.00 thf(fact_9543_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.64/6.00 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeast0_lessThan_Suc_eq_insert_0
% 5.64/6.00 thf(fact_9544_prod__Suc__fact,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.64/6.00 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % prod_Suc_fact
% 5.64/6.00 thf(fact_9545_prod__Suc__Suc__fact,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.64/6.00 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % prod_Suc_Suc_fact
% 5.64/6.00 thf(fact_9546_atLeastLessThan__nat__numeral,axiom,
% 5.64/6.00 ! [M: nat,K: num] :
% 5.64/6.00 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.64/6.00 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.64/6.00 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.64/6.00 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.64/6.00 = bot_bot_set_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeastLessThan_nat_numeral
% 5.64/6.00 thf(fact_9547_image__minus__const__atLeastLessThan__nat,axiom,
% 5.64/6.00 ! [C: nat,Y4: nat,X2: nat] :
% 5.64/6.00 ( ( ( ord_less_nat @ C @ Y4 )
% 5.64/6.00 => ( ( image_nat_nat
% 5.64/6.00 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.64/6.00 @ ( set_or4665077453230672383an_nat @ X2 @ Y4 ) )
% 5.64/6.00 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y4 @ C ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_nat @ C @ Y4 )
% 5.64/6.00 => ( ( ( ord_less_nat @ X2 @ Y4 )
% 5.64/6.00 => ( ( image_nat_nat
% 5.64/6.00 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.64/6.00 @ ( set_or4665077453230672383an_nat @ X2 @ Y4 ) )
% 5.64/6.00 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.64/6.00 & ( ~ ( ord_less_nat @ X2 @ Y4 )
% 5.64/6.00 => ( ( image_nat_nat
% 5.64/6.00 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.64/6.00 @ ( set_or4665077453230672383an_nat @ X2 @ Y4 ) )
% 5.64/6.00 = bot_bot_set_nat ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % image_minus_const_atLeastLessThan_nat
% 5.64/6.00 thf(fact_9548_atLeast1__lessThan__eq__remove0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.64/6.00 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeast1_lessThan_eq_remove0
% 5.64/6.00 thf(fact_9549_Chebyshev__sum__upper__nat,axiom,
% 5.64/6.00 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.64/6.00 ( ! [I3: nat,J2: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.64/6.00 => ( ( ord_less_nat @ J2 @ N )
% 5.64/6.00 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J2 ) ) ) )
% 5.64/6.00 => ( ! [I3: nat,J2: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ I3 @ J2 )
% 5.64/6.00 => ( ( ord_less_nat @ J2 @ N )
% 5.64/6.00 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I3 ) ) ) )
% 5.64/6.00 => ( ord_less_eq_nat
% 5.64/6.00 @ ( times_times_nat @ N
% 5.64/6.00 @ ( groups3542108847815614940at_nat
% 5.64/6.00 @ ^ [I4: nat] : ( times_times_nat @ ( A @ I4 ) @ ( B @ I4 ) )
% 5.64/6.00 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.64/6.00 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Chebyshev_sum_upper_nat
% 5.64/6.00 thf(fact_9550_VEBT_Osize__gen_I1_J,axiom,
% 5.64/6.00 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.64/6.00 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.64/6.00 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT.size_gen(1)
% 5.64/6.00 thf(fact_9551_VEBT_Osize__gen_I2_J,axiom,
% 5.64/6.00 ! [X21: $o,X222: $o] :
% 5.64/6.00 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.64/6.00 = zero_zero_nat ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT.size_gen(2)
% 5.64/6.00 thf(fact_9552_valid__eq2,axiom,
% 5.64/6.00 ! [T: vEBT_VEBT,D: nat] :
% 5.64/6.00 ( ( vEBT_VEBT_valid @ T @ D )
% 5.64/6.00 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.64/6.00
% 5.64/6.00 % valid_eq2
% 5.64/6.00 thf(fact_9553_valid__eq1,axiom,
% 5.64/6.00 ! [T: vEBT_VEBT,D: nat] :
% 5.64/6.00 ( ( vEBT_invar_vebt @ T @ D )
% 5.64/6.00 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.64/6.00
% 5.64/6.00 % valid_eq1
% 5.64/6.00 thf(fact_9554_valid__eq,axiom,
% 5.64/6.00 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.64/6.00
% 5.64/6.00 % valid_eq
% 5.64/6.00 thf(fact_9555_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.64/6.00 ! [Uu2: $o,Uv2: $o,D: nat] :
% 5.64/6.00 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D )
% 5.64/6.00 = ( D = one_one_nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % VEBT_internal.valid'.simps(1)
% 5.64/6.00 thf(fact_9556_divmod__step__integer__def,axiom,
% 5.64/6.00 ( unique4921790084139445826nteger
% 5.64/6.00 = ( ^ [L2: num] :
% 5.64/6.00 ( produc6916734918728496179nteger
% 5.64/6.00 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divmod_step_integer_def
% 5.64/6.00 thf(fact_9557_csqrt_Osimps_I1_J,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( re @ ( csqrt @ Z ) )
% 5.64/6.00 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt.simps(1)
% 5.64/6.00 thf(fact_9558_card__Collect__less__nat,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) )
% 5.64/6.00 = N ) ).
% 5.64/6.00
% 5.64/6.00 % card_Collect_less_nat
% 5.64/6.00 thf(fact_9559_card__atMost,axiom,
% 5.64/6.00 ! [U: nat] :
% 5.64/6.00 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.64/6.00 = ( suc @ U ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_atMost
% 5.64/6.00 thf(fact_9560_card__Collect__le__nat,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N ) ) )
% 5.64/6.00 = ( suc @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_Collect_le_nat
% 5.64/6.00 thf(fact_9561_card__atLeastAtMost,axiom,
% 5.64/6.00 ! [L: nat,U: nat] :
% 5.64/6.00 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.64/6.00 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_atLeastAtMost
% 5.64/6.00 thf(fact_9562_Re__divide__of__nat,axiom,
% 5.64/6.00 ! [Z: complex,N: nat] :
% 5.64/6.00 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( re @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_divide_of_nat
% 5.64/6.00 thf(fact_9563_Re__divide__of__real,axiom,
% 5.64/6.00 ! [Z: complex,R2: real] :
% 5.64/6.00 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( re @ Z ) @ R2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_divide_of_real
% 5.64/6.00 thf(fact_9564_Re__sgn,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( re @ ( sgn_sgn_complex @ Z ) )
% 5.64/6.00 = ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_sgn
% 5.64/6.00 thf(fact_9565_Re__divide__numeral,axiom,
% 5.64/6.00 ! [Z: complex,W: num] :
% 5.64/6.00 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_divide_numeral
% 5.64/6.00 thf(fact_9566_divmod__integer_H__def,axiom,
% 5.64/6.00 ( unique3479559517661332726nteger
% 5.64/6.00 = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divmod_integer'_def
% 5.64/6.00 thf(fact_9567_times__integer__code_I1_J,axiom,
% 5.64/6.00 ! [K: code_integer] :
% 5.64/6.00 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.64/6.00 = zero_z3403309356797280102nteger ) ).
% 5.64/6.00
% 5.64/6.00 % times_integer_code(1)
% 5.64/6.00 thf(fact_9568_times__integer__code_I2_J,axiom,
% 5.64/6.00 ! [L: code_integer] :
% 5.64/6.00 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 5.64/6.00 = zero_z3403309356797280102nteger ) ).
% 5.64/6.00
% 5.64/6.00 % times_integer_code(2)
% 5.64/6.00 thf(fact_9569_sgn__integer__code,axiom,
% 5.64/6.00 ( sgn_sgn_Code_integer
% 5.64/6.00 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_integer_code
% 5.64/6.00 thf(fact_9570_scaleR__complex_Osimps_I1_J,axiom,
% 5.64/6.00 ! [R2: real,X2: complex] :
% 5.64/6.00 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X2 ) )
% 5.64/6.00 = ( times_times_real @ R2 @ ( re @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % scaleR_complex.simps(1)
% 5.64/6.00 thf(fact_9571_card__less__Suc2,axiom,
% 5.64/6.00 ! [M7: set_nat,I: nat] :
% 5.64/6.00 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.64/6.00 => ( ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [K2: nat] :
% 5.64/6.00 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.64/6.00 & ( ord_less_nat @ K2 @ I ) ) ) )
% 5.64/6.00 = ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [K2: nat] :
% 5.64/6.00 ( ( member_nat @ K2 @ M7 )
% 5.64/6.00 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_less_Suc2
% 5.64/6.00 thf(fact_9572_card__less__Suc,axiom,
% 5.64/6.00 ! [M7: set_nat,I: nat] :
% 5.64/6.00 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.64/6.00 => ( ( suc
% 5.64/6.00 @ ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [K2: nat] :
% 5.64/6.00 ( ( member_nat @ ( suc @ K2 ) @ M7 )
% 5.64/6.00 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 5.64/6.00 = ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [K2: nat] :
% 5.64/6.00 ( ( member_nat @ K2 @ M7 )
% 5.64/6.00 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_less_Suc
% 5.64/6.00 thf(fact_9573_card__less,axiom,
% 5.64/6.00 ! [M7: set_nat,I: nat] :
% 5.64/6.00 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.64/6.00 => ( ( finite_card_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [K2: nat] :
% 5.64/6.00 ( ( member_nat @ K2 @ M7 )
% 5.64/6.00 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 5.64/6.00 != zero_zero_nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_less
% 5.64/6.00 thf(fact_9574_one__natural_Orsp,axiom,
% 5.64/6.00 one_one_nat = one_one_nat ).
% 5.64/6.00
% 5.64/6.00 % one_natural.rsp
% 5.64/6.00 thf(fact_9575_subset__card__intvl__is__intvl,axiom,
% 5.64/6.00 ! [A4: set_nat,K: nat] :
% 5.64/6.00 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) )
% 5.64/6.00 => ( A4
% 5.64/6.00 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % subset_card_intvl_is_intvl
% 5.64/6.00 thf(fact_9576_card__le__Suc__Max,axiom,
% 5.64/6.00 ! [S3: set_nat] :
% 5.64/6.00 ( ( finite_finite_nat @ S3 )
% 5.64/6.00 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_le_Suc_Max
% 5.64/6.00 thf(fact_9577_subset__eq__atLeast0__lessThan__card,axiom,
% 5.64/6.00 ! [N5: set_nat,N: nat] :
% 5.64/6.00 ( ( ord_less_eq_set_nat @ N5 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.64/6.00 => ( ord_less_eq_nat @ ( finite_card_nat @ N5 ) @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % subset_eq_atLeast0_lessThan_card
% 5.64/6.00 thf(fact_9578_card__sum__le__nat__sum,axiom,
% 5.64/6.00 ! [S3: set_nat] :
% 5.64/6.00 ( ord_less_eq_nat
% 5.64/6.00 @ ( groups3542108847815614940at_nat
% 5.64/6.00 @ ^ [X: nat] : X
% 5.64/6.00 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.64/6.00 @ ( groups3542108847815614940at_nat
% 5.64/6.00 @ ^ [X: nat] : X
% 5.64/6.00 @ S3 ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_sum_le_nat_sum
% 5.64/6.00 thf(fact_9579_card__nth__roots,axiom,
% 5.64/6.00 ! [C: complex,N: nat] :
% 5.64/6.00 ( ( C != zero_zero_complex )
% 5.64/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( finite_card_complex
% 5.64/6.00 @ ( collect_complex
% 5.64/6.00 @ ^ [Z4: complex] :
% 5.64/6.00 ( ( power_power_complex @ Z4 @ N )
% 5.64/6.00 = C ) ) )
% 5.64/6.00 = N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_nth_roots
% 5.64/6.00 thf(fact_9580_card__roots__unity__eq,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( finite_card_complex
% 5.64/6.00 @ ( collect_complex
% 5.64/6.00 @ ^ [Z4: complex] :
% 5.64/6.00 ( ( power_power_complex @ Z4 @ N )
% 5.64/6.00 = one_one_complex ) ) )
% 5.64/6.00 = N ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_roots_unity_eq
% 5.64/6.00 thf(fact_9581_cos__n__Re__cis__pow__n,axiom,
% 5.64/6.00 ! [N: nat,A: real] :
% 5.64/6.00 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.64/6.00 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cos_n_Re_cis_pow_n
% 5.64/6.00 thf(fact_9582_csqrt_Ocode,axiom,
% 5.64/6.00 ( csqrt
% 5.64/6.00 = ( ^ [Z4: complex] :
% 5.64/6.00 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/6.00 @ ( times_times_real
% 5.64/6.00 @ ( if_real
% 5.64/6.00 @ ( ( im @ Z4 )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 @ one_one_real
% 5.64/6.00 @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 5.64/6.00 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt.code
% 5.64/6.00 thf(fact_9583_csqrt_Osimps_I2_J,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( im @ ( csqrt @ Z ) )
% 5.64/6.00 = ( times_times_real
% 5.64/6.00 @ ( if_real
% 5.64/6.00 @ ( ( im @ Z )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 @ one_one_real
% 5.64/6.00 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.64/6.00 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt.simps(2)
% 5.64/6.00 thf(fact_9584_integer__of__int__code,axiom,
% 5.64/6.00 ( code_integer_of_int
% 5.64/6.00 = ( ^ [K2: int] :
% 5.64/6.00 ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.64/6.00 @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.64/6.00 @ ( if_Code_integer
% 5.64/6.00 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.64/6.00 = zero_zero_int )
% 5.64/6.00 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.64/6.00 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % integer_of_int_code
% 5.64/6.00 thf(fact_9585_csqrt__of__real__nonpos,axiom,
% 5.64/6.00 ! [X2: complex] :
% 5.64/6.00 ( ( ( im @ X2 )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 => ( ( ord_less_eq_real @ ( re @ X2 ) @ zero_zero_real )
% 5.64/6.00 => ( ( csqrt @ X2 )
% 5.64/6.00 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X2 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt_of_real_nonpos
% 5.64/6.00 thf(fact_9586_Im__i__times,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.64/6.00 = ( re @ Z ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_i_times
% 5.64/6.00 thf(fact_9587_Im__divide__of__real,axiom,
% 5.64/6.00 ! [Z: complex,R2: real] :
% 5.64/6.00 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( real_V4546457046886955230omplex @ R2 ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( im @ Z ) @ R2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_divide_of_real
% 5.64/6.00 thf(fact_9588_Im__sgn,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( im @ ( sgn_sgn_complex @ Z ) )
% 5.64/6.00 = ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_sgn
% 5.64/6.00 thf(fact_9589_Re__i__times,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.64/6.00 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_i_times
% 5.64/6.00 thf(fact_9590_Im__divide__numeral,axiom,
% 5.64/6.00 ! [Z: complex,W: num] :
% 5.64/6.00 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_divide_numeral
% 5.64/6.00 thf(fact_9591_Im__divide__of__nat,axiom,
% 5.64/6.00 ! [Z: complex,N: nat] :
% 5.64/6.00 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( im @ Z ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_divide_of_nat
% 5.64/6.00 thf(fact_9592_csqrt__minus,axiom,
% 5.64/6.00 ! [X2: complex] :
% 5.64/6.00 ( ( ( ord_less_real @ ( im @ X2 ) @ zero_zero_real )
% 5.64/6.00 | ( ( ( im @ X2 )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) ) ) )
% 5.64/6.00 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.64/6.00 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt_minus
% 5.64/6.00 thf(fact_9593_less__integer__code_I1_J,axiom,
% 5.64/6.00 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.64/6.00
% 5.64/6.00 % less_integer_code(1)
% 5.64/6.00 thf(fact_9594_less__integer_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: int,X2: int] :
% 5.64/6.00 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.64/6.00 = ( ord_less_int @ Xa2 @ X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_integer.abs_eq
% 5.64/6.00 thf(fact_9595_divide__integer_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: int,X2: int] :
% 5.64/6.00 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.64/6.00 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divide_integer.abs_eq
% 5.64/6.00 thf(fact_9596_abs__integer__code,axiom,
% 5.64/6.00 ( abs_abs_Code_integer
% 5.64/6.00 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % abs_integer_code
% 5.64/6.00 thf(fact_9597_times__integer_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: int,X2: int] :
% 5.64/6.00 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.64/6.00 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_integer.abs_eq
% 5.64/6.00 thf(fact_9598_scaleR__complex_Osimps_I2_J,axiom,
% 5.64/6.00 ! [R2: real,X2: complex] :
% 5.64/6.00 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X2 ) )
% 5.64/6.00 = ( times_times_real @ R2 @ ( im @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % scaleR_complex.simps(2)
% 5.64/6.00 thf(fact_9599_times__complex_Osimps_I2_J,axiom,
% 5.64/6.00 ! [X2: complex,Y4: complex] :
% 5.64/6.00 ( ( im @ ( times_times_complex @ X2 @ Y4 ) )
% 5.64/6.00 = ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_complex.simps(2)
% 5.64/6.00 thf(fact_9600_times__complex_Osimps_I1_J,axiom,
% 5.64/6.00 ! [X2: complex,Y4: complex] :
% 5.64/6.00 ( ( re @ ( times_times_complex @ X2 @ Y4 ) )
% 5.64/6.00 = ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_complex.simps(1)
% 5.64/6.00 thf(fact_9601_scaleR__complex_Ocode,axiom,
% 5.64/6.00 ( real_V2046097035970521341omplex
% 5.64/6.00 = ( ^ [R5: real,X: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X ) ) @ ( times_times_real @ R5 @ ( im @ X ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % scaleR_complex.code
% 5.64/6.00 thf(fact_9602_csqrt__principal,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.64/6.00 | ( ( ( re @ ( csqrt @ Z ) )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt_principal
% 5.64/6.00 thf(fact_9603_sin__n__Im__cis__pow__n,axiom,
% 5.64/6.00 ! [N: nat,A: real] :
% 5.64/6.00 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.64/6.00 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sin_n_Im_cis_pow_n
% 5.64/6.00 thf(fact_9604_Re__exp,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( re @ ( exp_complex @ Z ) )
% 5.64/6.00 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_exp
% 5.64/6.00 thf(fact_9605_Im__exp,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( im @ ( exp_complex @ Z ) )
% 5.64/6.00 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_exp
% 5.64/6.00 thf(fact_9606_complex__eq,axiom,
% 5.64/6.00 ! [A: complex] :
% 5.64/6.00 ( A
% 5.64/6.00 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_eq
% 5.64/6.00 thf(fact_9607_times__complex_Ocode,axiom,
% 5.64/6.00 ( times_times_complex
% 5.64/6.00 = ( ^ [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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_complex.code
% 5.64/6.00 thf(fact_9608_exp__eq__polar,axiom,
% 5.64/6.00 ( exp_complex
% 5.64/6.00 = ( ^ [Z4: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z4 ) ) ) @ ( cis @ ( im @ Z4 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % exp_eq_polar
% 5.64/6.00 thf(fact_9609_cmod__power2,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/6.00 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cmod_power2
% 5.64/6.00 thf(fact_9610_Im__power2,axiom,
% 5.64/6.00 ! [X2: complex] :
% 5.64/6.00 ( ( im @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X2 ) ) @ ( im @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_power2
% 5.64/6.00 thf(fact_9611_Re__power2,axiom,
% 5.64/6.00 ! [X2: complex] :
% 5.64/6.00 ( ( re @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = ( minus_minus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_power2
% 5.64/6.00 thf(fact_9612_complex__eq__0,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( Z = zero_zero_complex )
% 5.64/6.00 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_eq_0
% 5.64/6.00 thf(fact_9613_norm__complex__def,axiom,
% 5.64/6.00 ( real_V1022390504157884413omplex
% 5.64/6.00 = ( ^ [Z4: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % norm_complex_def
% 5.64/6.00 thf(fact_9614_inverse__complex_Osimps_I1_J,axiom,
% 5.64/6.00 ! [X2: complex] :
% 5.64/6.00 ( ( re @ ( invers8013647133539491842omplex @ X2 ) )
% 5.64/6.00 = ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % inverse_complex.simps(1)
% 5.64/6.00 thf(fact_9615_complex__neq__0,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( Z != zero_zero_complex )
% 5.64/6.00 = ( 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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_neq_0
% 5.64/6.00 thf(fact_9616_Re__divide,axiom,
% 5.64/6.00 ! [X2: complex,Y4: complex] :
% 5.64/6.00 ( ( re @ ( divide1717551699836669952omplex @ X2 @ Y4 ) )
% 5.64/6.00 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_divide
% 5.64/6.00 thf(fact_9617_csqrt__unique,axiom,
% 5.64/6.00 ! [W: complex,Z: complex] :
% 5.64/6.00 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.64/6.00 = Z )
% 5.64/6.00 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.64/6.00 | ( ( ( re @ W )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.64/6.00 => ( ( csqrt @ Z )
% 5.64/6.00 = W ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt_unique
% 5.64/6.00 thf(fact_9618_csqrt__square,axiom,
% 5.64/6.00 ! [B: complex] :
% 5.64/6.00 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.64/6.00 | ( ( ( re @ B )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.64/6.00 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = B ) ) ).
% 5.64/6.00
% 5.64/6.00 % csqrt_square
% 5.64/6.00 thf(fact_9619_inverse__complex_Osimps_I2_J,axiom,
% 5.64/6.00 ! [X2: complex] :
% 5.64/6.00 ( ( im @ ( invers8013647133539491842omplex @ X2 ) )
% 5.64/6.00 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X2 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % inverse_complex.simps(2)
% 5.64/6.00 thf(fact_9620_Im__divide,axiom,
% 5.64/6.00 ! [X2: complex,Y4: complex] :
% 5.64/6.00 ( ( im @ ( divide1717551699836669952omplex @ X2 @ Y4 ) )
% 5.64/6.00 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_divide
% 5.64/6.00 thf(fact_9621_complex__abs__le__norm,axiom,
% 5.64/6.00 ! [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 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_abs_le_norm
% 5.64/6.00 thf(fact_9622_complex__unit__circle,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( Z != zero_zero_complex )
% 5.64/6.00 => ( ( 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 ) ) ) )
% 5.64/6.00 = one_one_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_unit_circle
% 5.64/6.00 thf(fact_9623_inverse__complex_Ocode,axiom,
% 5.64/6.00 ( invers8013647133539491842omplex
% 5.64/6.00 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % inverse_complex.code
% 5.64/6.00 thf(fact_9624_Complex__divide,axiom,
% 5.64/6.00 ( divide1717551699836669952omplex
% 5.64/6.00 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Complex_divide
% 5.64/6.00 thf(fact_9625_Im__Reals__divide,axiom,
% 5.64/6.00 ! [R2: complex,Z: complex] :
% 5.64/6.00 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.64/6.00 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_Reals_divide
% 5.64/6.00 thf(fact_9626_Re__divide__Reals,axiom,
% 5.64/6.00 ! [R2: complex,Z: complex] :
% 5.64/6.00 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( re @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.64/6.00 = ( divide_divide_real @ ( re @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_divide_Reals
% 5.64/6.00 thf(fact_9627_imaginary__eq__real__iff,axiom,
% 5.64/6.00 ! [Y4: complex,X2: complex] :
% 5.64/6.00 ( ( member_complex @ Y4 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( member_complex @ X2 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( ( times_times_complex @ imaginary_unit @ Y4 )
% 5.64/6.00 = X2 )
% 5.64/6.00 = ( ( X2 = zero_zero_complex )
% 5.64/6.00 & ( Y4 = zero_zero_complex ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % imaginary_eq_real_iff
% 5.64/6.00 thf(fact_9628_real__eq__imaginary__iff,axiom,
% 5.64/6.00 ! [Y4: complex,X2: complex] :
% 5.64/6.00 ( ( member_complex @ Y4 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( member_complex @ X2 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( X2
% 5.64/6.00 = ( times_times_complex @ imaginary_unit @ Y4 ) )
% 5.64/6.00 = ( ( X2 = zero_zero_complex )
% 5.64/6.00 & ( Y4 = zero_zero_complex ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % real_eq_imaginary_iff
% 5.64/6.00 thf(fact_9629_Im__divide__Reals,axiom,
% 5.64/6.00 ! [R2: complex,Z: complex] :
% 5.64/6.00 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( im @ ( divide1717551699836669952omplex @ Z @ R2 ) )
% 5.64/6.00 = ( divide_divide_real @ ( im @ Z ) @ ( re @ R2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_divide_Reals
% 5.64/6.00 thf(fact_9630_Re__Reals__divide,axiom,
% 5.64/6.00 ! [R2: complex,Z: complex] :
% 5.64/6.00 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.64/6.00 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.64/6.00 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_Reals_divide
% 5.64/6.00 thf(fact_9631_complex__mult__cnj,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.64/6.00 = ( 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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_mult_cnj
% 5.64/6.00 thf(fact_9632_complex__cnj__mult,axiom,
% 5.64/6.00 ! [X2: complex,Y4: complex] :
% 5.64/6.00 ( ( cnj @ ( times_times_complex @ X2 @ Y4 ) )
% 5.64/6.00 = ( times_times_complex @ ( cnj @ X2 ) @ ( cnj @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_cnj_mult
% 5.64/6.00 thf(fact_9633_complex__cnj__divide,axiom,
% 5.64/6.00 ! [X2: complex,Y4: complex] :
% 5.64/6.00 ( ( cnj @ ( divide1717551699836669952omplex @ X2 @ Y4 ) )
% 5.64/6.00 = ( divide1717551699836669952omplex @ ( cnj @ X2 ) @ ( cnj @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_cnj_divide
% 5.64/6.00 thf(fact_9634_complex__In__mult__cnj__zero,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.64/6.00 = zero_zero_real ) ).
% 5.64/6.00
% 5.64/6.00 % complex_In_mult_cnj_zero
% 5.64/6.00 thf(fact_9635_Re__complex__div__eq__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.64/6.00 = zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_complex_div_eq_0
% 5.64/6.00 thf(fact_9636_Im__complex__div__eq__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.64/6.00 = zero_zero_real )
% 5.64/6.00 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.64/6.00 = zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_complex_div_eq_0
% 5.64/6.00 thf(fact_9637_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.64/6.00 ( real_V1022390504157884413omplex
% 5.64/6.00 = ( ^ [Z4: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z4 @ ( cnj @ Z4 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_mod_sqrt_Re_mult_cnj
% 5.64/6.00 thf(fact_9638_Re__complex__div__gt__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/6.00 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_complex_div_gt_0
% 5.64/6.00 thf(fact_9639_Re__complex__div__lt__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.64/6.00 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_complex_div_lt_0
% 5.64/6.00 thf(fact_9640_Re__complex__div__ge__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/6.00 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_complex_div_ge_0
% 5.64/6.00 thf(fact_9641_Re__complex__div__le__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.64/6.00 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % Re_complex_div_le_0
% 5.64/6.00 thf(fact_9642_Im__complex__div__gt__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/6.00 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_complex_div_gt_0
% 5.64/6.00 thf(fact_9643_Im__complex__div__lt__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.64/6.00 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_complex_div_lt_0
% 5.64/6.00 thf(fact_9644_Im__complex__div__ge__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/6.00 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_complex_div_ge_0
% 5.64/6.00 thf(fact_9645_Im__complex__div__le__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.64/6.00 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % Im_complex_div_le_0
% 5.64/6.00 thf(fact_9646_complex__mod__mult__cnj,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.64/6.00 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_mod_mult_cnj
% 5.64/6.00 thf(fact_9647_complex__div__gt__0,axiom,
% 5.64/6.00 ! [A: complex,B: complex] :
% 5.64/6.00 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/6.00 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.64/6.00 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.64/6.00 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_div_gt_0
% 5.64/6.00 thf(fact_9648_complex__norm__square,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_norm_square
% 5.64/6.00 thf(fact_9649_complex__add__cnj,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.64/6.00 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_add_cnj
% 5.64/6.00 thf(fact_9650_complex__diff__cnj,axiom,
% 5.64/6.00 ! [Z: complex] :
% 5.64/6.00 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.64/6.00 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_diff_cnj
% 5.64/6.00 thf(fact_9651_complex__div__cnj,axiom,
% 5.64/6.00 ( divide1717551699836669952omplex
% 5.64/6.00 = ( ^ [A3: complex,B3: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B3 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % complex_div_cnj
% 5.64/6.00 thf(fact_9652_cnj__add__mult__eq__Re,axiom,
% 5.64/6.00 ! [Z: complex,W: complex] :
% 5.64/6.00 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.64/6.00 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % cnj_add_mult_eq_Re
% 5.64/6.00 thf(fact_9653_int__of__integer__code,axiom,
% 5.64/6.00 ( code_int_of_integer
% 5.64/6.00 = ( ^ [K2: code_integer] :
% 5.64/6.00 ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 5.64/6.00 @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.64/6.00 @ ( produc1553301316500091796er_int
% 5.64/6.00 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.64/6.00 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % int_of_integer_code
% 5.64/6.00 thf(fact_9654_bit__cut__integer__def,axiom,
% 5.64/6.00 ( code_bit_cut_integer
% 5.64/6.00 = ( ^ [K2: code_integer] :
% 5.64/6.00 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.64/6.00 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bit_cut_integer_def
% 5.64/6.00 thf(fact_9655_num__of__integer__code,axiom,
% 5.64/6.00 ( code_num_of_integer
% 5.64/6.00 = ( ^ [K2: code_integer] :
% 5.64/6.00 ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 5.64/6.00 @ ( produc7336495610019696514er_num
% 5.64/6.00 @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 5.64/6.00 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_integer_code
% 5.64/6.00 thf(fact_9656_times__integer_Orep__eq,axiom,
% 5.64/6.00 ! [X2: code_integer,Xa2: code_integer] :
% 5.64/6.00 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X2 @ Xa2 ) )
% 5.64/6.00 = ( times_times_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_integer.rep_eq
% 5.64/6.00 thf(fact_9657_divide__integer_Orep__eq,axiom,
% 5.64/6.00 ! [X2: code_integer,Xa2: code_integer] :
% 5.64/6.00 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa2 ) )
% 5.64/6.00 = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divide_integer.rep_eq
% 5.64/6.00 thf(fact_9658_less__integer_Orep__eq,axiom,
% 5.64/6.00 ( ord_le6747313008572928689nteger
% 5.64/6.00 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_integer.rep_eq
% 5.64/6.00 thf(fact_9659_integer__less__iff,axiom,
% 5.64/6.00 ( ord_le6747313008572928689nteger
% 5.64/6.00 = ( ^ [K2: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % integer_less_iff
% 5.64/6.00 thf(fact_9660_divmod__integer__def,axiom,
% 5.64/6.00 ( code_divmod_integer
% 5.64/6.00 = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L2 ) @ ( modulo364778990260209775nteger @ K2 @ L2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divmod_integer_def
% 5.64/6.00 thf(fact_9661_bit__cut__integer__code,axiom,
% 5.64/6.00 ( code_bit_cut_integer
% 5.64/6.00 = ( ^ [K2: code_integer] :
% 5.64/6.00 ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.64/6.00 @ ( produc9125791028180074456eger_o
% 5.64/6.00 @ ^ [R5: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.64/6.00 @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bit_cut_integer_code
% 5.64/6.00 thf(fact_9662_nat__of__integer__code,axiom,
% 5.64/6.00 ( code_nat_of_integer
% 5.64/6.00 = ( ^ [K2: code_integer] :
% 5.64/6.00 ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.64/6.00 @ ( produc1555791787009142072er_nat
% 5.64/6.00 @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.64/6.00 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat_of_integer_code
% 5.64/6.00 thf(fact_9663_divmod__abs__def,axiom,
% 5.64/6.00 ( code_divmod_abs
% 5.64/6.00 = ( ^ [K2: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divmod_abs_def
% 5.64/6.00 thf(fact_9664_nat__of__integer__code__post_I3_J,axiom,
% 5.64/6.00 ! [K: num] :
% 5.64/6.00 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.64/6.00 = ( numeral_numeral_nat @ K ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat_of_integer_code_post(3)
% 5.64/6.00 thf(fact_9665_nat__of__integer__code__post_I2_J,axiom,
% 5.64/6.00 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.64/6.00 = one_one_nat ) ).
% 5.64/6.00
% 5.64/6.00 % nat_of_integer_code_post(2)
% 5.64/6.00 thf(fact_9666_divmod__integer__code,axiom,
% 5.64/6.00 ( code_divmod_integer
% 5.64/6.00 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.64/6.00 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.64/6.00 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.64/6.00 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.64/6.00 @ ( produc6916734918728496179nteger
% 5.64/6.00 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S6 ) ) )
% 5.64/6.00 @ ( code_divmod_abs @ K2 @ L2 ) ) )
% 5.64/6.00 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.64/6.00 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.64/6.00 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L2 )
% 5.64/6.00 @ ( produc6916734918728496179nteger
% 5.64/6.00 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S6 ) ) )
% 5.64/6.00 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divmod_integer_code
% 5.64/6.00 thf(fact_9667_nat_Odisc__eq__case_I1_J,axiom,
% 5.64/6.00 ! [Nat: nat] :
% 5.64/6.00 ( ( Nat = zero_zero_nat )
% 5.64/6.00 = ( case_nat_o @ $true
% 5.64/6.00 @ ^ [Uu3: nat] : $false
% 5.64/6.00 @ Nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat.disc_eq_case(1)
% 5.64/6.00 thf(fact_9668_nat_Odisc__eq__case_I2_J,axiom,
% 5.64/6.00 ! [Nat: nat] :
% 5.64/6.00 ( ( Nat != zero_zero_nat )
% 5.64/6.00 = ( case_nat_o @ $false
% 5.64/6.00 @ ^ [Uu3: nat] : $true
% 5.64/6.00 @ Nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat.disc_eq_case(2)
% 5.64/6.00 thf(fact_9669_less__eq__nat_Osimps_I2_J,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.64/6.00 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_eq_nat.simps(2)
% 5.64/6.00 thf(fact_9670_max__Suc2,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.64/6.00 = ( case_nat_nat @ ( suc @ N )
% 5.64/6.00 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 5.64/6.00 @ M ) ) ).
% 5.64/6.00
% 5.64/6.00 % max_Suc2
% 5.64/6.00 thf(fact_9671_max__Suc1,axiom,
% 5.64/6.00 ! [N: nat,M: nat] :
% 5.64/6.00 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.64/6.00 = ( case_nat_nat @ ( suc @ N )
% 5.64/6.00 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 5.64/6.00 @ M ) ) ).
% 5.64/6.00
% 5.64/6.00 % max_Suc1
% 5.64/6.00 thf(fact_9672_diff__Suc,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.64/6.00 = ( case_nat_nat @ zero_zero_nat
% 5.64/6.00 @ ^ [K2: nat] : K2
% 5.64/6.00 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % diff_Suc
% 5.64/6.00 thf(fact_9673_pred__def,axiom,
% 5.64/6.00 ( pred
% 5.64/6.00 = ( case_nat_nat @ zero_zero_nat
% 5.64/6.00 @ ^ [X24: nat] : X24 ) ) ).
% 5.64/6.00
% 5.64/6.00 % pred_def
% 5.64/6.00 thf(fact_9674_prod__decode__aux_Osimps,axiom,
% 5.64/6.00 ( nat_prod_decode_aux
% 5.64/6.00 = ( ^ [K2: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K2 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K2 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M2 @ ( suc @ K2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % prod_decode_aux.simps
% 5.64/6.00 thf(fact_9675_prod__decode__aux_Oelims,axiom,
% 5.64/6.00 ! [X2: nat,Xa2: nat,Y4: product_prod_nat_nat] :
% 5.64/6.00 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % prod_decode_aux.elims
% 5.64/6.00 thf(fact_9676_drop__bit__numeral__minus__bit1,axiom,
% 5.64/6.00 ! [L: num,K: num] :
% 5.64/6.00 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.64/6.00 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_numeral_minus_bit1
% 5.64/6.00 thf(fact_9677_Suc__0__div__numeral,axiom,
% 5.64/6.00 ! [K: num] :
% 5.64/6.00 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.64/6.00 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Suc_0_div_numeral
% 5.64/6.00 thf(fact_9678_Suc__0__mod__numeral,axiom,
% 5.64/6.00 ! [K: num] :
% 5.64/6.00 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.64/6.00 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Suc_0_mod_numeral
% 5.64/6.00 thf(fact_9679_drop__bit__negative__int__iff,axiom,
% 5.64/6.00 ! [N: nat,K: int] :
% 5.64/6.00 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.64/6.00 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_negative_int_iff
% 5.64/6.00 thf(fact_9680_fst__divmod__nat,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.64/6.00 = ( divide_divide_nat @ M @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % fst_divmod_nat
% 5.64/6.00 thf(fact_9681_drop__bit__Suc__minus__bit0,axiom,
% 5.64/6.00 ! [N: nat,K: num] :
% 5.64/6.00 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.64/6.00 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_Suc_minus_bit0
% 5.64/6.00 thf(fact_9682_drop__bit__numeral__minus__bit0,axiom,
% 5.64/6.00 ! [L: num,K: num] :
% 5.64/6.00 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.64/6.00 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_numeral_minus_bit0
% 5.64/6.00 thf(fact_9683_drop__bit__Suc__minus__bit1,axiom,
% 5.64/6.00 ! [N: nat,K: num] :
% 5.64/6.00 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.64/6.00 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_Suc_minus_bit1
% 5.64/6.00 thf(fact_9684_drop__bit__int__def,axiom,
% 5.64/6.00 ( bit_se8568078237143864401it_int
% 5.64/6.00 = ( ^ [N2: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_int_def
% 5.64/6.00 thf(fact_9685_fst__divmod__integer,axiom,
% 5.64/6.00 ! [K: code_integer,L: code_integer] :
% 5.64/6.00 ( ( produc8508995932063986495nteger @ ( code_divmod_integer @ K @ L ) )
% 5.64/6.00 = ( divide6298287555418463151nteger @ K @ L ) ) ).
% 5.64/6.00
% 5.64/6.00 % fst_divmod_integer
% 5.64/6.00 thf(fact_9686_drop__bit__of__Suc__0,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.64/6.00 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_of_Suc_0
% 5.64/6.00 thf(fact_9687_fst__divmod__abs,axiom,
% 5.64/6.00 ! [K: code_integer,L: code_integer] :
% 5.64/6.00 ( ( produc8508995932063986495nteger @ ( code_divmod_abs @ K @ L ) )
% 5.64/6.00 = ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % fst_divmod_abs
% 5.64/6.00 thf(fact_9688_quotient__of__denom__pos_H,axiom,
% 5.64/6.00 ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % quotient_of_denom_pos'
% 5.64/6.00 thf(fact_9689_drop__bit__nat__def,axiom,
% 5.64/6.00 ( bit_se8570568707652914677it_nat
% 5.64/6.00 = ( ^ [N2: nat,M2: nat] : ( divide_divide_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % drop_bit_nat_def
% 5.64/6.00 thf(fact_9690_minus__one__mod__numeral,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % minus_one_mod_numeral
% 5.64/6.00 thf(fact_9691_one__mod__minus__numeral,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % one_mod_minus_numeral
% 5.64/6.00 thf(fact_9692_bezw_Osimps,axiom,
% 5.64/6.00 ( bezw
% 5.64/6.00 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezw.simps
% 5.64/6.00 thf(fact_9693_bezw__non__0,axiom,
% 5.64/6.00 ! [Y4: nat,X2: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ Y4 )
% 5.64/6.00 => ( ( bezw @ X2 @ Y4 )
% 5.64/6.00 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X2 @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X2 @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X2 @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y4 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezw_non_0
% 5.64/6.00 thf(fact_9694_bezw_Oelims,axiom,
% 5.64/6.00 ! [X2: nat,Xa2: nat,Y4: product_prod_int_int] :
% 5.64/6.00 ( ( ( bezw @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ( Xa2 = zero_zero_nat )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.64/6.00 & ( ( Xa2 != zero_zero_nat )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezw.elims
% 5.64/6.00 thf(fact_9695_bezw_Opelims,axiom,
% 5.64/6.00 ! [X2: nat,Xa2: nat,Y4: product_prod_int_int] :
% 5.64/6.00 ( ( ( bezw @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.64/6.00 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.64/6.00 & ( ( Xa2 != zero_zero_nat )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) )
% 5.64/6.00 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezw.pelims
% 5.64/6.00 thf(fact_9696_normalize__def,axiom,
% 5.64/6.00 ( normalize
% 5.64/6.00 = ( ^ [P5: product_prod_int_int] :
% 5.64/6.00 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.64/6.00 @ ( if_Pro3027730157355071871nt_int
% 5.64/6.00 @ ( ( product_snd_int_int @ P5 )
% 5.64/6.00 = zero_zero_int )
% 5.64/6.00 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.64/6.00 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % normalize_def
% 5.64/6.00 thf(fact_9697_gcd__pos__int,axiom,
% 5.64/6.00 ! [M: int,N: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.64/6.00 = ( ( M != zero_zero_int )
% 5.64/6.00 | ( N != zero_zero_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_pos_int
% 5.64/6.00 thf(fact_9698_bezout__int,axiom,
% 5.64/6.00 ! [X2: int,Y4: int] :
% 5.64/6.00 ? [U3: int,V2: int] :
% 5.64/6.00 ( ( plus_plus_int @ ( times_times_int @ U3 @ X2 ) @ ( times_times_int @ V2 @ Y4 ) )
% 5.64/6.00 = ( gcd_gcd_int @ X2 @ Y4 ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezout_int
% 5.64/6.00 thf(fact_9699_gcd__mult__distrib__int,axiom,
% 5.64/6.00 ! [K: int,M: int,N: int] :
% 5.64/6.00 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.64/6.00 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_mult_distrib_int
% 5.64/6.00 thf(fact_9700_gcd__le2__int,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_le2_int
% 5.64/6.00 thf(fact_9701_gcd__le1__int,axiom,
% 5.64/6.00 ! [A: int,B: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ A )
% 5.64/6.00 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_le1_int
% 5.64/6.00 thf(fact_9702_gcd__non__0__int,axiom,
% 5.64/6.00 ! [Y4: int,X2: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ Y4 )
% 5.64/6.00 => ( ( gcd_gcd_int @ X2 @ Y4 )
% 5.64/6.00 = ( gcd_gcd_int @ Y4 @ ( modulo_modulo_int @ X2 @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_non_0_int
% 5.64/6.00 thf(fact_9703_nat__descend__induct,axiom,
% 5.64/6.00 ! [N: nat,P: nat > $o,M: nat] :
% 5.64/6.00 ( ! [K3: nat] :
% 5.64/6.00 ( ( ord_less_nat @ N @ K3 )
% 5.64/6.00 => ( P @ K3 ) )
% 5.64/6.00 => ( ! [K3: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ K3 @ N )
% 5.64/6.00 => ( ! [I2: nat] :
% 5.64/6.00 ( ( ord_less_nat @ K3 @ I2 )
% 5.64/6.00 => ( P @ I2 ) )
% 5.64/6.00 => ( P @ K3 ) ) )
% 5.64/6.00 => ( P @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat_descend_induct
% 5.64/6.00 thf(fact_9704_prod__decode__aux_Opelims,axiom,
% 5.64/6.00 ! [X2: nat,Xa2: nat,Y4: product_prod_nat_nat] :
% 5.64/6.00 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.64/6.00 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) )
% 5.64/6.00 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % prod_decode_aux.pelims
% 5.64/6.00 thf(fact_9705_finite__enumerate,axiom,
% 5.64/6.00 ! [S3: set_nat] :
% 5.64/6.00 ( ( finite_finite_nat @ S3 )
% 5.64/6.00 => ? [R3: nat > nat] :
% 5.64/6.00 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.64/6.00 & ! [N7: nat] :
% 5.64/6.00 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S3 ) )
% 5.64/6.00 => ( member_nat @ ( R3 @ N7 ) @ S3 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % finite_enumerate
% 5.64/6.00 thf(fact_9706_divmod__integer__eq__cases,axiom,
% 5.64/6.00 ( code_divmod_integer
% 5.64/6.00 = ( ^ [K2: code_integer,L2: code_integer] :
% 5.64/6.00 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.64/6.00 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.64/6.00 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.64/6.00 @ ( if_Pro6119634080678213985nteger
% 5.64/6.00 @ ( ( sgn_sgn_Code_integer @ K2 )
% 5.64/6.00 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.64/6.00 @ ( code_divmod_abs @ K2 @ L2 )
% 5.64/6.00 @ ( produc6916734918728496179nteger
% 5.64/6.00 @ ^ [R5: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 5.64/6.00 @ ( code_divmod_abs @ K2 @ L2 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divmod_integer_eq_cases
% 5.64/6.00 thf(fact_9707_gcd__1__nat,axiom,
% 5.64/6.00 ! [M: nat] :
% 5.64/6.00 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.64/6.00 = one_one_nat ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_1_nat
% 5.64/6.00 thf(fact_9708_gcd__Suc__0,axiom,
% 5.64/6.00 ! [M: nat] :
% 5.64/6.00 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.64/6.00 = ( suc @ zero_zero_nat ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_Suc_0
% 5.64/6.00 thf(fact_9709_gcd__pos__nat,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.64/6.00 = ( ( M != zero_zero_nat )
% 5.64/6.00 | ( N != zero_zero_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_pos_nat
% 5.64/6.00 thf(fact_9710_gcd__mult__distrib__nat,axiom,
% 5.64/6.00 ! [K: nat,M: nat,N: nat] :
% 5.64/6.00 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.64/6.00 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_mult_distrib_nat
% 5.64/6.00 thf(fact_9711_gcd__le1__nat,axiom,
% 5.64/6.00 ! [A: nat,B: nat] :
% 5.64/6.00 ( ( A != zero_zero_nat )
% 5.64/6.00 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_le1_nat
% 5.64/6.00 thf(fact_9712_gcd__le2__nat,axiom,
% 5.64/6.00 ! [B: nat,A: nat] :
% 5.64/6.00 ( ( B != zero_zero_nat )
% 5.64/6.00 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_le2_nat
% 5.64/6.00 thf(fact_9713_gcd__diff1__nat,axiom,
% 5.64/6.00 ! [N: nat,M: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ N @ M )
% 5.64/6.00 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.64/6.00 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_diff1_nat
% 5.64/6.00 thf(fact_9714_gcd__diff2__nat,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ M @ N )
% 5.64/6.00 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.64/6.00 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_diff2_nat
% 5.64/6.00 thf(fact_9715_bezout__nat,axiom,
% 5.64/6.00 ! [A: nat,B: nat] :
% 5.64/6.00 ( ( A != zero_zero_nat )
% 5.64/6.00 => ? [X4: nat,Y3: nat] :
% 5.64/6.00 ( ( times_times_nat @ A @ X4 )
% 5.64/6.00 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezout_nat
% 5.64/6.00 thf(fact_9716_bezout__gcd__nat_H,axiom,
% 5.64/6.00 ! [B: nat,A: nat] :
% 5.64/6.00 ? [X4: nat,Y3: nat] :
% 5.64/6.00 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X4 ) )
% 5.64/6.00 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X4 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.64/6.00 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.64/6.00 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X4 ) )
% 5.64/6.00 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X4 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.64/6.00 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezout_gcd_nat'
% 5.64/6.00 thf(fact_9717_gcd__is__Max__divisors__nat,axiom,
% 5.64/6.00 ! [N: nat,M: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( gcd_gcd_nat @ M @ N )
% 5.64/6.00 = ( lattic8265883725875713057ax_nat
% 5.64/6.00 @ ( collect_nat
% 5.64/6.00 @ ^ [D2: nat] :
% 5.64/6.00 ( ( dvd_dvd_nat @ D2 @ M )
% 5.64/6.00 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_is_Max_divisors_nat
% 5.64/6.00 thf(fact_9718_bezw__aux,axiom,
% 5.64/6.00 ! [X2: nat,Y4: nat] :
% 5.64/6.00 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X2 @ Y4 ) )
% 5.64/6.00 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X2 @ Y4 ) ) @ ( semiri1314217659103216013at_int @ X2 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X2 @ Y4 ) ) @ ( semiri1314217659103216013at_int @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % bezw_aux
% 5.64/6.00 thf(fact_9719_gcd__nat_Opelims,axiom,
% 5.64/6.00 ! [X2: nat,Xa2: nat,Y4: nat] :
% 5.64/6.00 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.64/6.00 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.64/6.00 => ( Y4 = X2 ) )
% 5.64/6.00 & ( ( Xa2 != zero_zero_nat )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) )
% 5.64/6.00 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % gcd_nat.pelims
% 5.64/6.00 thf(fact_9720_card_Ocomp__fun__commute__on,axiom,
% 5.64/6.00 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.64/6.00 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.64/6.00
% 5.64/6.00 % card.comp_fun_commute_on
% 5.64/6.00 thf(fact_9721_xor__minus__numerals_I2_J,axiom,
% 5.64/6.00 ! [K: int,N: num] :
% 5.64/6.00 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_minus_numerals(2)
% 5.64/6.00 thf(fact_9722_xor__minus__numerals_I1_J,axiom,
% 5.64/6.00 ! [N: num,K: int] :
% 5.64/6.00 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.64/6.00 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_minus_numerals(1)
% 5.64/6.00 thf(fact_9723_sub__BitM__One__eq,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.64/6.00 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sub_BitM_One_eq
% 5.64/6.00 thf(fact_9724_Suc__funpow,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( compow_nat_nat @ N @ suc )
% 5.64/6.00 = ( plus_plus_nat @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % Suc_funpow
% 5.64/6.00 thf(fact_9725_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.64/6.00 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] : ( ord_less_eq_nat @ Y @ X )
% 5.64/6.00 @ ^ [X: nat,Y: nat] : ( ord_less_nat @ Y @ X ) ) ).
% 5.64/6.00
% 5.64/6.00 % max_nat.semilattice_neutr_order_axioms
% 5.64/6.00 thf(fact_9726_times__int_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.64/6.00 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.64/6.00 = ( abs_Integ
% 5.64/6.00 @ ( produc27273713700761075at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) )
% 5.64/6.00 @ Xa2
% 5.64/6.00 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_int.abs_eq
% 5.64/6.00 thf(fact_9727_eq__Abs__Integ,axiom,
% 5.64/6.00 ! [Z: int] :
% 5.64/6.00 ~ ! [X4: nat,Y3: nat] :
% 5.64/6.00 ( Z
% 5.64/6.00 != ( abs_Integ @ ( product_Pair_nat_nat @ X4 @ Y3 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % eq_Abs_Integ
% 5.64/6.00 thf(fact_9728_zero__int__def,axiom,
% 5.64/6.00 ( zero_zero_int
% 5.64/6.00 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % zero_int_def
% 5.64/6.00 thf(fact_9729_int__def,axiom,
% 5.64/6.00 ( semiri1314217659103216013at_int
% 5.64/6.00 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % int_def
% 5.64/6.00 thf(fact_9730_uminus__int_Oabs__eq,axiom,
% 5.64/6.00 ! [X2: product_prod_nat_nat] :
% 5.64/6.00 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 5.64/6.00 = ( abs_Integ
% 5.64/6.00 @ ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X )
% 5.64/6.00 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % uminus_int.abs_eq
% 5.64/6.00 thf(fact_9731_one__int__def,axiom,
% 5.64/6.00 ( one_one_int
% 5.64/6.00 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % one_int_def
% 5.64/6.00 thf(fact_9732_less__int_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.64/6.00 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.64/6.00 = ( produc8739625826339149834_nat_o
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc6081775807080527818_nat_o
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.64/6.00 @ Xa2
% 5.64/6.00 @ X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_int.abs_eq
% 5.64/6.00 thf(fact_9733_less__eq__int_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.64/6.00 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.64/6.00 = ( produc8739625826339149834_nat_o
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc6081775807080527818_nat_o
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) )
% 5.64/6.00 @ Xa2
% 5.64/6.00 @ X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_eq_int.abs_eq
% 5.64/6.00 thf(fact_9734_plus__int_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.64/6.00 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.64/6.00 = ( abs_Integ
% 5.64/6.00 @ ( produc27273713700761075at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) )
% 5.64/6.00 @ Xa2
% 5.64/6.00 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % plus_int.abs_eq
% 5.64/6.00 thf(fact_9735_minus__int_Oabs__eq,axiom,
% 5.64/6.00 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.64/6.00 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.64/6.00 = ( abs_Integ
% 5.64/6.00 @ ( produc27273713700761075at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) )
% 5.64/6.00 @ Xa2
% 5.64/6.00 @ X2 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % minus_int.abs_eq
% 5.64/6.00 thf(fact_9736_num__of__nat_Osimps_I2_J,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( num_of_nat @ ( suc @ N ) )
% 5.64/6.00 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( num_of_nat @ ( suc @ N ) )
% 5.64/6.00 = one ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_nat.simps(2)
% 5.64/6.00 thf(fact_9737_num__of__nat__numeral__eq,axiom,
% 5.64/6.00 ! [Q3: num] :
% 5.64/6.00 ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 5.64/6.00 = Q3 ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_nat_numeral_eq
% 5.64/6.00 thf(fact_9738_num__of__nat_Osimps_I1_J,axiom,
% 5.64/6.00 ( ( num_of_nat @ zero_zero_nat )
% 5.64/6.00 = one ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_nat.simps(1)
% 5.64/6.00 thf(fact_9739_numeral__num__of__nat,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.64/6.00 = N ) ) ).
% 5.64/6.00
% 5.64/6.00 % numeral_num_of_nat
% 5.64/6.00 thf(fact_9740_num__of__nat__One,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.64/6.00 => ( ( num_of_nat @ N )
% 5.64/6.00 = one ) ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_nat_One
% 5.64/6.00 thf(fact_9741_num__of__nat__double,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.64/6.00 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_nat_double
% 5.64/6.00 thf(fact_9742_num__of__nat__plus__distrib,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.64/6.00 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.64/6.00 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % num_of_nat_plus_distrib
% 5.64/6.00 thf(fact_9743_less__eq__int_Orep__eq,axiom,
% 5.64/6.00 ( ord_less_eq_int
% 5.64/6.00 = ( ^ [X: int,Xa4: int] :
% 5.64/6.00 ( produc8739625826339149834_nat_o
% 5.64/6.00 @ ^ [Y: nat,Z4: nat] :
% 5.64/6.00 ( produc6081775807080527818_nat_o
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 5.64/6.00 @ ( rep_Integ @ X )
% 5.64/6.00 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_eq_int.rep_eq
% 5.64/6.00 thf(fact_9744_less__int_Orep__eq,axiom,
% 5.64/6.00 ( ord_less_int
% 5.64/6.00 = ( ^ [X: int,Xa4: int] :
% 5.64/6.00 ( produc8739625826339149834_nat_o
% 5.64/6.00 @ ^ [Y: nat,Z4: nat] :
% 5.64/6.00 ( produc6081775807080527818_nat_o
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y @ V4 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 5.64/6.00 @ ( rep_Integ @ X )
% 5.64/6.00 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_int.rep_eq
% 5.64/6.00 thf(fact_9745_uminus__int__def,axiom,
% 5.64/6.00 ( uminus_uminus_int
% 5.64/6.00 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.64/6.00 @ ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % uminus_int_def
% 5.64/6.00 thf(fact_9746_pow_Osimps_I3_J,axiom,
% 5.64/6.00 ! [X2: num,Y4: num] :
% 5.64/6.00 ( ( pow @ X2 @ ( bit1 @ Y4 ) )
% 5.64/6.00 = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y4 ) ) @ X2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % pow.simps(3)
% 5.64/6.00 thf(fact_9747_sqr_Osimps_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( sqr @ ( bit0 @ N ) )
% 5.64/6.00 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sqr.simps(2)
% 5.64/6.00 thf(fact_9748_sqr_Osimps_I1_J,axiom,
% 5.64/6.00 ( ( sqr @ one )
% 5.64/6.00 = one ) ).
% 5.64/6.00
% 5.64/6.00 % sqr.simps(1)
% 5.64/6.00 thf(fact_9749_sqr__conv__mult,axiom,
% 5.64/6.00 ( sqr
% 5.64/6.00 = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sqr_conv_mult
% 5.64/6.00 thf(fact_9750_pow_Osimps_I2_J,axiom,
% 5.64/6.00 ! [X2: num,Y4: num] :
% 5.64/6.00 ( ( pow @ X2 @ ( bit0 @ Y4 ) )
% 5.64/6.00 = ( sqr @ ( pow @ X2 @ Y4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % pow.simps(2)
% 5.64/6.00 thf(fact_9751_sqr_Osimps_I3_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( sqr @ ( bit1 @ N ) )
% 5.64/6.00 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sqr.simps(3)
% 5.64/6.00 thf(fact_9752_times__int__def,axiom,
% 5.64/6.00 ( times_times_int
% 5.64/6.00 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.64/6.00 @ ( produc27273713700761075at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % times_int_def
% 5.64/6.00 thf(fact_9753_minus__int__def,axiom,
% 5.64/6.00 ( minus_minus_int
% 5.64/6.00 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.64/6.00 @ ( produc27273713700761075at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % minus_int_def
% 5.64/6.00 thf(fact_9754_plus__int__def,axiom,
% 5.64/6.00 ( plus_plus_int
% 5.64/6.00 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.64/6.00 @ ( produc27273713700761075at_nat
% 5.64/6.00 @ ^ [X: nat,Y: nat] :
% 5.64/6.00 ( produc2626176000494625587at_nat
% 5.64/6.00 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % plus_int_def
% 5.64/6.00 thf(fact_9755_integer__of__num__triv_I2_J,axiom,
% 5.64/6.00 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.64/6.00 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % integer_of_num_triv(2)
% 5.64/6.00 thf(fact_9756_rat__floor__lemma,axiom,
% 5.64/6.00 ! [A: int,B: int] :
% 5.64/6.00 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.64/6.00 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % rat_floor_lemma
% 5.64/6.00 thf(fact_9757_mult__rat,axiom,
% 5.64/6.00 ! [A: int,B: int,C: int,D: int] :
% 5.64/6.00 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.64/6.00 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % mult_rat
% 5.64/6.00 thf(fact_9758_divide__rat,axiom,
% 5.64/6.00 ! [A: int,B: int,C: int,D: int] :
% 5.64/6.00 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.64/6.00 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % divide_rat
% 5.64/6.00 thf(fact_9759_floor__Fract,axiom,
% 5.64/6.00 ! [A: int,B: int] :
% 5.64/6.00 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.64/6.00 = ( divide_divide_int @ A @ B ) ) ).
% 5.64/6.00
% 5.64/6.00 % floor_Fract
% 5.64/6.00 thf(fact_9760_less__rat,axiom,
% 5.64/6.00 ! [B: int,D: int,A: int,C: int] :
% 5.64/6.00 ( ( B != zero_zero_int )
% 5.64/6.00 => ( ( D != zero_zero_int )
% 5.64/6.00 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.64/6.00 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_rat
% 5.64/6.00 thf(fact_9761_add__rat,axiom,
% 5.64/6.00 ! [B: int,D: int,A: int,C: int] :
% 5.64/6.00 ( ( B != zero_zero_int )
% 5.64/6.00 => ( ( D != zero_zero_int )
% 5.64/6.00 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.64/6.00 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % add_rat
% 5.64/6.00 thf(fact_9762_le__rat,axiom,
% 5.64/6.00 ! [B: int,D: int,A: int,C: int] :
% 5.64/6.00 ( ( B != zero_zero_int )
% 5.64/6.00 => ( ( D != zero_zero_int )
% 5.64/6.00 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.64/6.00 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % le_rat
% 5.64/6.00 thf(fact_9763_diff__rat,axiom,
% 5.64/6.00 ! [B: int,D: int,A: int,C: int] :
% 5.64/6.00 ( ( B != zero_zero_int )
% 5.64/6.00 => ( ( D != zero_zero_int )
% 5.64/6.00 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.64/6.00 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % diff_rat
% 5.64/6.00 thf(fact_9764_sgn__rat,axiom,
% 5.64/6.00 ! [A: int,B: int] :
% 5.64/6.00 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.64/6.00 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sgn_rat
% 5.64/6.00 thf(fact_9765_Rat__induct__pos,axiom,
% 5.64/6.00 ! [P: rat > $o,Q3: rat] :
% 5.64/6.00 ( ! [A5: int,B5: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.64/6.00 => ( P @ ( fract @ A5 @ B5 ) ) )
% 5.64/6.00 => ( P @ Q3 ) ) ).
% 5.64/6.00
% 5.64/6.00 % Rat_induct_pos
% 5.64/6.00 thf(fact_9766_mult__rat__cancel,axiom,
% 5.64/6.00 ! [C: int,A: int,B: int] :
% 5.64/6.00 ( ( C != zero_zero_int )
% 5.64/6.00 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.64/6.00 = ( fract @ A @ B ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % mult_rat_cancel
% 5.64/6.00 thf(fact_9767_eq__rat_I1_J,axiom,
% 5.64/6.00 ! [B: int,D: int,A: int,C: int] :
% 5.64/6.00 ( ( B != zero_zero_int )
% 5.64/6.00 => ( ( D != zero_zero_int )
% 5.64/6.00 => ( ( ( fract @ A @ B )
% 5.64/6.00 = ( fract @ C @ D ) )
% 5.64/6.00 = ( ( times_times_int @ A @ D )
% 5.64/6.00 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % eq_rat(1)
% 5.64/6.00 thf(fact_9768_Fract__coprime,axiom,
% 5.64/6.00 ! [A: int,B: int] :
% 5.64/6.00 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.64/6.00 = ( fract @ A @ B ) ) ).
% 5.64/6.00
% 5.64/6.00 % Fract_coprime
% 5.64/6.00 thf(fact_9769_Fract__of__int__quotient,axiom,
% 5.64/6.00 ( fract
% 5.64/6.00 = ( ^ [K2: int,L2: int] : ( divide_divide_rat @ ( ring_1_of_int_rat @ K2 ) @ ( ring_1_of_int_rat @ L2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Fract_of_int_quotient
% 5.64/6.00 thf(fact_9770_zero__less__Fract__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.64/6.00 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % zero_less_Fract_iff
% 5.64/6.00 thf(fact_9771_Fract__less__zero__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.64/6.00 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Fract_less_zero_iff
% 5.64/6.00 thf(fact_9772_one__less__Fract__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.64/6.00 = ( ord_less_int @ B @ A ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % one_less_Fract_iff
% 5.64/6.00 thf(fact_9773_Fract__less__one__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.64/6.00 = ( ord_less_int @ A @ B ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Fract_less_one_iff
% 5.64/6.00 thf(fact_9774_integer__of__num__triv_I1_J,axiom,
% 5.64/6.00 ( ( code_integer_of_num @ one )
% 5.64/6.00 = one_one_Code_integer ) ).
% 5.64/6.00
% 5.64/6.00 % integer_of_num_triv(1)
% 5.64/6.00 thf(fact_9775_Fract__le__zero__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.64/6.00 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Fract_le_zero_iff
% 5.64/6.00 thf(fact_9776_zero__le__Fract__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.64/6.00 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % zero_le_Fract_iff
% 5.64/6.00 thf(fact_9777_Fract__le__one__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.64/6.00 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Fract_le_one_iff
% 5.64/6.00 thf(fact_9778_one__le__Fract__iff,axiom,
% 5.64/6.00 ! [B: int,A: int] :
% 5.64/6.00 ( ( ord_less_int @ zero_zero_int @ B )
% 5.64/6.00 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.64/6.00 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % one_le_Fract_iff
% 5.64/6.00 thf(fact_9779_integer__of__num_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.64/6.00 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % integer_of_num(2)
% 5.64/6.00 thf(fact_9780_take__bit__numeral__minus__numeral__int,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = ( case_option_int_num @ zero_zero_int
% 5.64/6.00 @ ^ [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 ) ) )
% 5.64/6.00 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_numeral_minus_numeral_int
% 5.64/6.00 thf(fact_9781_positive__rat,axiom,
% 5.64/6.00 ! [A: int,B: int] :
% 5.64/6.00 ( ( positive @ ( fract @ A @ B ) )
% 5.64/6.00 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % positive_rat
% 5.64/6.00 thf(fact_9782_take__bit__num__simps_I1_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.64/6.00 = none_num ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(1)
% 5.64/6.00 thf(fact_9783_take__bit__num__simps_I2_J,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.64/6.00 = ( some_num @ one ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(2)
% 5.64/6.00 thf(fact_9784_take__bit__num__simps_I5_J,axiom,
% 5.64/6.00 ! [R2: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.64/6.00 = ( some_num @ one ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(5)
% 5.64/6.00 thf(fact_9785_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( bit_take_bit_num @ N @ one )
% 5.64/6.00 = ( case_nat_option_num @ none_num
% 5.64/6.00 @ ^ [N2: nat] : ( some_num @ one )
% 5.64/6.00 @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.64/6.00 thf(fact_9786_Rat_Opositive__mult,axiom,
% 5.64/6.00 ! [X2: rat,Y4: rat] :
% 5.64/6.00 ( ( positive @ X2 )
% 5.64/6.00 => ( ( positive @ Y4 )
% 5.64/6.00 => ( positive @ ( times_times_rat @ X2 @ Y4 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Rat.positive_mult
% 5.64/6.00 thf(fact_9787_less__rat__def,axiom,
% 5.64/6.00 ( ord_less_rat
% 5.64/6.00 = ( ^ [X: rat,Y: rat] : ( positive @ ( minus_minus_rat @ Y @ X ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % less_rat_def
% 5.64/6.00 thf(fact_9788_take__bit__num__def,axiom,
% 5.64/6.00 ( bit_take_bit_num
% 5.64/6.00 = ( ^ [N2: nat,M2: num] :
% 5.64/6.00 ( if_option_num
% 5.64/6.00 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M2 ) )
% 5.64/6.00 = zero_zero_nat )
% 5.64/6.00 @ none_num
% 5.64/6.00 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_def
% 5.64/6.00 thf(fact_9789_and__minus__numerals_I7_J,axiom,
% 5.64/6.00 ! [N: num,M: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.64/6.00 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_minus_numerals(7)
% 5.64/6.00 thf(fact_9790_and__minus__numerals_I3_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.64/6.00 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_minus_numerals(3)
% 5.64/6.00 thf(fact_9791_and__minus__numerals_I8_J,axiom,
% 5.64/6.00 ! [N: num,M: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.64/6.00 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_minus_numerals(8)
% 5.64/6.00 thf(fact_9792_take__bit__num__simps_I4_J,axiom,
% 5.64/6.00 ! [N: nat,M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.64/6.00 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(4)
% 5.64/6.00 thf(fact_9793_take__bit__num__simps_I3_J,axiom,
% 5.64/6.00 ! [N: nat,M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.64/6.00 = ( case_o6005452278849405969um_num @ none_num
% 5.64/6.00 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.64/6.00 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(3)
% 5.64/6.00 thf(fact_9794_take__bit__num__simps_I7_J,axiom,
% 5.64/6.00 ! [R2: num,M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.64/6.00 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(7)
% 5.64/6.00 thf(fact_9795_take__bit__num__simps_I6_J,axiom,
% 5.64/6.00 ! [R2: num,M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.64/6.00 = ( case_o6005452278849405969um_num @ none_num
% 5.64/6.00 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.64/6.00 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % take_bit_num_simps(6)
% 5.64/6.00 thf(fact_9796_and__minus__numerals_I4_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.64/6.00 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_minus_numerals(4)
% 5.64/6.00 thf(fact_9797_and__not__num_Osimps_I8_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/6.00 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.64/6.00 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.64/6.00 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(8)
% 5.64/6.00 thf(fact_9798_and__not__num_Osimps_I1_J,axiom,
% 5.64/6.00 ( ( bit_and_not_num @ one @ one )
% 5.64/6.00 = none_num ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(1)
% 5.64/6.00 thf(fact_9799_and__not__num_Osimps_I4_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.64/6.00 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(4)
% 5.64/6.00 thf(fact_9800_and__not__num_Osimps_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.64/6.00 = ( some_num @ one ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(2)
% 5.64/6.00 thf(fact_9801_and__not__num_Osimps_I3_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.64/6.00 = none_num ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(3)
% 5.64/6.00 thf(fact_9802_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.64/6.00 ! [N: nat,M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.64/6.00 = ( case_nat_option_num @ none_num
% 5.64/6.00 @ ^ [N2: nat] :
% 5.64/6.00 ( case_o6005452278849405969um_num @ none_num
% 5.64/6.00 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.64/6.00 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.64/6.00 @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.64/6.00 thf(fact_9803_and__not__num_Osimps_I7_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.64/6.00 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(7)
% 5.64/6.00 thf(fact_9804_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.64/6.00 ! [N: nat,M: num] :
% 5.64/6.00 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.64/6.00 = ( case_nat_option_num @ none_num
% 5.64/6.00 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.64/6.00 @ N ) ) ).
% 5.64/6.00
% 5.64/6.00 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.64/6.00 thf(fact_9805_and__not__num__eq__None__iff,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( ( bit_and_not_num @ M @ N )
% 5.64/6.00 = none_num )
% 5.64/6.00 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = zero_zero_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num_eq_None_iff
% 5.64/6.00 thf(fact_9806_Bit__Operations_Otake__bit__num__code,axiom,
% 5.64/6.00 ( bit_take_bit_num
% 5.64/6.00 = ( ^ [N2: nat,M2: num] :
% 5.64/6.00 ( produc478579273971653890on_num
% 5.64/6.00 @ ^ [A3: nat,X: num] :
% 5.64/6.00 ( case_nat_option_num @ none_num
% 5.64/6.00 @ ^ [O: nat] :
% 5.64/6.00 ( case_num_option_num @ ( some_num @ one )
% 5.64/6.00 @ ^ [P5: num] :
% 5.64/6.00 ( case_o6005452278849405969um_num @ none_num
% 5.64/6.00 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.64/6.00 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.64/6.00 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.64/6.00 @ X )
% 5.64/6.00 @ A3 )
% 5.64/6.00 @ ( product_Pair_nat_num @ N2 @ M2 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Bit_Operations.take_bit_num_code
% 5.64/6.00 thf(fact_9807_Rat_Opositive_Orep__eq,axiom,
% 5.64/6.00 ( positive
% 5.64/6.00 = ( ^ [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 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Rat.positive.rep_eq
% 5.64/6.00 thf(fact_9808_and__not__num_Oelims,axiom,
% 5.64/6.00 ! [X2: num,Xa2: num,Y4: option_num] :
% 5.64/6.00 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4 != none_num ) ) )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ? [N3: num] :
% 5.64/6.00 ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ one ) ) ) )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ? [N3: num] :
% 5.64/6.00 ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4 != none_num ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.64/6.00 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.64/6.00 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ~ ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.elims
% 5.64/6.00 thf(fact_9809_xor__num_Osimps_I8_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/6.00 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(8)
% 5.64/6.00 thf(fact_9810_xor__num_Osimps_I9_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(9)
% 5.64/6.00 thf(fact_9811_xor__num_Osimps_I5_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(5)
% 5.64/6.00 thf(fact_9812_and__not__num_Osimps_I5_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(5)
% 5.64/6.00 thf(fact_9813_and__not__num_Osimps_I6_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(6)
% 5.64/6.00 thf(fact_9814_and__not__num_Osimps_I9_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_not_num.simps(9)
% 5.64/6.00 thf(fact_9815_xor__num_Osimps_I1_J,axiom,
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.64/6.00 = none_num ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(1)
% 5.64/6.00 thf(fact_9816_xor__num_Oelims,axiom,
% 5.64/6.00 ! [X2: num,Xa2: num,Y4: option_num] :
% 5.64/6.00 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4 != none_num ) ) )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( bit1 @ M4 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( bit0 @ M4 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) )
% 5.64/6.00 => ~ ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.elims
% 5.64/6.00 thf(fact_9817_xor__num_Osimps_I7_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.64/6.00 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(7)
% 5.64/6.00 thf(fact_9818_xor__num_Osimps_I4_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.64/6.00 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(4)
% 5.64/6.00 thf(fact_9819_xor__num_Osimps_I3_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N ) )
% 5.64/6.00 = ( some_num @ ( bit0 @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(3)
% 5.64/6.00 thf(fact_9820_xor__num_Osimps_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N ) )
% 5.64/6.00 = ( some_num @ ( bit1 @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(2)
% 5.64/6.00 thf(fact_9821_xor__num_Osimps_I6_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/6.00 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % xor_num.simps(6)
% 5.64/6.00 thf(fact_9822_and__num_Oelims,axiom,
% 5.64/6.00 ! [X2: num,Xa2: num,Y4: option_num] :
% 5.64/6.00 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ one ) ) ) )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ? [N3: num] :
% 5.64/6.00 ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4 != none_num ) ) )
% 5.64/6.00 => ( ( ( X2 = one )
% 5.64/6.00 => ( ? [N3: num] :
% 5.64/6.00 ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ one ) ) ) )
% 5.64/6.00 => ( ( ? [M4: num] :
% 5.64/6.00 ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4 != none_num ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit0 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ( ( ? [M4: num] :
% 5.64/6.00 ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ( ( Xa2 = one )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( some_num @ one ) ) ) )
% 5.64/6.00 => ( ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit0 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) )
% 5.64/6.00 => ~ ! [M4: num] :
% 5.64/6.00 ( ( X2
% 5.64/6.00 = ( bit1 @ M4 ) )
% 5.64/6.00 => ! [N3: num] :
% 5.64/6.00 ( ( Xa2
% 5.64/6.00 = ( bit1 @ N3 ) )
% 5.64/6.00 => ( Y4
% 5.64/6.00 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.64/6.00 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.64/6.00 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.elims
% 5.64/6.00 thf(fact_9823_and__num_Osimps_I1_J,axiom,
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.64/6.00 = ( some_num @ one ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(1)
% 5.64/6.00 thf(fact_9824_and__num_Osimps_I5_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(5)
% 5.64/6.00 thf(fact_9825_and__num_Osimps_I7_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.64/6.00 = ( some_num @ one ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(7)
% 5.64/6.00 thf(fact_9826_and__num_Osimps_I3_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N ) )
% 5.64/6.00 = ( some_num @ one ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(3)
% 5.64/6.00 thf(fact_9827_and__num_Osimps_I2_J,axiom,
% 5.64/6.00 ! [N: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N ) )
% 5.64/6.00 = none_num ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(2)
% 5.64/6.00 thf(fact_9828_and__num_Osimps_I4_J,axiom,
% 5.64/6.00 ! [M: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.64/6.00 = none_num ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(4)
% 5.64/6.00 thf(fact_9829_and__num_Osimps_I8_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(8)
% 5.64/6.00 thf(fact_9830_and__num_Osimps_I6_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.64/6.00 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(6)
% 5.64/6.00 thf(fact_9831_and__num_Osimps_I9_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.64/6.00 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.64/6.00 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.64/6.00 @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % and_num.simps(9)
% 5.64/6.00 thf(fact_9832_min__Suc__Suc,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.64/6.00 = ( suc @ ( ord_min_nat @ M @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % min_Suc_Suc
% 5.64/6.00 thf(fact_9833_min__0R,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_min_nat @ N @ zero_zero_nat )
% 5.64/6.00 = zero_zero_nat ) ).
% 5.64/6.00
% 5.64/6.00 % min_0R
% 5.64/6.00 thf(fact_9834_min__0L,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_min_nat @ zero_zero_nat @ N )
% 5.64/6.00 = zero_zero_nat ) ).
% 5.64/6.00
% 5.64/6.00 % min_0L
% 5.64/6.00 thf(fact_9835_min__enat__simps_I2_J,axiom,
% 5.64/6.00 ! [Q3: extended_enat] :
% 5.64/6.00 ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.64/6.00 = zero_z5237406670263579293d_enat ) ).
% 5.64/6.00
% 5.64/6.00 % min_enat_simps(2)
% 5.64/6.00 thf(fact_9836_min__enat__simps_I3_J,axiom,
% 5.64/6.00 ! [Q3: extended_enat] :
% 5.64/6.00 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.64/6.00 = zero_z5237406670263579293d_enat ) ).
% 5.64/6.00
% 5.64/6.00 % min_enat_simps(3)
% 5.64/6.00 thf(fact_9837_min__Suc__numeral,axiom,
% 5.64/6.00 ! [N: nat,K: num] :
% 5.64/6.00 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.64/6.00 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % min_Suc_numeral
% 5.64/6.00 thf(fact_9838_min__numeral__Suc,axiom,
% 5.64/6.00 ! [K: num,N: nat] :
% 5.64/6.00 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.64/6.00 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % min_numeral_Suc
% 5.64/6.00 thf(fact_9839_nat__mult__min__left,axiom,
% 5.64/6.00 ! [M: nat,N: nat,Q3: nat] :
% 5.64/6.00 ( ( times_times_nat @ ( ord_min_nat @ M @ N ) @ Q3 )
% 5.64/6.00 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N @ Q3 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat_mult_min_left
% 5.64/6.00 thf(fact_9840_nat__mult__min__right,axiom,
% 5.64/6.00 ! [M: nat,N: nat,Q3: nat] :
% 5.64/6.00 ( ( times_times_nat @ M @ ( ord_min_nat @ N @ Q3 ) )
% 5.64/6.00 = ( ord_min_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat_mult_min_right
% 5.64/6.00 thf(fact_9841_min__diff,axiom,
% 5.64/6.00 ! [M: nat,I: nat,N: nat] :
% 5.64/6.00 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I ) @ ( minus_minus_nat @ N @ I ) )
% 5.64/6.00 = ( minus_minus_nat @ ( ord_min_nat @ M @ N ) @ I ) ) ).
% 5.64/6.00
% 5.64/6.00 % min_diff
% 5.64/6.00 thf(fact_9842_min__Suc2,axiom,
% 5.64/6.00 ! [M: nat,N: nat] :
% 5.64/6.00 ( ( ord_min_nat @ M @ ( suc @ N ) )
% 5.64/6.00 = ( case_nat_nat @ zero_zero_nat
% 5.64/6.00 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ M6 @ N ) )
% 5.64/6.00 @ M ) ) ).
% 5.64/6.00
% 5.64/6.00 % min_Suc2
% 5.64/6.00 thf(fact_9843_min__Suc1,axiom,
% 5.64/6.00 ! [N: nat,M: nat] :
% 5.64/6.00 ( ( ord_min_nat @ ( suc @ N ) @ M )
% 5.64/6.00 = ( case_nat_nat @ zero_zero_nat
% 5.64/6.00 @ ^ [M6: nat] : ( suc @ ( ord_min_nat @ N @ M6 ) )
% 5.64/6.00 @ M ) ) ).
% 5.64/6.00
% 5.64/6.00 % min_Suc1
% 5.64/6.00 thf(fact_9844_inf__nat__def,axiom,
% 5.64/6.00 inf_inf_nat = ord_min_nat ).
% 5.64/6.00
% 5.64/6.00 % inf_nat_def
% 5.64/6.00 thf(fact_9845_inf__enat__def,axiom,
% 5.64/6.00 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.64/6.00
% 5.64/6.00 % inf_enat_def
% 5.64/6.00 thf(fact_9846_sorted__list__of__set__lessThan__Suc,axiom,
% 5.64/6.00 ! [K: nat] :
% 5.64/6.00 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.64/6.00 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sorted_list_of_set_lessThan_Suc
% 5.64/6.00 thf(fact_9847_sorted__list__of__set__atMost__Suc,axiom,
% 5.64/6.00 ! [K: nat] :
% 5.64/6.00 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.64/6.00 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % sorted_list_of_set_atMost_Suc
% 5.64/6.00 thf(fact_9848_upto__aux__rec,axiom,
% 5.64/6.00 ( upto_aux
% 5.64/6.00 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_aux_rec
% 5.64/6.00 thf(fact_9849_range__mod,axiom,
% 5.64/6.00 ! [N: nat] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( image_nat_nat
% 5.64/6.00 @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 5.64/6.00 @ top_top_set_nat )
% 5.64/6.00 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % range_mod
% 5.64/6.00 thf(fact_9850_UNIV__nat__eq,axiom,
% 5.64/6.00 ( top_top_set_nat
% 5.64/6.00 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % UNIV_nat_eq
% 5.64/6.00 thf(fact_9851_upto_Opsimps,axiom,
% 5.64/6.00 ! [I: int,J: int] :
% 5.64/6.00 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.64/6.00 => ( ( ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( upto @ I @ J )
% 5.64/6.00 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( upto @ I @ J )
% 5.64/6.00 = nil_int ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto.psimps
% 5.64/6.00 thf(fact_9852_upto_Opelims,axiom,
% 5.64/6.00 ! [X2: int,Xa2: int,Y4: list_int] :
% 5.64/6.00 ( ( ( upto @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.64/6.00 => ~ ( ( ( ( ord_less_eq_int @ X2 @ Xa2 )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa2 ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ X2 @ Xa2 )
% 5.64/6.00 => ( Y4 = nil_int ) ) )
% 5.64/6.00 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto.pelims
% 5.64/6.00 thf(fact_9853_card__UNIV__unit,axiom,
% 5.64/6.00 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.64/6.00 = one_one_nat ) ).
% 5.64/6.00
% 5.64/6.00 % card_UNIV_unit
% 5.64/6.00 thf(fact_9854_range__mult,axiom,
% 5.64/6.00 ! [A: real] :
% 5.64/6.00 ( ( ( A = zero_zero_real )
% 5.64/6.00 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.64/6.00 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.64/6.00 & ( ( A != zero_zero_real )
% 5.64/6.00 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.64/6.00 = top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % range_mult
% 5.64/6.00 thf(fact_9855_card__UNIV__bool,axiom,
% 5.64/6.00 ( ( finite_card_o @ top_top_set_o )
% 5.64/6.00 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_UNIV_bool
% 5.64/6.00 thf(fact_9856_upto__Nil,axiom,
% 5.64/6.00 ! [I: int,J: int] :
% 5.64/6.00 ( ( ( upto @ I @ J )
% 5.64/6.00 = nil_int )
% 5.64/6.00 = ( ord_less_int @ J @ I ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_Nil
% 5.64/6.00 thf(fact_9857_upto__Nil2,axiom,
% 5.64/6.00 ! [I: int,J: int] :
% 5.64/6.00 ( ( nil_int
% 5.64/6.00 = ( upto @ I @ J ) )
% 5.64/6.00 = ( ord_less_int @ J @ I ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_Nil2
% 5.64/6.00 thf(fact_9858_upto__empty,axiom,
% 5.64/6.00 ! [J: int,I: int] :
% 5.64/6.00 ( ( ord_less_int @ J @ I )
% 5.64/6.00 => ( ( upto @ I @ J )
% 5.64/6.00 = nil_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_empty
% 5.64/6.00 thf(fact_9859_upto__single,axiom,
% 5.64/6.00 ! [I: int] :
% 5.64/6.00 ( ( upto @ I @ I )
% 5.64/6.00 = ( cons_int @ I @ nil_int ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_single
% 5.64/6.00 thf(fact_9860_nth__upto,axiom,
% 5.64/6.00 ! [I: int,K: nat,J: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.64/6.00 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.64/6.00 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % nth_upto
% 5.64/6.00 thf(fact_9861_length__upto,axiom,
% 5.64/6.00 ! [I: int,J: int] :
% 5.64/6.00 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.64/6.00 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % length_upto
% 5.64/6.00 thf(fact_9862_upto__rec__numeral_I1_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 = nil_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_rec_numeral(1)
% 5.64/6.00 thf(fact_9863_upto__rec__numeral_I4_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = ( 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 ) ) ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = nil_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_rec_numeral(4)
% 5.64/6.00 thf(fact_9864_upto__rec__numeral_I3_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 = ( 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 ) ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.64/6.00 = nil_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_rec_numeral(3)
% 5.64/6.00 thf(fact_9865_upto__rec__numeral_I2_J,axiom,
% 5.64/6.00 ! [M: num,N: num] :
% 5.64/6.00 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.64/6.00 = nil_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_rec_numeral(2)
% 5.64/6.00 thf(fact_9866_upto__aux__def,axiom,
% 5.64/6.00 ( upto_aux
% 5.64/6.00 = ( ^ [I4: int,J3: int] : ( append_int @ ( upto @ I4 @ J3 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_aux_def
% 5.64/6.00 thf(fact_9867_upto__code,axiom,
% 5.64/6.00 ( upto
% 5.64/6.00 = ( ^ [I4: int,J3: int] : ( upto_aux @ I4 @ J3 @ nil_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_code
% 5.64/6.00 thf(fact_9868_distinct__upto,axiom,
% 5.64/6.00 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 5.64/6.00
% 5.64/6.00 % distinct_upto
% 5.64/6.00 thf(fact_9869_atLeastAtMost__upto,axiom,
% 5.64/6.00 ( set_or1266510415728281911st_int
% 5.64/6.00 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ J3 ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeastAtMost_upto
% 5.64/6.00 thf(fact_9870_atLeastLessThan__upto,axiom,
% 5.64/6.00 ( set_or4662586982721622107an_int
% 5.64/6.00 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % atLeastLessThan_upto
% 5.64/6.00 thf(fact_9871_upto__split2,axiom,
% 5.64/6.00 ! [I: int,J: int,K: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( ord_less_eq_int @ J @ K )
% 5.64/6.00 => ( ( upto @ I @ K )
% 5.64/6.00 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_split2
% 5.64/6.00 thf(fact_9872_upto__split1,axiom,
% 5.64/6.00 ! [I: int,J: int,K: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( ord_less_eq_int @ J @ K )
% 5.64/6.00 => ( ( upto @ I @ K )
% 5.64/6.00 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_split1
% 5.64/6.00 thf(fact_9873_upto__rec1,axiom,
% 5.64/6.00 ! [I: int,J: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( upto @ I @ J )
% 5.64/6.00 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_rec1
% 5.64/6.00 thf(fact_9874_upto_Osimps,axiom,
% 5.64/6.00 ( upto
% 5.64/6.00 = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto.simps
% 5.64/6.00 thf(fact_9875_upto_Oelims,axiom,
% 5.64/6.00 ! [X2: int,Xa2: int,Y4: list_int] :
% 5.64/6.00 ( ( ( upto @ X2 @ Xa2 )
% 5.64/6.00 = Y4 )
% 5.64/6.00 => ( ( ( ord_less_eq_int @ X2 @ Xa2 )
% 5.64/6.00 => ( Y4
% 5.64/6.00 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa2 ) ) ) )
% 5.64/6.00 & ( ~ ( ord_less_eq_int @ X2 @ Xa2 )
% 5.64/6.00 => ( Y4 = nil_int ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto.elims
% 5.64/6.00 thf(fact_9876_upto__rec2,axiom,
% 5.64/6.00 ! [I: int,J: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( upto @ I @ J )
% 5.64/6.00 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_rec2
% 5.64/6.00 thf(fact_9877_upto__split3,axiom,
% 5.64/6.00 ! [I: int,J: int,K: int] :
% 5.64/6.00 ( ( ord_less_eq_int @ I @ J )
% 5.64/6.00 => ( ( ord_less_eq_int @ J @ K )
% 5.64/6.00 => ( ( upto @ I @ K )
% 5.64/6.00 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % upto_split3
% 5.64/6.00 thf(fact_9878_root__def,axiom,
% 5.64/6.00 ( root
% 5.64/6.00 = ( ^ [N2: nat,X: real] :
% 5.64/6.00 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.64/6.00 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.64/6.00 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) )
% 5.64/6.00 @ X ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % root_def
% 5.64/6.00 thf(fact_9879_card__UNIV__char,axiom,
% 5.64/6.00 ( ( finite_card_char @ top_top_set_char )
% 5.64/6.00 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % card_UNIV_char
% 5.64/6.00 thf(fact_9880_UNIV__char__of__nat,axiom,
% 5.64/6.00 ( top_top_set_char
% 5.64/6.00 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % UNIV_char_of_nat
% 5.64/6.00 thf(fact_9881_char_Osize_I2_J,axiom,
% 5.64/6.00 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.64/6.00 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.64/6.00 = zero_zero_nat ) ).
% 5.64/6.00
% 5.64/6.00 % char.size(2)
% 5.64/6.00 thf(fact_9882_nat__of__char__less__256,axiom,
% 5.64/6.00 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % nat_of_char_less_256
% 5.64/6.00 thf(fact_9883_range__nat__of__char,axiom,
% 5.64/6.00 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.64/6.00 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % range_nat_of_char
% 5.64/6.00 thf(fact_9884_integer__of__char__code,axiom,
% 5.64/6.00 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.64/6.00 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.64/6.00 = ( 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 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % integer_of_char_code
% 5.64/6.00 thf(fact_9885_String_Ochar__of__ascii__of,axiom,
% 5.64/6.00 ! [C: char] :
% 5.64/6.00 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.64/6.00 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % String.char_of_ascii_of
% 5.64/6.00 thf(fact_9886_DERIV__even__real__root,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.00 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_even_real_root
% 5.64/6.00 thf(fact_9887_DERIV__const__ratio__const2,axiom,
% 5.64/6.00 ! [A: real,B: real,F: real > real,K: real] :
% 5.64/6.00 ( ( A != B )
% 5.64/6.00 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.00 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.64/6.00 = K ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_const_ratio_const2
% 5.64/6.00 thf(fact_9888_DERIV__pos__inc__left,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_pos_inc_left
% 5.64/6.00 thf(fact_9889_DERIV__neg__dec__left,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_neg_dec_left
% 5.64/6.00 thf(fact_9890_DERIV__const__ratio__const,axiom,
% 5.64/6.00 ! [A: real,B: real,F: real > real,K: real] :
% 5.64/6.00 ( ( A != B )
% 5.64/6.00 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.00 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.64/6.00 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_const_ratio_const
% 5.64/6.00 thf(fact_9891_DERIV__pos__inc__right,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_pos_inc_right
% 5.64/6.00 thf(fact_9892_DERIV__neg__dec__right,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_neg_dec_right
% 5.64/6.00 thf(fact_9893_DERIV__pos__imp__increasing,axiom,
% 5.64/6.00 ! [A: real,B: real,F: real > real] :
% 5.64/6.00 ( ( ord_less_real @ A @ B )
% 5.64/6.00 => ( ! [X4: real] :
% 5.64/6.00 ( ( ord_less_eq_real @ A @ X4 )
% 5.64/6.00 => ( ( ord_less_eq_real @ X4 @ B )
% 5.64/6.00 => ? [Y5: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.00 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.64/6.00 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_pos_imp_increasing
% 5.64/6.00 thf(fact_9894_DERIV__neg__imp__decreasing,axiom,
% 5.64/6.00 ! [A: real,B: real,F: real > real] :
% 5.64/6.00 ( ( ord_less_real @ A @ B )
% 5.64/6.00 => ( ! [X4: real] :
% 5.64/6.00 ( ( ord_less_eq_real @ A @ X4 )
% 5.64/6.00 => ( ( ord_less_eq_real @ X4 @ B )
% 5.64/6.00 => ? [Y5: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.00 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.64/6.00 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_neg_imp_decreasing
% 5.64/6.00 thf(fact_9895_has__real__derivative__neg__dec__right,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.64/6.00 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S3 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % has_real_derivative_neg_dec_right
% 5.64/6.00 thf(fact_9896_has__real__derivative__pos__inc__right,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S3 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % has_real_derivative_pos_inc_right
% 5.64/6.00 thf(fact_9897_has__real__derivative__pos__inc__left,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S3 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % has_real_derivative_pos_inc_left
% 5.64/6.00 thf(fact_9898_has__real__derivative__neg__dec__left,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.64/6.00 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.64/6.00 => ? [D3: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.64/6.00 & ! [H4: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.64/6.00 => ( ( member_real @ ( minus_minus_real @ X2 @ H4 ) @ S3 )
% 5.64/6.00 => ( ( ord_less_real @ H4 @ D3 )
% 5.64/6.00 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( minus_minus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % has_real_derivative_neg_dec_left
% 5.64/6.00 thf(fact_9899_MVT2,axiom,
% 5.64/6.00 ! [A: real,B: real,F: real > real,F3: real > real] :
% 5.64/6.00 ( ( ord_less_real @ A @ B )
% 5.64/6.00 => ( ! [X4: real] :
% 5.64/6.00 ( ( ord_less_eq_real @ A @ X4 )
% 5.64/6.00 => ( ( ord_less_eq_real @ X4 @ B )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ F @ ( F3 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.00 => ? [Z2: real] :
% 5.64/6.00 ( ( ord_less_real @ A @ Z2 )
% 5.64/6.00 & ( ord_less_real @ Z2 @ B )
% 5.64/6.00 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.64/6.00 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F3 @ Z2 ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % MVT2
% 5.64/6.00 thf(fact_9900_DERIV__local__const,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,D: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.64/6.00 => ( ! [Y3: real] :
% 5.64/6.00 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D )
% 5.64/6.00 => ( ( F @ X2 )
% 5.64/6.00 = ( F @ Y3 ) ) )
% 5.64/6.00 => ( L = zero_zero_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_local_const
% 5.64/6.00 thf(fact_9901_DERIV__ln,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_ln
% 5.64/6.00 thf(fact_9902_DERIV__const__average,axiom,
% 5.64/6.00 ! [A: real,B: real,V: real > real,K: real] :
% 5.64/6.00 ( ( A != B )
% 5.64/6.00 => ( ! [X4: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.00 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.64/6.00 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_const_average
% 5.64/6.00 thf(fact_9903_DERIV__local__min,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,D: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.64/6.00 => ( ! [Y3: real] :
% 5.64/6.00 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D )
% 5.64/6.00 => ( ord_less_eq_real @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 5.64/6.00 => ( L = zero_zero_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_local_min
% 5.64/6.00 thf(fact_9904_DERIV__local__max,axiom,
% 5.64/6.00 ! [F: real > real,L: real,X2: real,D: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.64/6.00 => ( ! [Y3: real] :
% 5.64/6.00 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ Y3 ) ) @ D )
% 5.64/6.00 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X2 ) ) )
% 5.64/6.00 => ( L = zero_zero_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_local_max
% 5.64/6.00 thf(fact_9905_DERIV__ln__divide,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_ln_divide
% 5.64/6.00 thf(fact_9906_DERIV__pow,axiom,
% 5.64/6.00 ! [N: nat,X2: real,S2: set_real] :
% 5.64/6.00 ( has_fi5821293074295781190e_real
% 5.64/6.00 @ ^ [X: real] : ( power_power_real @ X @ N )
% 5.64/6.00 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.64/6.00 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_pow
% 5.64/6.00 thf(fact_9907_DERIV__fun__pow,axiom,
% 5.64/6.00 ! [G: real > real,M: real,X2: real,N: nat] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( has_fi5821293074295781190e_real
% 5.64/6.00 @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N )
% 5.64/6.00 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X2 ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.64/6.00 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_fun_pow
% 5.64/6.00 thf(fact_9908_has__real__derivative__powr,axiom,
% 5.64/6.00 ! [Z: real,R2: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.64/6.00 => ( has_fi5821293074295781190e_real
% 5.64/6.00 @ ^ [Z4: real] : ( powr_real @ Z4 @ R2 )
% 5.64/6.00 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.64/6.00 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % has_real_derivative_powr
% 5.64/6.00 thf(fact_9909_DERIV__log,axiom,
% 5.64/6.00 ! [X2: real,B: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_log
% 5.64/6.00 thf(fact_9910_DERIV__fun__powr,axiom,
% 5.64/6.00 ! [G: real > real,M: real,X2: real,R2: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.64/6.00 => ( has_fi5821293074295781190e_real
% 5.64/6.00 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R2 )
% 5.64/6.00 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X2 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.64/6.00 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_fun_powr
% 5.64/6.00 thf(fact_9911_DERIV__powr,axiom,
% 5.64/6.00 ! [G: real > real,M: real,X2: real,F: real > real,R2: real] :
% 5.64/6.00 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.64/6.00 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.00 => ( has_fi5821293074295781190e_real
% 5.64/6.00 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 5.64/6.00 @ ( times_times_real @ ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G @ X2 ) ) ) )
% 5.64/6.00 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_powr
% 5.64/6.00 thf(fact_9912_DERIV__real__sqrt,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_real_sqrt
% 5.64/6.00 thf(fact_9913_DERIV__arctan,axiom,
% 5.64/6.00 ! [X2: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_arctan
% 5.64/6.00 thf(fact_9914_arsinh__real__has__field__derivative,axiom,
% 5.64/6.00 ! [X2: real,A4: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A4 ) ) ).
% 5.64/6.00
% 5.64/6.00 % arsinh_real_has_field_derivative
% 5.64/6.00 thf(fact_9915_DERIV__real__sqrt__generic,axiom,
% 5.64/6.00 ! [X2: real,D4: real] :
% 5.64/6.00 ( ( X2 != zero_zero_real )
% 5.64/6.00 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( D4
% 5.64/6.00 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/6.00 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/6.00 => ( D4
% 5.64/6.00 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_real_sqrt_generic
% 5.64/6.00 thf(fact_9916_arcosh__real__has__field__derivative,axiom,
% 5.64/6.00 ! [X2: real,A4: set_real] :
% 5.64/6.00 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % arcosh_real_has_field_derivative
% 5.64/6.00 thf(fact_9917_artanh__real__has__field__derivative,axiom,
% 5.64/6.00 ! [X2: real,A4: set_real] :
% 5.64/6.00 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A4 ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % artanh_real_has_field_derivative
% 5.64/6.00 thf(fact_9918_DERIV__real__root,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.00 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_real_root
% 5.64/6.00 thf(fact_9919_DERIV__arccos,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/6.00 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_arccos
% 5.64/6.00 thf(fact_9920_DERIV__arcsin,axiom,
% 5.64/6.00 ! [X2: real] :
% 5.64/6.00 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/6.00 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_arcsin
% 5.64/6.00 thf(fact_9921_Maclaurin__all__le__objl,axiom,
% 5.64/6.00 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.64/6.00 ( ( ( ( Diff @ zero_zero_nat )
% 5.64/6.00 = F )
% 5.64/6.00 & ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.64/6.00 => ? [T4: real] :
% 5.64/6.00 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/6.00 & ( ( F @ X2 )
% 5.64/6.00 = ( plus_plus_real
% 5.64/6.00 @ ( groups6591440286371151544t_real
% 5.64/6.00 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/6.00 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.00 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Maclaurin_all_le_objl
% 5.64/6.00 thf(fact_9922_Maclaurin__all__le,axiom,
% 5.64/6.00 ! [Diff: nat > real > real,F: real > real,X2: real,N: nat] :
% 5.64/6.00 ( ( ( Diff @ zero_zero_nat )
% 5.64/6.00 = F )
% 5.64/6.00 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.00 => ? [T4: real] :
% 5.64/6.00 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/6.00 & ( ( F @ X2 )
% 5.64/6.00 = ( plus_plus_real
% 5.64/6.00 @ ( groups6591440286371151544t_real
% 5.64/6.00 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/6.00 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.00 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % Maclaurin_all_le
% 5.64/6.00 thf(fact_9923_DERIV__odd__real__root,axiom,
% 5.64/6.00 ! [N: nat,X2: real] :
% 5.64/6.00 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.00 => ( ( X2 != zero_zero_real )
% 5.64/6.00 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.64/6.00
% 5.64/6.00 % DERIV_odd_real_root
% 5.64/6.01 thf(fact_9924_Maclaurin,axiom,
% 5.64/6.01 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.64/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.64/6.01 & ( ord_less_real @ T4 @ H2 )
% 5.64/6.01 & ( ( F @ H2 )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Maclaurin
% 5.64/6.01 thf(fact_9925_Maclaurin2,axiom,
% 5.64/6.01 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.64/6.01 => ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ H2 )
% 5.64/6.01 & ( ( F @ H2 )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Maclaurin2
% 5.64/6.01 thf(fact_9926_Maclaurin__minus,axiom,
% 5.64/6.01 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.64/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ H2 @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ zero_zero_real ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_real @ H2 @ T4 )
% 5.64/6.01 & ( ord_less_real @ T4 @ zero_zero_real )
% 5.64/6.01 & ( ( F @ H2 )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ H2 @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Maclaurin_minus
% 5.64/6.01 thf(fact_9927_Maclaurin__all__lt,axiom,
% 5.64/6.01 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.64/6.01 ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( X2 != zero_zero_real )
% 5.64/6.01 => ( ! [M4: nat,X4: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T4 ) )
% 5.64/6.01 & ( ord_less_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/6.01 & ( ( F @ X2 )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Maclaurin_all_lt
% 5.64/6.01 thf(fact_9928_Maclaurin__bi__le,axiom,
% 5.64/6.01 ! [Diff: nat > real > real,F: real > real,N: nat,X2: real] :
% 5.64/6.01 ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ T4 ) @ ( abs_abs_real @ X2 ) )
% 5.64/6.01 & ( ( F @ X2 )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ X2 @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X2 @ N ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Maclaurin_bi_le
% 5.64/6.01 thf(fact_9929_Taylor,axiom,
% 5.64/6.01 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X2: real] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ A @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ B ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ( ( ord_less_eq_real @ A @ C )
% 5.64/6.01 => ( ( ord_less_eq_real @ C @ B )
% 5.64/6.01 => ( ( ord_less_eq_real @ A @ X2 )
% 5.64/6.01 => ( ( ord_less_eq_real @ X2 @ B )
% 5.64/6.01 => ( ( X2 != C )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ( ord_less_real @ X2 @ C )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ T4 )
% 5.64/6.01 & ( ord_less_real @ T4 @ C ) ) )
% 5.64/6.01 & ( ~ ( ord_less_real @ X2 @ C )
% 5.64/6.01 => ( ( ord_less_real @ C @ T4 )
% 5.64/6.01 & ( ord_less_real @ T4 @ X2 ) ) )
% 5.64/6.01 & ( ( F @ X2 )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Taylor
% 5.64/6.01 thf(fact_9930_Taylor__up,axiom,
% 5.64/6.01 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ A @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ B ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ( ( ord_less_eq_real @ A @ C )
% 5.64/6.01 => ( ( ord_less_real @ C @ B )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_real @ C @ T4 )
% 5.64/6.01 & ( ord_less_real @ T4 @ B )
% 5.64/6.01 & ( ( F @ B )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Taylor_up
% 5.64/6.01 thf(fact_9931_Taylor__down,axiom,
% 5.64/6.01 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( ( Diff @ zero_zero_nat )
% 5.64/6.01 = F )
% 5.64/6.01 => ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ A @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ B ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ( ( ord_less_real @ A @ C )
% 5.64/6.01 => ( ( ord_less_eq_real @ C @ B )
% 5.64/6.01 => ? [T4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ T4 )
% 5.64/6.01 & ( ord_less_real @ T4 @ C )
% 5.64/6.01 & ( ( F @ A )
% 5.64/6.01 = ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [M2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M2 @ C ) @ ( semiri2265585572941072030t_real @ M2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M2 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ N ) )
% 5.64/6.01 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T4 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Taylor_down
% 5.64/6.01 thf(fact_9932_Maclaurin__lemma2,axiom,
% 5.64/6.01 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.64/6.01 ( ! [M4: nat,T4: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M4 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.64/6.01 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T4 ) @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) )
% 5.64/6.01 => ( ( N
% 5.64/6.01 = ( suc @ K ) )
% 5.64/6.01 => ! [M5: nat,T7: real] :
% 5.64/6.01 ( ( ( ord_less_nat @ M5 @ N )
% 5.64/6.01 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.64/6.01 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real
% 5.64/6.01 @ ^ [U2: real] :
% 5.64/6.01 ( minus_minus_real @ ( Diff @ M5 @ U2 )
% 5.64/6.01 @ ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M5 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M5 ) ) )
% 5.64/6.01 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M5 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M5 ) ) ) ) ) )
% 5.64/6.01 @ ( minus_minus_real @ ( Diff @ ( suc @ M5 ) @ T7 )
% 5.64/6.01 @ ( plus_plus_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M5 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) )
% 5.64/6.01 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M5 ) ) ) ) ) ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Maclaurin_lemma2
% 5.64/6.01 thf(fact_9933_DERIV__arctan__series,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/6.01 => ( has_fi5821293074295781190e_real
% 5.64/6.01 @ ^ [X9: real] :
% 5.64/6.01 ( suminf_real
% 5.64/6.01 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( power_power_real @ X2 @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_arctan_series
% 5.64/6.01 thf(fact_9934_DERIV__real__root__generic,axiom,
% 5.64/6.01 ! [N: nat,X2: real,D4: real] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( X2 != zero_zero_real )
% 5.64/6.01 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.01 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.64/6.01 => ( D4
% 5.64/6.01 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.64/6.01 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.64/6.01 => ( D4
% 5.64/6.01 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.64/6.01 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.01 => ( D4
% 5.64/6.01 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X2 ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_real_root_generic
% 5.64/6.01 thf(fact_9935_DERIV__power__series_H,axiom,
% 5.64/6.01 ! [R: real,F: nat > real,X0: real] :
% 5.64/6.01 ( ! [X4: real] :
% 5.64/6.01 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.64/6.01 => ( summable_real
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X4 @ N2 ) ) ) )
% 5.64/6.01 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.64/6.01 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.64/6.01 => ( has_fi5821293074295781190e_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( suminf_real
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X @ ( suc @ N2 ) ) ) )
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_power_series'
% 5.64/6.01 thf(fact_9936_DERIV__isconst3,axiom,
% 5.64/6.01 ! [A: real,B: real,X2: real,Y4: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( member_real @ X2 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( ( member_real @ Y4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.64/6.01 => ( ( F @ X2 )
% 5.64/6.01 = ( F @ Y4 ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_isconst3
% 5.64/6.01 thf(fact_9937_DERIV__series_H,axiom,
% 5.64/6.01 ! [F: real > nat > real,F3: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.64/6.01 ( ! [N3: nat] :
% 5.64/6.01 ( has_fi5821293074295781190e_real
% 5.64/6.01 @ ^ [X: real] : ( F @ X @ N3 )
% 5.64/6.01 @ ( F3 @ X0 @ N3 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( summable_real @ ( F @ X4 ) ) )
% 5.64/6.01 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( ( summable_real @ ( F3 @ X0 ) )
% 5.64/6.01 => ( ( summable_real @ L5 )
% 5.64/6.01 => ( ! [N3: nat,X4: real,Y3: real] :
% 5.64/6.01 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X4 @ N3 ) @ ( F @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) ) ) ) )
% 5.64/6.01 => ( has_fi5821293074295781190e_real
% 5.64/6.01 @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 5.64/6.01 @ ( suminf_real @ ( F3 @ X0 ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_series'
% 5.64/6.01 thf(fact_9938_card__greaterThanLessThan,axiom,
% 5.64/6.01 ! [L: nat,U: nat] :
% 5.64/6.01 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.64/6.01 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % card_greaterThanLessThan
% 5.64/6.01 thf(fact_9939_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.64/6.01 ! [L: nat,U: nat] :
% 5.64/6.01 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.64/6.01 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeastSucLessThan_greaterThanLessThan
% 5.64/6.01 thf(fact_9940_LIM__fun__less__zero,axiom,
% 5.64/6.01 ! [F: real > real,L: real,C: real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.64/6.01 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.64/6.01 => ? [R3: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.64/6.01 & ! [X3: real] :
% 5.64/6.01 ( ( ( X3 != C )
% 5.64/6.01 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X3 ) ) @ R3 ) )
% 5.64/6.01 => ( ord_less_real @ ( F @ X3 ) @ zero_zero_real ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIM_fun_less_zero
% 5.64/6.01 thf(fact_9941_LIM__fun__not__zero,axiom,
% 5.64/6.01 ! [F: real > real,L: real,C: real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.64/6.01 => ( ( L != zero_zero_real )
% 5.64/6.01 => ? [R3: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.64/6.01 & ! [X3: real] :
% 5.64/6.01 ( ( ( X3 != C )
% 5.64/6.01 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X3 ) ) @ R3 ) )
% 5.64/6.01 => ( ( F @ X3 )
% 5.64/6.01 != zero_zero_real ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIM_fun_not_zero
% 5.64/6.01 thf(fact_9942_LIM__fun__gt__zero,axiom,
% 5.64/6.01 ! [F: real > real,L: real,C: real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.64/6.01 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.64/6.01 => ? [R3: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.64/6.01 & ! [X3: real] :
% 5.64/6.01 ( ( ( X3 != C )
% 5.64/6.01 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X3 ) ) @ R3 ) )
% 5.64/6.01 => ( ord_less_real @ zero_zero_real @ ( F @ X3 ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIM_fun_gt_zero
% 5.64/6.01 thf(fact_9943_isCont__inverse__function2,axiom,
% 5.64/6.01 ! [A: real,X2: real,B: real,G: real > real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X2 )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ B )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ A @ Z2 )
% 5.64/6.01 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.64/6.01 => ( ( G @ ( F @ Z2 ) )
% 5.64/6.01 = Z2 ) ) )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ A @ Z2 )
% 5.64/6.01 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % isCont_inverse_function2
% 5.64/6.01 thf(fact_9944_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.64/6.01 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.64/6.01 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_list_of_set_greaterThanLessThan
% 5.64/6.01 thf(fact_9945_isCont__arcosh,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.64/6.01
% 5.64/6.01 % isCont_arcosh
% 5.64/6.01 thf(fact_9946_LIM__cos__div__sin,axiom,
% 5.64/6.01 ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIM_cos_div_sin
% 5.64/6.01 thf(fact_9947_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.64/6.01 ! [N: nat,J: nat,I: nat] :
% 5.64/6.01 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.64/6.01 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.64/6.01 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % nth_sorted_list_of_set_greaterThanLessThan
% 5.64/6.01 thf(fact_9948_DERIV__inverse__function,axiom,
% 5.64/6.01 ! [F: real > real,D4: real,G: real > real,X2: real,A: real,B: real] :
% 5.64/6.01 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X2 ) @ top_top_set_real ) )
% 5.64/6.01 => ( ( D4 != zero_zero_real )
% 5.64/6.01 => ( ( ord_less_real @ A @ X2 )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ B )
% 5.64/6.01 => ( ! [Y3: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Y3 )
% 5.64/6.01 => ( ( ord_less_real @ Y3 @ B )
% 5.64/6.01 => ( ( F @ ( G @ Y3 ) )
% 5.64/6.01 = Y3 ) ) )
% 5.64/6.01 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ G )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_inverse_function
% 5.64/6.01 thf(fact_9949_isCont__arccos,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % isCont_arccos
% 5.64/6.01 thf(fact_9950_isCont__arcsin,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % isCont_arcsin
% 5.64/6.01 thf(fact_9951_LIM__less__bound,axiom,
% 5.64/6.01 ! [B: real,X2: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ B @ X2 )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ B @ X2 ) )
% 5.64/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) )
% 5.64/6.01 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ F )
% 5.64/6.01 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIM_less_bound
% 5.64/6.01 thf(fact_9952_isCont__artanh,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % isCont_artanh
% 5.64/6.01 thf(fact_9953_greaterThanLessThan__upto,axiom,
% 5.64/6.01 ( set_or5832277885323065728an_int
% 5.64/6.01 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % greaterThanLessThan_upto
% 5.64/6.01 thf(fact_9954_isCont__inverse__function,axiom,
% 5.64/6.01 ! [D: real,X2: real,G: real > real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ D )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X2 ) ) @ D )
% 5.64/6.01 => ( ( G @ ( F @ Z2 ) )
% 5.64/6.01 = Z2 ) )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X2 ) ) @ D )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X2 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % isCont_inverse_function
% 5.64/6.01 thf(fact_9955_GMVT_H,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F3: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ A @ Z2 )
% 5.64/6.01 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ A @ Z2 )
% 5.64/6.01 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Z2 )
% 5.64/6.01 => ( ( ord_less_real @ Z2 @ B )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ( ! [Z2: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Z2 )
% 5.64/6.01 => ( ( ord_less_real @ Z2 @ B )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ F @ ( F3 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ? [C3: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ C3 )
% 5.64/6.01 & ( ord_less_real @ C3 @ B )
% 5.64/6.01 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.64/6.01 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F3 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % GMVT'
% 5.64/6.01 thf(fact_9956_summable__Leibniz_I3_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ( topolo6980174941875973593q_real @ A )
% 5.64/6.01 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.64/6.01 => ! [N7: nat] :
% 5.64/6.01 ( member_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.64/6.01 @ ( set_or1222579329274155063t_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz(3)
% 5.64/6.01 thf(fact_9957_summable__Leibniz_I2_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ( topolo6980174941875973593q_real @ A )
% 5.64/6.01 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.64/6.01 => ! [N7: nat] :
% 5.64/6.01 ( member_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.64/6.01 @ ( set_or1222579329274155063t_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz(2)
% 5.64/6.01 thf(fact_9958_mult__nat__right__at__top,axiom,
% 5.64/6.01 ! [C: nat] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/6.01 => ( filterlim_nat_nat
% 5.64/6.01 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.64/6.01 @ at_top_nat
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % mult_nat_right_at_top
% 5.64/6.01 thf(fact_9959_mult__nat__left__at__top,axiom,
% 5.64/6.01 ! [C: nat] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.64/6.01 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % mult_nat_left_at_top
% 5.64/6.01 thf(fact_9960_nested__sequence__unique,axiom,
% 5.64/6.01 ! [F: nat > real,G: nat > real] :
% 5.64/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.64/6.01 => ( ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat )
% 5.64/6.01 => ? [L4: real] :
% 5.64/6.01 ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 5.64/6.01 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.64/6.01 & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 5.64/6.01 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % nested_sequence_unique
% 5.64/6.01 thf(fact_9961_LIMSEQ__inverse__zero,axiom,
% 5.64/6.01 ! [X8: nat > real] :
% 5.64/6.01 ( ! [R3: real] :
% 5.64/6.01 ? [N8: nat] :
% 5.64/6.01 ! [N3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.64/6.01 => ( ord_less_real @ R3 @ ( X8 @ N3 ) ) )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_inverse_zero
% 5.64/6.01 thf(fact_9962_lim__inverse__n_H,axiom,
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ).
% 5.64/6.01
% 5.64/6.01 % lim_inverse_n'
% 5.64/6.01 thf(fact_9963_LIMSEQ__root__const,axiom,
% 5.64/6.01 ! [C: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ C )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_root_const
% 5.64/6.01 thf(fact_9964_LIMSEQ__inverse__real__of__nat,axiom,
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_inverse_real_of_nat
% 5.64/6.01 thf(fact_9965_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.64/6.01 ! [R2: real] :
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ R2 )
% 5.64/6.01 @ at_top_nat ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_inverse_real_of_nat_add
% 5.64/6.01 thf(fact_9966_increasing__LIMSEQ,axiom,
% 5.64/6.01 ! [F: nat > real,L: real] :
% 5.64/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 5.64/6.01 => ( ! [E2: real] :
% 5.64/6.01 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.64/6.01 => ? [N7: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 5.64/6.01 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % increasing_LIMSEQ
% 5.64/6.01 thf(fact_9967_LIMSEQ__realpow__zero,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/6.01 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.64/6.01 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_realpow_zero
% 5.64/6.01 thf(fact_9968_LIMSEQ__divide__realpow__zero,axiom,
% 5.64/6.01 ! [X2: real,A: real] :
% 5.64/6.01 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X2 @ N2 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_divide_realpow_zero
% 5.64/6.01 thf(fact_9969_LIMSEQ__abs__realpow__zero,axiom,
% 5.64/6.01 ! [C: real] :
% 5.64/6.01 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.64/6.01 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_abs_realpow_zero
% 5.64/6.01 thf(fact_9970_LIMSEQ__abs__realpow__zero2,axiom,
% 5.64/6.01 ! [C: real] :
% 5.64/6.01 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.64/6.01 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_abs_realpow_zero2
% 5.64/6.01 thf(fact_9971_LIMSEQ__inverse__realpow__zero,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_real @ one_one_real @ X2 )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N2 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_inverse_realpow_zero
% 5.64/6.01 thf(fact_9972_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.64/6.01 ! [R2: real] :
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ R2 )
% 5.64/6.01 @ at_top_nat ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.64/6.01 thf(fact_9973_tendsto__exp__limit__sequentially,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.64/6.01 @ at_top_nat ) ).
% 5.64/6.01
% 5.64/6.01 % tendsto_exp_limit_sequentially
% 5.64/6.01 thf(fact_9974_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.64/6.01 ! [R2: real] :
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ R2 )
% 5.64/6.01 @ at_top_nat ) ).
% 5.64/6.01
% 5.64/6.01 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.64/6.01 thf(fact_9975_summable__Leibniz_I1_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ( topolo6980174941875973593q_real @ A )
% 5.64/6.01 => ( summable_real
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz(1)
% 5.64/6.01 thf(fact_9976_summable,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.64/6.01 => ( summable_real
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable
% 5.64/6.01 thf(fact_9977_cos__diff__limit__1,axiom,
% 5.64/6.01 ! [Theta: nat > real,Theta2: real] :
% 5.64/6.01 ( ( filterlim_nat_real
% 5.64/6.01 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.64/6.01 @ at_top_nat )
% 5.64/6.01 => ~ ! [K3: nat > int] :
% 5.64/6.01 ~ ( filterlim_nat_real
% 5.64/6.01 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % cos_diff_limit_1
% 5.64/6.01 thf(fact_9978_cos__limit__1,axiom,
% 5.64/6.01 ! [Theta: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real
% 5.64/6.01 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.64/6.01 @ at_top_nat )
% 5.64/6.01 => ? [K3: nat > int] :
% 5.64/6.01 ( filterlim_nat_real
% 5.64/6.01 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % cos_limit_1
% 5.64/6.01 thf(fact_9979_summable__Leibniz_I4_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ( topolo6980174941875973593q_real @ A )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] :
% 5.64/6.01 ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.64/6.01 @ at_top_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz(4)
% 5.64/6.01 thf(fact_9980_zeroseq__arctan__series,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [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 @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % zeroseq_arctan_series
% 5.64/6.01 thf(fact_9981_summable__Leibniz_H_I3_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] :
% 5.64/6.01 ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.64/6.01 @ at_top_nat ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz'(3)
% 5.64/6.01 thf(fact_9982_summable__Leibniz_H_I2_J,axiom,
% 5.64/6.01 ! [A: nat > real,N: nat] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.64/6.01 => ( ord_less_eq_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz'(2)
% 5.64/6.01 thf(fact_9983_sums__alternating__upper__lower,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.64/6.01 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ? [L4: real] :
% 5.64/6.01 ( ! [N7: nat] :
% 5.64/6.01 ( ord_less_eq_real
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.64/6.01 @ L4 )
% 5.64/6.01 & ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] :
% 5.64/6.01 ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ L4 )
% 5.64/6.01 @ at_top_nat )
% 5.64/6.01 & ! [N7: nat] :
% 5.64/6.01 ( ord_less_eq_real @ L4
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 5.64/6.01 & ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] :
% 5.64/6.01 ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ L4 )
% 5.64/6.01 @ at_top_nat ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % sums_alternating_upper_lower
% 5.64/6.01 thf(fact_9984_summable__Leibniz_I5_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ( topolo6980174941875973593q_real @ A )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] :
% 5.64/6.01 ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.64/6.01 @ at_top_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz(5)
% 5.64/6.01 thf(fact_9985_summable__Leibniz_H_I5_J,axiom,
% 5.64/6.01 ! [A: nat > real] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.64/6.01 => ( filterlim_nat_real
% 5.64/6.01 @ ^ [N2: nat] :
% 5.64/6.01 ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) ) )
% 5.64/6.01 @ at_top_nat ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz'(5)
% 5.64/6.01 thf(fact_9986_summable__Leibniz_H_I4_J,axiom,
% 5.64/6.01 ! [A: nat > real,N: nat] :
% 5.64/6.01 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.64/6.01 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.64/6.01 => ( ord_less_eq_real
% 5.64/6.01 @ ( suminf_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) ) )
% 5.64/6.01 @ ( groups6591440286371151544t_real
% 5.64/6.01 @ ^ [I4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I4 ) @ ( A @ I4 ) )
% 5.64/6.01 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % summable_Leibniz'(4)
% 5.64/6.01 thf(fact_9987_real__bounded__linear,axiom,
% 5.64/6.01 ( real_V5970128139526366754l_real
% 5.64/6.01 = ( ^ [F4: real > real] :
% 5.64/6.01 ? [C2: real] :
% 5.64/6.01 ( F4
% 5.64/6.01 = ( ^ [X: real] : ( times_times_real @ X @ C2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % real_bounded_linear
% 5.64/6.01 thf(fact_9988_filterlim__Suc,axiom,
% 5.64/6.01 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.64/6.01
% 5.64/6.01 % filterlim_Suc
% 5.64/6.01 thf(fact_9989_tendsto__exp__limit__at__right,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( filterlim_real_real
% 5.64/6.01 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X2 @ Y ) ) @ ( divide_divide_real @ one_one_real @ Y ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % tendsto_exp_limit_at_right
% 5.64/6.01 thf(fact_9990_filterlim__tan__at__right,axiom,
% 5.64/6.01 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 ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % filterlim_tan_at_right
% 5.64/6.01 thf(fact_9991_tendsto__arctan__at__bot,axiom,
% 5.64/6.01 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.64/6.01
% 5.64/6.01 % tendsto_arctan_at_bot
% 5.64/6.01 thf(fact_9992_greaterThan__0,axiom,
% 5.64/6.01 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.64/6.01 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % greaterThan_0
% 5.64/6.01 thf(fact_9993_greaterThan__Suc,axiom,
% 5.64/6.01 ! [K: nat] :
% 5.64/6.01 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.64/6.01 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % greaterThan_Suc
% 5.64/6.01 thf(fact_9994_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.64/6.01 ! [B: real,F: real > real,Flim: real] :
% 5.64/6.01 ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ X4 @ B )
% 5.64/6.01 => ? [Y5: real] :
% 5.64/6.01 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.01 & ( ord_less_real @ zero_zero_real @ Y5 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.64/6.01 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_pos_imp_increasing_at_bot
% 5.64/6.01 thf(fact_9995_filterlim__pow__at__bot__odd,axiom,
% 5.64/6.01 ! [N: nat,F: real > real,F5: filter_real] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.64/6.01 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ F5 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % filterlim_pow_at_bot_odd
% 5.64/6.01 thf(fact_9996_filterlim__pow__at__bot__even,axiom,
% 5.64/6.01 ! [N: nat,F: real > real,F5: filter_real] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.64/6.01 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ F5 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % filterlim_pow_at_bot_even
% 5.64/6.01 thf(fact_9997_ln__x__over__x__tendsto__0,axiom,
% 5.64/6.01 ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ X ) @ X )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_real ) ).
% 5.64/6.01
% 5.64/6.01 % ln_x_over_x_tendsto_0
% 5.64/6.01 thf(fact_9998_tendsto__power__div__exp__0,axiom,
% 5.64/6.01 ! [K: nat] :
% 5.64/6.01 ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.64/6.01 @ at_top_real ) ).
% 5.64/6.01
% 5.64/6.01 % tendsto_power_div_exp_0
% 5.64/6.01 thf(fact_9999_tendsto__exp__limit__at__top,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( filterlim_real_real
% 5.64/6.01 @ ^ [Y: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ Y ) ) @ Y )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.64/6.01 @ at_top_real ) ).
% 5.64/6.01
% 5.64/6.01 % tendsto_exp_limit_at_top
% 5.64/6.01 thf(fact_10000_filterlim__tan__at__left,axiom,
% 5.64/6.01 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 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % filterlim_tan_at_left
% 5.64/6.01 thf(fact_10001_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.64/6.01 ! [B: real,F: real > real,Flim: real] :
% 5.64/6.01 ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_eq_real @ B @ X4 )
% 5.64/6.01 => ? [Y5: real] :
% 5.64/6.01 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.01 & ( ord_less_real @ Y5 @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.64/6.01 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_neg_imp_decreasing_at_top
% 5.64/6.01 thf(fact_10002_tendsto__arctan__at__top,axiom,
% 5.64/6.01 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.64/6.01
% 5.64/6.01 % tendsto_arctan_at_top
% 5.64/6.01 thf(fact_10003_lhopital__right__0__at__top,axiom,
% 5.64/6.01 ! [G: real > real,G2: real > real,F: real > real,F3: real > real,X2: real] :
% 5.64/6.01 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ X2 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ X2 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_right_0_at_top
% 5.64/6.01 thf(fact_10004_eventually__sequentially__Suc,axiom,
% 5.64/6.01 ! [P: nat > $o] :
% 5.64/6.01 ( ( eventually_nat
% 5.64/6.01 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 5.64/6.01 @ at_top_nat )
% 5.64/6.01 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % eventually_sequentially_Suc
% 5.64/6.01 thf(fact_10005_eventually__sequentially__seg,axiom,
% 5.64/6.01 ! [P: nat > $o,K: nat] :
% 5.64/6.01 ( ( eventually_nat
% 5.64/6.01 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.64/6.01 @ at_top_nat )
% 5.64/6.01 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % eventually_sequentially_seg
% 5.64/6.01 thf(fact_10006_sequentially__offset,axiom,
% 5.64/6.01 ! [P: nat > $o,K: nat] :
% 5.64/6.01 ( ( eventually_nat @ P @ at_top_nat )
% 5.64/6.01 => ( eventually_nat
% 5.64/6.01 @ ^ [I4: nat] : ( P @ ( plus_plus_nat @ I4 @ K ) )
% 5.64/6.01 @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % sequentially_offset
% 5.64/6.01 thf(fact_10007_le__sequentially,axiom,
% 5.64/6.01 ! [F5: filter_nat] :
% 5.64/6.01 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.64/6.01 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F5 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % le_sequentially
% 5.64/6.01 thf(fact_10008_eventually__sequentially,axiom,
% 5.64/6.01 ! [P: nat > $o] :
% 5.64/6.01 ( ( eventually_nat @ P @ at_top_nat )
% 5.64/6.01 = ( ? [N6: nat] :
% 5.64/6.01 ! [N2: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.64/6.01 => ( P @ N2 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % eventually_sequentially
% 5.64/6.01 thf(fact_10009_eventually__sequentiallyI,axiom,
% 5.64/6.01 ! [C: nat,P: nat > $o] :
% 5.64/6.01 ( ! [X4: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ C @ X4 )
% 5.64/6.01 => ( P @ X4 ) )
% 5.64/6.01 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % eventually_sequentiallyI
% 5.64/6.01 thf(fact_10010_eventually__at__left__real,axiom,
% 5.64/6.01 ! [B: real,A: real] :
% 5.64/6.01 ( ( ord_less_real @ B @ A )
% 5.64/6.01 => ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % eventually_at_left_real
% 5.64/6.01 thf(fact_10011_eventually__at__right__real,axiom,
% 5.64/6.01 ! [A: real,B: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % eventually_at_right_real
% 5.64/6.01 thf(fact_10012_lhopital__left__at__top__at__top,axiom,
% 5.64/6.01 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_left_at_top_at_top
% 5.64/6.01 thf(fact_10013_lhopital__at__top__at__top,axiom,
% 5.64/6.01 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_at_top_at_top
% 5.64/6.01 thf(fact_10014_lhopital__left,axiom,
% 5.64/6.01 ! [F: real > real,X2: real,G: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_left
% 5.64/6.01 thf(fact_10015_lhopital,axiom,
% 5.64/6.01 ! [F: real > real,X2: real,G: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital
% 5.64/6.01 thf(fact_10016_lhopital__right__at__top__at__top,axiom,
% 5.64/6.01 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ at_top_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_right_at_top_at_top
% 5.64/6.01 thf(fact_10017_lhopital__left__at__top__at__bot,axiom,
% 5.64/6.01 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_left_at_top_at_bot
% 5.64/6.01 thf(fact_10018_lhopital__at__top__at__bot,axiom,
% 5.64/6.01 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_at_top_at_bot
% 5.64/6.01 thf(fact_10019_lhopital__left__at__top,axiom,
% 5.64/6.01 ! [G: real > real,X2: real,G2: real > real,F: real > real,F3: real > real,Y4: real] :
% 5.64/6.01 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5984915006950818249n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_left_at_top
% 5.64/6.01 thf(fact_10020_lhospital__at__top__at__top,axiom,
% 5.64/6.01 ! [G: real > real,G2: real > real,F: real > real,F3: real > real,X2: real] :
% 5.64/6.01 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ at_top_real )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ at_top_real )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ at_top_real )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ X2 )
% 5.64/6.01 @ at_top_real )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ X2 )
% 5.64/6.01 @ at_top_real ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhospital_at_top_at_top
% 5.64/6.01 thf(fact_10021_lhopital__at__top,axiom,
% 5.64/6.01 ! [G: real > real,X2: real,G2: real > real,F: real > real,F3: real > real,Y4: real] :
% 5.64/6.01 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_at_top
% 5.64/6.01 thf(fact_10022_lhopital__right__0,axiom,
% 5.64/6.01 ! [F0: real > real,G0: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.64/6.01 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G0 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F0 @ X ) @ ( G0 @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_right_0
% 5.64/6.01 thf(fact_10023_lhopital__right,axiom,
% 5.64/6.01 ! [F: real > real,X2: real,G: real > real,G2: real > real,F3: real > real,F5: filter_real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ F5
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_right
% 5.64/6.01 thf(fact_10024_lhopital__right__at__top__at__bot,axiom,
% 5.64/6.01 ! [F: real > real,A: real,G: real > real,F3: real > real,G2: real > real] :
% 5.64/6.01 ( ( filterlim_real_real @ F @ at_top_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real @ G @ at_bot_real @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ at_bot_real
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_right_at_top_at_bot
% 5.64/6.01 thf(fact_10025_lhopital__right__at__top,axiom,
% 5.64/6.01 ! [G: real > real,X2: real,G2: real > real,F: real > real,F3: real > real,Y4: real] :
% 5.64/6.01 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] :
% 5.64/6.01 ( ( G2 @ X )
% 5.64/6.01 != zero_zero_real )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( eventually_real
% 5.64/6.01 @ ^ [X: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F3 @ X ) @ ( G2 @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) )
% 5.64/6.01 => ( filterlim_real_real
% 5.64/6.01 @ ^ [X: real] : ( divide_divide_real @ ( F @ X ) @ ( G @ X ) )
% 5.64/6.01 @ ( topolo2815343760600316023s_real @ Y4 )
% 5.64/6.01 @ ( topolo2177554685111907308n_real @ X2 @ ( set_or5849166863359141190n_real @ X2 ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % lhopital_right_at_top
% 5.64/6.01 thf(fact_10026_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.64/6.01 ! [L: nat,U: nat] :
% 5.64/6.01 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.64/6.01 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeastSucAtMost_greaterThanAtMost
% 5.64/6.01 thf(fact_10027_GreatestI__ex__nat,axiom,
% 5.64/6.01 ! [P: nat > $o,B: nat] :
% 5.64/6.01 ( ? [X_1: nat] : ( P @ X_1 )
% 5.64/6.01 => ( ! [Y3: nat] :
% 5.64/6.01 ( ( P @ Y3 )
% 5.64/6.01 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.64/6.01 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % GreatestI_ex_nat
% 5.64/6.01 thf(fact_10028_Greatest__le__nat,axiom,
% 5.64/6.01 ! [P: nat > $o,K: nat,B: nat] :
% 5.64/6.01 ( ( P @ K )
% 5.64/6.01 => ( ! [Y3: nat] :
% 5.64/6.01 ( ( P @ Y3 )
% 5.64/6.01 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.64/6.01 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Greatest_le_nat
% 5.64/6.01 thf(fact_10029_GreatestI__nat,axiom,
% 5.64/6.01 ! [P: nat > $o,K: nat,B: nat] :
% 5.64/6.01 ( ( P @ K )
% 5.64/6.01 => ( ! [Y3: nat] :
% 5.64/6.01 ( ( P @ Y3 )
% 5.64/6.01 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.64/6.01 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % GreatestI_nat
% 5.64/6.01 thf(fact_10030_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.64/6.01 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.64/6.01 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_list_of_set_greaterThanAtMost
% 5.64/6.01 thf(fact_10031_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.64/6.01 ! [N: nat,J: nat,I: nat] :
% 5.64/6.01 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.64/6.01 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.64/6.01 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % nth_sorted_list_of_set_greaterThanAtMost
% 5.64/6.01 thf(fact_10032_atLeast__Suc__greaterThan,axiom,
% 5.64/6.01 ! [K: nat] :
% 5.64/6.01 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.64/6.01 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeast_Suc_greaterThan
% 5.64/6.01 thf(fact_10033_greaterThanAtMost__upto,axiom,
% 5.64/6.01 ( set_or6656581121297822940st_int
% 5.64/6.01 = ( ^ [I4: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % greaterThanAtMost_upto
% 5.64/6.01 thf(fact_10034_atLeast__Suc,axiom,
% 5.64/6.01 ! [K: nat] :
% 5.64/6.01 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.64/6.01 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeast_Suc
% 5.64/6.01 thf(fact_10035_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/6.01 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( ? [Uu: $o,Uv: $o] :
% 5.64/6.01 ( X2
% 5.64/6.01 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/6.01 => ( Y4
% 5.64/6.01 = ( Xa2 != one_one_nat ) ) )
% 5.64/6.01 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.01 => ( Y4
% 5.64/6.01 = ( ~ ( ( Deg2 = Xa2 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.elims(1)
% 5.64/6.01 thf(fact_10036_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/6.01 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.64/6.01 => ( ( ? [Uu: $o,Uv: $o] :
% 5.64/6.01 ( X2
% 5.64/6.01 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/6.01 => ( Xa2 != one_one_nat ) )
% 5.64/6.01 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.01 => ~ ( ( Deg2 = Xa2 )
% 5.64/6.01 & ! [X3: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.elims(2)
% 5.64/6.01 thf(fact_10037_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.64/6.01 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.64/6.01 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.64/6.01 = ( ( Deg = Deg4 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima2 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.simps(2)
% 5.64/6.01 thf(fact_10038_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/6.01 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.64/6.01 => ( ( ? [Uu: $o,Uv: $o] :
% 5.64/6.01 ( X2
% 5.64/6.01 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/6.01 => ( Xa2 = one_one_nat ) )
% 5.64/6.01 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.01 => ( ( Deg2 = Xa2 )
% 5.64/6.01 & ! [X4: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.elims(3)
% 5.64/6.01 thf(fact_10039_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/6.01 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ! [Uu: $o,Uv: $o] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 5.64/6.01 => ( Xa2 = one_one_nat ) ) )
% 5.64/6.01 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.64/6.01 => ( ( Deg2 = Xa2 )
% 5.64/6.01 & ! [X4: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.pelims(3)
% 5.64/6.01 thf(fact_10040_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.64/6.01 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ! [Uu: $o,Uv: $o] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) )
% 5.64/6.01 => ( Xa2 != one_one_nat ) ) )
% 5.64/6.01 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.64/6.01 => ~ ( ( Deg2 = Xa2 )
% 5.64/6.01 & ! [X3: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.pelims(2)
% 5.64/6.01 thf(fact_10041_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Xa2: nat,Y4: $o] :
% 5.64/6.01 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ! [Uu: $o,Uv: $o] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Leaf @ Uu @ Uv ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( Xa2 = one_one_nat ) )
% 5.64/6.01 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu @ Uv ) @ Xa2 ) ) ) )
% 5.64/6.01 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( ( Deg2 = Xa2 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.64/6.01 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.64/6.01 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 & ( case_o184042715313410164at_nat
% 5.64/6.01 @ ( ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X5 )
% 5.64/6.01 & ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [Mi3: nat,Ma3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.64/6.01 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 & ! [I4: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.64/6.01 => ( ( ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X5 ) )
% 5.64/6.01 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 5.64/6.01 & ( ( Mi3 = Ma3 )
% 5.64/6.01 => ! [X: vEBT_VEBT] :
% 5.64/6.01 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.64/6.01 => ~ ? [X5: nat] : ( vEBT_V8194947554948674370ptions @ X @ X5 ) ) )
% 5.64/6.01 & ( ( Mi3 != Ma3 )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.64/6.01 & ! [X: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.64/6.01 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.64/6.01 => ( ( ord_less_nat @ Mi3 @ X )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.64/6.01 @ Mima ) ) )
% 5.64/6.01 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % VEBT_internal.valid'.pelims(1)
% 5.64/6.01 thf(fact_10042_GMVT,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.64/6.01 & ( ord_less_eq_real @ X4 @ B ) )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F ) )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 & ( ord_less_real @ X4 @ B ) )
% 5.64/6.01 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.64/6.01 & ( ord_less_eq_real @ X4 @ B ) )
% 5.64/6.01 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G ) )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 & ( ord_less_real @ X4 @ B ) )
% 5.64/6.01 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) )
% 5.64/6.01 => ? [G_c: real,F_c: real,C3: real] :
% 5.64/6.01 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.64/6.01 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.64/6.01 & ( ord_less_real @ A @ C3 )
% 5.64/6.01 & ( ord_less_real @ C3 @ B )
% 5.64/6.01 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.64/6.01 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % GMVT
% 5.64/6.01 thf(fact_10043_MVT,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ? [L4: real,Z2: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Z2 )
% 5.64/6.01 & ( ord_less_real @ Z2 @ B )
% 5.64/6.01 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.64/6.01 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.64/6.01 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % MVT
% 5.64/6.01 thf(fact_10044_Rolle__deriv,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real,F3: real > real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( ( F @ A )
% 5.64/6.01 = ( F @ B ) )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ( has_de1759254742604945161l_real @ F @ ( F3 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ? [Z2: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Z2 )
% 5.64/6.01 & ( ord_less_real @ Z2 @ B )
% 5.64/6.01 & ( ( F3 @ Z2 )
% 5.64/6.01 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rolle_deriv
% 5.64/6.01 thf(fact_10045_mvt,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real,F3: real > real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ( has_de1759254742604945161l_real @ F @ ( F3 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ~ ! [Xi: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Xi )
% 5.64/6.01 => ( ( ord_less_real @ Xi @ B )
% 5.64/6.01 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.64/6.01 != ( F3 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % mvt
% 5.64/6.01 thf(fact_10046_DERIV__isconst__end,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ( ( F @ B )
% 5.64/6.01 = ( F @ A ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_isconst_end
% 5.64/6.01 thf(fact_10047_DERIV__neg__imp__decreasing__open,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ? [Y5: real] :
% 5.64/6.01 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.01 & ( ord_less_real @ Y5 @ zero_zero_real ) ) ) )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_neg_imp_decreasing_open
% 5.64/6.01 thf(fact_10048_DERIV__pos__imp__increasing__open,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ? [Y5: real] :
% 5.64/6.01 ( ( has_fi5821293074295781190e_real @ F @ Y5 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.01 & ( ord_less_real @ zero_zero_real @ Y5 ) ) ) )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_pos_imp_increasing_open
% 5.64/6.01 thf(fact_10049_DERIV__isconst2,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real,X2: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ( ( ord_less_eq_real @ A @ X2 )
% 5.64/6.01 => ( ( ord_less_eq_real @ X2 @ B )
% 5.64/6.01 => ( ( F @ X2 )
% 5.64/6.01 = ( F @ A ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DERIV_isconst2
% 5.64/6.01 thf(fact_10050_Rolle,axiom,
% 5.64/6.01 ! [A: real,B: real,F: real > real] :
% 5.64/6.01 ( ( ord_less_real @ A @ B )
% 5.64/6.01 => ( ( ( F @ A )
% 5.64/6.01 = ( F @ B ) )
% 5.64/6.01 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.64/6.01 => ( ! [X4: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ X4 )
% 5.64/6.01 => ( ( ord_less_real @ X4 @ B )
% 5.64/6.01 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) )
% 5.64/6.01 => ? [Z2: real] :
% 5.64/6.01 ( ( ord_less_real @ A @ Z2 )
% 5.64/6.01 & ( ord_less_real @ Z2 @ B )
% 5.64/6.01 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rolle
% 5.64/6.01 thf(fact_10051_mono__Suc,axiom,
% 5.64/6.01 order_mono_nat_nat @ suc ).
% 5.64/6.01
% 5.64/6.01 % mono_Suc
% 5.64/6.01 thf(fact_10052_mono__times__nat,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % mono_times_nat
% 5.64/6.01 thf(fact_10053_mono__ge2__power__minus__self,axiom,
% 5.64/6.01 ! [K: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.64/6.01 => ( order_mono_nat_nat
% 5.64/6.01 @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % mono_ge2_power_minus_self
% 5.64/6.01 thf(fact_10054_inj__sgn__power,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( inj_on_real_real
% 5.64/6.01 @ ^ [Y: real] : ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) )
% 5.64/6.01 @ top_top_set_real ) ) ).
% 5.64/6.01
% 5.64/6.01 % inj_sgn_power
% 5.64/6.01 thf(fact_10055_log__inj,axiom,
% 5.64/6.01 ! [B: real] :
% 5.64/6.01 ( ( ord_less_real @ one_one_real @ B )
% 5.64/6.01 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % log_inj
% 5.64/6.01 thf(fact_10056_inj__Suc,axiom,
% 5.64/6.01 ! [N5: set_nat] : ( inj_on_nat_nat @ suc @ N5 ) ).
% 5.64/6.01
% 5.64/6.01 % inj_Suc
% 5.64/6.01 thf(fact_10057_inj__on__diff__nat,axiom,
% 5.64/6.01 ! [N5: set_nat,K: nat] :
% 5.64/6.01 ( ! [N3: nat] :
% 5.64/6.01 ( ( member_nat @ N3 @ N5 )
% 5.64/6.01 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.64/6.01 => ( inj_on_nat_nat
% 5.64/6.01 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 5.64/6.01 @ N5 ) ) ).
% 5.64/6.01
% 5.64/6.01 % inj_on_diff_nat
% 5.64/6.01 thf(fact_10058_inj__on__char__of__nat,axiom,
% 5.64/6.01 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % inj_on_char_of_nat
% 5.64/6.01 thf(fact_10059_sup__nat__def,axiom,
% 5.64/6.01 sup_sup_nat = ord_max_nat ).
% 5.64/6.01
% 5.64/6.01 % sup_nat_def
% 5.64/6.01 thf(fact_10060_sup__enat__def,axiom,
% 5.64/6.01 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.64/6.01
% 5.64/6.01 % sup_enat_def
% 5.64/6.01 thf(fact_10061_atLeastLessThan__add__Un,axiom,
% 5.64/6.01 ! [I: nat,J: nat,K: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.64/6.01 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.64/6.01 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeastLessThan_add_Un
% 5.64/6.01 thf(fact_10062_remdups__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( remdups_nat @ ( upt @ M @ N ) )
% 5.64/6.01 = ( upt @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % remdups_upt
% 5.64/6.01 thf(fact_10063_hd__upt,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I @ J )
% 5.64/6.01 => ( ( hd_nat @ ( upt @ I @ J ) )
% 5.64/6.01 = I ) ) ).
% 5.64/6.01
% 5.64/6.01 % hd_upt
% 5.64/6.01 thf(fact_10064_drop__upt,axiom,
% 5.64/6.01 ! [M: nat,I: nat,J: nat] :
% 5.64/6.01 ( ( drop_nat @ M @ ( upt @ I @ J ) )
% 5.64/6.01 = ( upt @ ( plus_plus_nat @ I @ M ) @ J ) ) ).
% 5.64/6.01
% 5.64/6.01 % drop_upt
% 5.64/6.01 thf(fact_10065_length__upt,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 5.64/6.01 = ( minus_minus_nat @ J @ I ) ) ).
% 5.64/6.01
% 5.64/6.01 % length_upt
% 5.64/6.01 thf(fact_10066_take__upt,axiom,
% 5.64/6.01 ! [I: nat,M: nat,N: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ M ) @ N )
% 5.64/6.01 => ( ( take_nat @ M @ ( upt @ I @ N ) )
% 5.64/6.01 = ( upt @ I @ ( plus_plus_nat @ I @ M ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % take_upt
% 5.64/6.01 thf(fact_10067_upt__conv__Nil,axiom,
% 5.64/6.01 ! [J: nat,I: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ J @ I )
% 5.64/6.01 => ( ( upt @ I @ J )
% 5.64/6.01 = nil_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_conv_Nil
% 5.64/6.01 thf(fact_10068_sorted__list__of__set__range,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.64/6.01 = ( upt @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_list_of_set_range
% 5.64/6.01 thf(fact_10069_upt__eq__Nil__conv,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ( upt @ I @ J )
% 5.64/6.01 = nil_nat )
% 5.64/6.01 = ( ( J = zero_zero_nat )
% 5.64/6.01 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_eq_Nil_conv
% 5.64/6.01 thf(fact_10070_nth__upt,axiom,
% 5.64/6.01 ! [I: nat,K: nat,J: nat] :
% 5.64/6.01 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.64/6.01 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.64/6.01 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % nth_upt
% 5.64/6.01 thf(fact_10071_upt__rec__numeral,axiom,
% 5.64/6.01 ! [M: num,N: num] :
% 5.64/6.01 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/6.01 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/6.01 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.64/6.01 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/6.01 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.64/6.01 = nil_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_rec_numeral
% 5.64/6.01 thf(fact_10072_map__add__upt,axiom,
% 5.64/6.01 ! [N: nat,M: nat] :
% 5.64/6.01 ( ( map_nat_nat
% 5.64/6.01 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N )
% 5.64/6.01 @ ( upt @ zero_zero_nat @ M ) )
% 5.64/6.01 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % map_add_upt
% 5.64/6.01 thf(fact_10073_map__Suc__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.64/6.01 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % map_Suc_upt
% 5.64/6.01 thf(fact_10074_distinct__upt,axiom,
% 5.64/6.01 ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 5.64/6.01
% 5.64/6.01 % distinct_upt
% 5.64/6.01 thf(fact_10075_upt__0,axiom,
% 5.64/6.01 ! [I: nat] :
% 5.64/6.01 ( ( upt @ I @ zero_zero_nat )
% 5.64/6.01 = nil_nat ) ).
% 5.64/6.01
% 5.64/6.01 % upt_0
% 5.64/6.01 thf(fact_10076_greaterThanLessThan__upt,axiom,
% 5.64/6.01 ( set_or5834768355832116004an_nat
% 5.64/6.01 = ( ^ [N2: nat,M2: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M2 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % greaterThanLessThan_upt
% 5.64/6.01 thf(fact_10077_atLeastLessThan__upt,axiom,
% 5.64/6.01 ( set_or4665077453230672383an_nat
% 5.64/6.01 = ( ^ [I4: nat,J3: nat] : ( set_nat2 @ ( upt @ I4 @ J3 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeastLessThan_upt
% 5.64/6.01 thf(fact_10078_atLeastAtMost__upt,axiom,
% 5.64/6.01 ( set_or1269000886237332187st_nat
% 5.64/6.01 = ( ^ [N2: nat,M2: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeastAtMost_upt
% 5.64/6.01 thf(fact_10079_atLeast__upt,axiom,
% 5.64/6.01 ( set_ord_lessThan_nat
% 5.64/6.01 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % atLeast_upt
% 5.64/6.01 thf(fact_10080_greaterThanAtMost__upt,axiom,
% 5.64/6.01 ( set_or6659071591806873216st_nat
% 5.64/6.01 = ( ^ [N2: nat,M2: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % greaterThanAtMost_upt
% 5.64/6.01 thf(fact_10081_upt__conv__Cons__Cons,axiom,
% 5.64/6.01 ! [M: nat,N: nat,Ns: list_nat,Q3: nat] :
% 5.64/6.01 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.64/6.01 = ( upt @ M @ Q3 ) )
% 5.64/6.01 = ( ( cons_nat @ N @ Ns )
% 5.64/6.01 = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_conv_Cons_Cons
% 5.64/6.01 thf(fact_10082_atMost__upto,axiom,
% 5.64/6.01 ( set_ord_atMost_nat
% 5.64/6.01 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % atMost_upto
% 5.64/6.01 thf(fact_10083_upt__conv__Cons,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ord_less_nat @ I @ J )
% 5.64/6.01 => ( ( upt @ I @ J )
% 5.64/6.01 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_conv_Cons
% 5.64/6.01 thf(fact_10084_map__decr__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( map_nat_nat
% 5.64/6.01 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.64/6.01 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.64/6.01 = ( upt @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % map_decr_upt
% 5.64/6.01 thf(fact_10085_upt__add__eq__append,axiom,
% 5.64/6.01 ! [I: nat,J: nat,K: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.64/6.01 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.64/6.01 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_add_eq_append
% 5.64/6.01 thf(fact_10086_upt__eq__Cons__conv,axiom,
% 5.64/6.01 ! [I: nat,J: nat,X2: nat,Xs2: list_nat] :
% 5.64/6.01 ( ( ( upt @ I @ J )
% 5.64/6.01 = ( cons_nat @ X2 @ Xs2 ) )
% 5.64/6.01 = ( ( ord_less_nat @ I @ J )
% 5.64/6.01 & ( I = X2 )
% 5.64/6.01 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.64/6.01 = Xs2 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_eq_Cons_conv
% 5.64/6.01 thf(fact_10087_upt__rec,axiom,
% 5.64/6.01 ( upt
% 5.64/6.01 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_rec
% 5.64/6.01 thf(fact_10088_upt__Suc__append,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ I @ J )
% 5.64/6.01 => ( ( upt @ I @ ( suc @ J ) )
% 5.64/6.01 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_Suc_append
% 5.64/6.01 thf(fact_10089_upt__Suc,axiom,
% 5.64/6.01 ! [I: nat,J: nat] :
% 5.64/6.01 ( ( ( ord_less_eq_nat @ I @ J )
% 5.64/6.01 => ( ( upt @ I @ ( suc @ J ) )
% 5.64/6.01 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.64/6.01 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.64/6.01 => ( ( upt @ I @ ( suc @ J ) )
% 5.64/6.01 = nil_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % upt_Suc
% 5.64/6.01 thf(fact_10090_tl__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( tl_nat @ ( upt @ M @ N ) )
% 5.64/6.01 = ( upt @ ( suc @ M ) @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % tl_upt
% 5.64/6.01 thf(fact_10091_sum__list__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ M @ N )
% 5.64/6.01 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.64/6.01 = ( groups3542108847815614940at_nat
% 5.64/6.01 @ ^ [X: nat] : X
% 5.64/6.01 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % sum_list_upt
% 5.64/6.01 thf(fact_10092_card__length__sum__list__rec,axiom,
% 5.64/6.01 ! [M: nat,N5: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.64/6.01 => ( ( finite_card_list_nat
% 5.64/6.01 @ ( collect_list_nat
% 5.64/6.01 @ ^ [L2: list_nat] :
% 5.64/6.01 ( ( ( size_size_list_nat @ L2 )
% 5.64/6.01 = M )
% 5.64/6.01 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.64/6.01 = N5 ) ) ) )
% 5.64/6.01 = ( plus_plus_nat
% 5.64/6.01 @ ( finite_card_list_nat
% 5.64/6.01 @ ( collect_list_nat
% 5.64/6.01 @ ^ [L2: list_nat] :
% 5.64/6.01 ( ( ( size_size_list_nat @ L2 )
% 5.64/6.01 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.64/6.01 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.64/6.01 = N5 ) ) ) )
% 5.64/6.01 @ ( finite_card_list_nat
% 5.64/6.01 @ ( collect_list_nat
% 5.64/6.01 @ ^ [L2: list_nat] :
% 5.64/6.01 ( ( ( size_size_list_nat @ L2 )
% 5.64/6.01 = M )
% 5.64/6.01 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.64/6.01 = N5 ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % card_length_sum_list_rec
% 5.64/6.01 thf(fact_10093_card__length__sum__list,axiom,
% 5.64/6.01 ! [M: nat,N5: nat] :
% 5.64/6.01 ( ( finite_card_list_nat
% 5.64/6.01 @ ( collect_list_nat
% 5.64/6.01 @ ^ [L2: list_nat] :
% 5.64/6.01 ( ( ( size_size_list_nat @ L2 )
% 5.64/6.01 = M )
% 5.64/6.01 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.64/6.01 = N5 ) ) ) )
% 5.64/6.01 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N5 @ M ) @ one_one_nat ) @ N5 ) ) ).
% 5.64/6.01
% 5.64/6.01 % card_length_sum_list
% 5.64/6.01 thf(fact_10094_sorted__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_upt
% 5.64/6.01 thf(fact_10095_sorted__wrt__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_wrt_upt
% 5.64/6.01 thf(fact_10096_sorted__wrt__upto,axiom,
% 5.64/6.01 ! [I: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I @ J ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_wrt_upto
% 5.64/6.01 thf(fact_10097_sorted__upto,axiom,
% 5.64/6.01 ! [M: int,N: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_upto
% 5.64/6.01 thf(fact_10098_sorted__wrt__less__idx,axiom,
% 5.64/6.01 ! [Ns: list_nat,I: nat] :
% 5.64/6.01 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.64/6.01 => ( ( ord_less_nat @ I @ ( size_size_list_nat @ Ns ) )
% 5.64/6.01 => ( ord_less_eq_nat @ I @ ( nth_nat @ Ns @ I ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % sorted_wrt_less_idx
% 5.64/6.01 thf(fact_10099_powr__real__of__int_H,axiom,
% 5.64/6.01 ! [X2: real,N: int] :
% 5.64/6.01 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.64/6.01 => ( ( ( X2 != zero_zero_real )
% 5.64/6.01 | ( ord_less_int @ zero_zero_int @ N ) )
% 5.64/6.01 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N ) )
% 5.64/6.01 = ( power_int_real @ X2 @ N ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % powr_real_of_int'
% 5.64/6.01 thf(fact_10100_pred__nat__def,axiom,
% 5.64/6.01 ( pred_nat
% 5.64/6.01 = ( collec3392354462482085612at_nat
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [M2: nat,N2: nat] :
% 5.64/6.01 ( N2
% 5.64/6.01 = ( suc @ M2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % pred_nat_def
% 5.64/6.01 thf(fact_10101_less__eq,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.64/6.01 = ( ord_less_nat @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % less_eq
% 5.64/6.01 thf(fact_10102_pred__nat__trancl__eq__le,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.64/6.01 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % pred_nat_trancl_eq_le
% 5.64/6.01 thf(fact_10103_Rats__eq__int__div__nat,axiom,
% 5.64/6.01 ( field_5140801741446780682s_real
% 5.64/6.01 = ( collect_real
% 5.64/6.01 @ ^ [Uu3: real] :
% 5.64/6.01 ? [I4: int,N2: nat] :
% 5.64/6.01 ( ( Uu3
% 5.64/6.01 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.64/6.01 & ( N2 != zero_zero_nat ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rats_eq_int_div_nat
% 5.64/6.01 thf(fact_10104_Rats__no__bot__less,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ? [X4: real] :
% 5.64/6.01 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.64/6.01 & ( ord_less_real @ X4 @ X2 ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rats_no_bot_less
% 5.64/6.01 thf(fact_10105_Rats__dense__in__real,axiom,
% 5.64/6.01 ! [X2: real,Y4: real] :
% 5.64/6.01 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/6.01 => ? [X4: real] :
% 5.64/6.01 ( ( member_real @ X4 @ field_5140801741446780682s_real )
% 5.64/6.01 & ( ord_less_real @ X2 @ X4 )
% 5.64/6.01 & ( ord_less_real @ X4 @ Y4 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rats_dense_in_real
% 5.64/6.01 thf(fact_10106_Rats__eq__int__div__int,axiom,
% 5.64/6.01 ( field_5140801741446780682s_real
% 5.64/6.01 = ( collect_real
% 5.64/6.01 @ ^ [Uu3: real] :
% 5.64/6.01 ? [I4: int,J3: int] :
% 5.64/6.01 ( ( Uu3
% 5.64/6.01 = ( divide_divide_real @ ( ring_1_of_int_real @ I4 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.64/6.01 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rats_eq_int_div_int
% 5.64/6.01 thf(fact_10107_pairs__le__eq__Sigma,axiom,
% 5.64/6.01 ! [M: nat] :
% 5.64/6.01 ( ( collec3392354462482085612at_nat
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ M ) ) )
% 5.64/6.01 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.64/6.01 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % pairs_le_eq_Sigma
% 5.64/6.01 thf(fact_10108_pos__deriv__imp__strict__mono,axiom,
% 5.64/6.01 ! [F: real > real,F3: real > real] :
% 5.64/6.01 ( ! [X4: real] : ( has_fi5821293074295781190e_real @ F @ ( F3 @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.64/6.01 => ( ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( F3 @ X4 ) )
% 5.64/6.01 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % pos_deriv_imp_strict_mono
% 5.64/6.01 thf(fact_10109_strict__mono__imp__increasing,axiom,
% 5.64/6.01 ! [F: nat > nat,N: nat] :
% 5.64/6.01 ( ( order_5726023648592871131at_nat @ F )
% 5.64/6.01 => ( ord_less_eq_nat @ N @ ( F @ N ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % strict_mono_imp_increasing
% 5.64/6.01 thf(fact_10110_vimage__Suc__insert__0,axiom,
% 5.64/6.01 ! [A4: set_nat] :
% 5.64/6.01 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A4 ) )
% 5.64/6.01 = ( vimage_nat_nat @ suc @ A4 ) ) ).
% 5.64/6.01
% 5.64/6.01 % vimage_Suc_insert_0
% 5.64/6.01 thf(fact_10111_finite__vimage__Suc__iff,axiom,
% 5.64/6.01 ! [F5: set_nat] :
% 5.64/6.01 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F5 ) )
% 5.64/6.01 = ( finite_finite_nat @ F5 ) ) ).
% 5.64/6.01
% 5.64/6.01 % finite_vimage_Suc_iff
% 5.64/6.01 thf(fact_10112_vimage__Suc__insert__Suc,axiom,
% 5.64/6.01 ! [N: nat,A4: set_nat] :
% 5.64/6.01 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A4 ) )
% 5.64/6.01 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A4 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % vimage_Suc_insert_Suc
% 5.64/6.01 thf(fact_10113_set__decode__div__2,axiom,
% 5.64/6.01 ! [X2: nat] :
% 5.64/6.01 ( ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.64/6.01 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X2 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % set_decode_div_2
% 5.64/6.01 thf(fact_10114_set__encode__vimage__Suc,axiom,
% 5.64/6.01 ! [A4: set_nat] :
% 5.64/6.01 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A4 ) )
% 5.64/6.01 = ( divide_divide_nat @ ( nat_set_encode @ A4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % set_encode_vimage_Suc
% 5.64/6.01 thf(fact_10115_Field__natLeq__on,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( field_nat
% 5.64/6.01 @ ( collec3392354462482085612at_nat
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ N )
% 5.64/6.01 & ( ord_less_nat @ Y @ N )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Y ) ) ) ) )
% 5.64/6.01 = ( collect_nat
% 5.64/6.01 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Field_natLeq_on
% 5.64/6.01 thf(fact_10116_natLess__def,axiom,
% 5.64/6.01 ( bNF_Ca8459412986667044542atLess
% 5.64/6.01 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % natLess_def
% 5.64/6.01 thf(fact_10117_wf__less,axiom,
% 5.64/6.01 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % wf_less
% 5.64/6.01 thf(fact_10118_Restr__natLeq,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.64/6.01 @ ( produc457027306803732586at_nat
% 5.64/6.01 @ ( collect_nat
% 5.64/6.01 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) )
% 5.64/6.01 @ ^ [Uu3: nat] :
% 5.64/6.01 ( collect_nat
% 5.64/6.01 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) )
% 5.64/6.01 = ( collec3392354462482085612at_nat
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ N )
% 5.64/6.01 & ( ord_less_nat @ Y @ N )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Restr_natLeq
% 5.64/6.01 thf(fact_10119_prod__encode__prod__decode__aux,axiom,
% 5.64/6.01 ! [K: nat,M: nat] :
% 5.64/6.01 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.64/6.01 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.64/6.01
% 5.64/6.01 % prod_encode_prod_decode_aux
% 5.64/6.01 thf(fact_10120_natLeq__def,axiom,
% 5.64/6.01 ( bNF_Ca8665028551170535155natLeq
% 5.64/6.01 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % natLeq_def
% 5.64/6.01 thf(fact_10121_le__prod__encode__1,axiom,
% 5.64/6.01 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % le_prod_encode_1
% 5.64/6.01 thf(fact_10122_le__prod__encode__2,axiom,
% 5.64/6.01 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % le_prod_encode_2
% 5.64/6.01 thf(fact_10123_prod__encode__def,axiom,
% 5.64/6.01 ( nat_prod_encode
% 5.64/6.01 = ( produc6842872674320459806at_nat
% 5.64/6.01 @ ^ [M2: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M2 @ N2 ) ) @ M2 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % prod_encode_def
% 5.64/6.01 thf(fact_10124_list__encode_Oelims,axiom,
% 5.64/6.01 ! [X2: list_nat,Y4: nat] :
% 5.64/6.01 ( ( ( nat_list_encode @ X2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( ( X2 = nil_nat )
% 5.64/6.01 => ( Y4 != zero_zero_nat ) )
% 5.64/6.01 => ~ ! [X4: nat,Xs3: list_nat] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( cons_nat @ X4 @ Xs3 ) )
% 5.64/6.01 => ( Y4
% 5.64/6.01 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % list_encode.elims
% 5.64/6.01 thf(fact_10125_Restr__natLeq2,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.64/6.01 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.64/6.01 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 5.64/6.01 = ( collec3392354462482085612at_nat
% 5.64/6.01 @ ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( ( ord_less_nat @ X @ N )
% 5.64/6.01 & ( ord_less_nat @ Y @ N )
% 5.64/6.01 & ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Restr_natLeq2
% 5.64/6.01 thf(fact_10126_natLeq__underS__less,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 5.64/6.01 = ( collect_nat
% 5.64/6.01 @ ^ [X: nat] : ( ord_less_nat @ X @ N ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % natLeq_underS_less
% 5.64/6.01 thf(fact_10127_list__encode_Osimps_I2_J,axiom,
% 5.64/6.01 ! [X2: nat,Xs2: list_nat] :
% 5.64/6.01 ( ( nat_list_encode @ ( cons_nat @ X2 @ Xs2 ) )
% 5.64/6.01 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % list_encode.simps(2)
% 5.64/6.01 thf(fact_10128_list__encode_Opelims,axiom,
% 5.64/6.01 ! [X2: list_nat,Y4: nat] :
% 5.64/6.01 ( ( ( nat_list_encode @ X2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 5.64/6.01 => ( ( ( X2 = nil_nat )
% 5.64/6.01 => ( ( Y4 = zero_zero_nat )
% 5.64/6.01 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.64/6.01 => ~ ! [X4: nat,Xs3: list_nat] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( cons_nat @ X4 @ Xs3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.64/6.01 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X4 @ Xs3 ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % list_encode.pelims
% 5.64/6.01 thf(fact_10129_quotient__of__def,axiom,
% 5.64/6.01 ( quotient_of
% 5.64/6.01 = ( ^ [X: rat] :
% 5.64/6.01 ( the_Pr4378521158711661632nt_int
% 5.64/6.01 @ ^ [Pair: product_prod_int_int] :
% 5.64/6.01 ( ( X
% 5.64/6.01 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.64/6.01 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.64/6.01 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % quotient_of_def
% 5.64/6.01 thf(fact_10130_normalize__stable,axiom,
% 5.64/6.01 ! [Q3: int,P2: int] :
% 5.64/6.01 ( ( ord_less_int @ zero_zero_int @ Q3 )
% 5.64/6.01 => ( ( algebr932160517623751201me_int @ P2 @ Q3 )
% 5.64/6.01 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.64/6.01 = ( product_Pair_int_int @ P2 @ Q3 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % normalize_stable
% 5.64/6.01 thf(fact_10131_Rat__cases,axiom,
% 5.64/6.01 ! [Q3: rat] :
% 5.64/6.01 ~ ! [A5: int,B5: int] :
% 5.64/6.01 ( ( Q3
% 5.64/6.01 = ( fract @ A5 @ B5 ) )
% 5.64/6.01 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.64/6.01 => ~ ( algebr932160517623751201me_int @ A5 @ B5 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rat_cases
% 5.64/6.01 thf(fact_10132_Rat__induct,axiom,
% 5.64/6.01 ! [P: rat > $o,Q3: rat] :
% 5.64/6.01 ( ! [A5: int,B5: int] :
% 5.64/6.01 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.64/6.01 => ( ( algebr932160517623751201me_int @ A5 @ B5 )
% 5.64/6.01 => ( P @ ( fract @ A5 @ B5 ) ) ) )
% 5.64/6.01 => ( P @ Q3 ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rat_induct
% 5.64/6.01 thf(fact_10133_coprime__crossproduct__int,axiom,
% 5.64/6.01 ! [A: int,D: int,B: int,C: int] :
% 5.64/6.01 ( ( algebr932160517623751201me_int @ A @ D )
% 5.64/6.01 => ( ( algebr932160517623751201me_int @ B @ C )
% 5.64/6.01 => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C ) )
% 5.64/6.01 = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 5.64/6.01 = ( ( ( abs_abs_int @ A )
% 5.64/6.01 = ( abs_abs_int @ B ) )
% 5.64/6.01 & ( ( abs_abs_int @ C )
% 5.64/6.01 = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_crossproduct_int
% 5.64/6.01 thf(fact_10134_Rat__cases__nonzero,axiom,
% 5.64/6.01 ! [Q3: rat] :
% 5.64/6.01 ( ! [A5: int,B5: int] :
% 5.64/6.01 ( ( Q3
% 5.64/6.01 = ( fract @ A5 @ B5 ) )
% 5.64/6.01 => ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.64/6.01 => ( ( A5 != zero_zero_int )
% 5.64/6.01 => ~ ( algebr932160517623751201me_int @ A5 @ B5 ) ) ) )
% 5.64/6.01 => ( Q3 = zero_zero_rat ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rat_cases_nonzero
% 5.64/6.01 thf(fact_10135_quotient__of__unique,axiom,
% 5.64/6.01 ! [R2: rat] :
% 5.64/6.01 ? [X4: product_prod_int_int] :
% 5.64/6.01 ( ( R2
% 5.64/6.01 = ( fract @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.64/6.01 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X4 ) )
% 5.64/6.01 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) )
% 5.64/6.01 & ! [Y5: product_prod_int_int] :
% 5.64/6.01 ( ( ( R2
% 5.64/6.01 = ( fract @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.64/6.01 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y5 ) )
% 5.64/6.01 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y5 ) @ ( product_snd_int_int @ Y5 ) ) )
% 5.64/6.01 => ( Y5 = X4 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % quotient_of_unique
% 5.64/6.01 thf(fact_10136_coprime__common__divisor__nat,axiom,
% 5.64/6.01 ! [A: nat,B: nat,X2: nat] :
% 5.64/6.01 ( ( algebr934650988132801477me_nat @ A @ B )
% 5.64/6.01 => ( ( dvd_dvd_nat @ X2 @ A )
% 5.64/6.01 => ( ( dvd_dvd_nat @ X2 @ B )
% 5.64/6.01 => ( X2 = one_one_nat ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_common_divisor_nat
% 5.64/6.01 thf(fact_10137_coprime__Suc__0__right,axiom,
% 5.64/6.01 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_Suc_0_right
% 5.64/6.01 thf(fact_10138_coprime__Suc__0__left,axiom,
% 5.64/6.01 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_Suc_0_left
% 5.64/6.01 thf(fact_10139_coprime__crossproduct__nat,axiom,
% 5.64/6.01 ! [A: nat,D: nat,B: nat,C: nat] :
% 5.64/6.01 ( ( algebr934650988132801477me_nat @ A @ D )
% 5.64/6.01 => ( ( algebr934650988132801477me_nat @ B @ C )
% 5.64/6.01 => ( ( ( times_times_nat @ A @ C )
% 5.64/6.01 = ( times_times_nat @ B @ D ) )
% 5.64/6.01 = ( ( A = B )
% 5.64/6.01 & ( C = D ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_crossproduct_nat
% 5.64/6.01 thf(fact_10140_coprime__Suc__left__nat,axiom,
% 5.64/6.01 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_Suc_left_nat
% 5.64/6.01 thf(fact_10141_coprime__Suc__right__nat,axiom,
% 5.64/6.01 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_Suc_right_nat
% 5.64/6.01 thf(fact_10142_coprime__diff__one__left__nat,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_diff_one_left_nat
% 5.64/6.01 thf(fact_10143_coprime__diff__one__right__nat,axiom,
% 5.64/6.01 ! [N: nat] :
% 5.64/6.01 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.64/6.01 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % coprime_diff_one_right_nat
% 5.64/6.01 thf(fact_10144_Rats__abs__nat__div__natE,axiom,
% 5.64/6.01 ! [X2: real] :
% 5.64/6.01 ( ( member_real @ X2 @ field_5140801741446780682s_real )
% 5.64/6.01 => ~ ! [M4: nat,N3: nat] :
% 5.64/6.01 ( ( N3 != zero_zero_nat )
% 5.64/6.01 => ( ( ( abs_abs_real @ X2 )
% 5.64/6.01 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M4 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.64/6.01 => ~ ( algebr934650988132801477me_nat @ M4 @ N3 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rats_abs_nat_div_natE
% 5.64/6.01 thf(fact_10145_sort__upt,axiom,
% 5.64/6.01 ! [M: nat,N: nat] :
% 5.64/6.01 ( ( linord738340561235409698at_nat
% 5.64/6.01 @ ^ [X: nat] : X
% 5.64/6.01 @ ( upt @ M @ N ) )
% 5.64/6.01 = ( upt @ M @ N ) ) ).
% 5.64/6.01
% 5.64/6.01 % sort_upt
% 5.64/6.01 thf(fact_10146_sort__upto,axiom,
% 5.64/6.01 ! [I: int,J: int] :
% 5.64/6.01 ( ( linord1735203802627413978nt_int
% 5.64/6.01 @ ^ [X: int] : X
% 5.64/6.01 @ ( upto @ I @ J ) )
% 5.64/6.01 = ( upto @ I @ J ) ) ).
% 5.64/6.01
% 5.64/6.01 % sort_upto
% 5.64/6.01 thf(fact_10147_of__nat__eq__id,axiom,
% 5.64/6.01 semiri1316708129612266289at_nat = id_nat ).
% 5.64/6.01
% 5.64/6.01 % of_nat_eq_id
% 5.64/6.01 thf(fact_10148_Rat_Opositive__def,axiom,
% 5.64/6.01 ( positive
% 5.64/6.01 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.64/6.01 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rat.positive_def
% 5.64/6.01 thf(fact_10149_vanishes__mult__bounded,axiom,
% 5.64/6.01 ! [X8: nat > rat,Y7: nat > rat] :
% 5.64/6.01 ( ? [A8: rat] :
% 5.64/6.01 ( ( ord_less_rat @ zero_zero_rat @ A8 )
% 5.64/6.01 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A8 ) )
% 5.64/6.01 => ( ( vanishes @ Y7 )
% 5.64/6.01 => ( vanishes
% 5.64/6.01 @ ^ [N2: nat] : ( times_times_rat @ ( X8 @ N2 ) @ ( Y7 @ N2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % vanishes_mult_bounded
% 5.64/6.01 thf(fact_10150_of__rat__dense,axiom,
% 5.64/6.01 ! [X2: real,Y4: real] :
% 5.64/6.01 ( ( ord_less_real @ X2 @ Y4 )
% 5.64/6.01 => ? [Q2: rat] :
% 5.64/6.01 ( ( ord_less_real @ X2 @ ( field_7254667332652039916t_real @ Q2 ) )
% 5.64/6.01 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q2 ) @ Y4 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % of_rat_dense
% 5.64/6.01 thf(fact_10151_vanishesD,axiom,
% 5.64/6.01 ! [X8: nat > rat,R2: rat] :
% 5.64/6.01 ( ( vanishes @ X8 )
% 5.64/6.01 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.64/6.01 => ? [K3: nat] :
% 5.64/6.01 ! [N7: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.64/6.01 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N7 ) ) @ R2 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % vanishesD
% 5.64/6.01 thf(fact_10152_vanishesI,axiom,
% 5.64/6.01 ! [X8: nat > rat] :
% 5.64/6.01 ( ! [R3: rat] :
% 5.64/6.01 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.64/6.01 => ? [K4: nat] :
% 5.64/6.01 ! [N3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.64/6.01 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R3 ) ) )
% 5.64/6.01 => ( vanishes @ X8 ) ) ).
% 5.64/6.01
% 5.64/6.01 % vanishesI
% 5.64/6.01 thf(fact_10153_vanishes__def,axiom,
% 5.64/6.01 ( vanishes
% 5.64/6.01 = ( ^ [X5: nat > rat] :
% 5.64/6.01 ! [R5: rat] :
% 5.64/6.01 ( ( ord_less_rat @ zero_zero_rat @ R5 )
% 5.64/6.01 => ? [K2: nat] :
% 5.64/6.01 ! [N2: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.64/6.01 => ( ord_less_rat @ ( abs_abs_rat @ ( X5 @ N2 ) ) @ R5 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % vanishes_def
% 5.64/6.01 thf(fact_10154_plus__rat__def,axiom,
% 5.64/6.01 ( plus_plus_rat
% 5.64/6.01 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.64/6.01 @ ^ [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 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % plus_rat_def
% 5.64/6.01 thf(fact_10155_times__rat__def,axiom,
% 5.64/6.01 ( times_times_rat
% 5.64/6.01 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.64/6.01 @ ^ [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 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % times_rat_def
% 5.64/6.01 thf(fact_10156_plus__rat_Oabs__eq,axiom,
% 5.64/6.01 ! [Xa2: product_prod_int_int,X2: product_prod_int_int] :
% 5.64/6.01 ( ( ratrel @ Xa2 @ Xa2 )
% 5.64/6.01 => ( ( ratrel @ X2 @ X2 )
% 5.64/6.01 => ( ( plus_plus_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X2 ) )
% 5.64/6.01 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_snd_int_int @ X2 ) ) @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % plus_rat.abs_eq
% 5.64/6.01 thf(fact_10157_Rat_Opositive_Oabs__eq,axiom,
% 5.64/6.01 ! [X2: product_prod_int_int] :
% 5.64/6.01 ( ( ratrel @ X2 @ X2 )
% 5.64/6.01 => ( ( positive @ ( abs_Rat @ X2 ) )
% 5.64/6.01 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rat.positive.abs_eq
% 5.64/6.01 thf(fact_10158_ratrel__iff,axiom,
% 5.64/6.01 ( ratrel
% 5.64/6.01 = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.64/6.01 ( ( ( product_snd_int_int @ X )
% 5.64/6.01 != zero_zero_int )
% 5.64/6.01 & ( ( product_snd_int_int @ Y )
% 5.64/6.01 != zero_zero_int )
% 5.64/6.01 & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 5.64/6.01 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % ratrel_iff
% 5.64/6.01 thf(fact_10159_ratrel__def,axiom,
% 5.64/6.01 ( ratrel
% 5.64/6.01 = ( ^ [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.64/6.01 ( ( ( product_snd_int_int @ X )
% 5.64/6.01 != zero_zero_int )
% 5.64/6.01 & ( ( product_snd_int_int @ Y )
% 5.64/6.01 != zero_zero_int )
% 5.64/6.01 & ( ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Y ) )
% 5.64/6.01 = ( times_times_int @ ( product_fst_int_int @ Y ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % ratrel_def
% 5.64/6.01 thf(fact_10160_times__rat_Oabs__eq,axiom,
% 5.64/6.01 ! [Xa2: product_prod_int_int,X2: product_prod_int_int] :
% 5.64/6.01 ( ( ratrel @ Xa2 @ Xa2 )
% 5.64/6.01 => ( ( ratrel @ X2 @ X2 )
% 5.64/6.01 => ( ( times_times_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X2 ) )
% 5.64/6.01 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_fst_int_int @ X2 ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X2 ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % times_rat.abs_eq
% 5.64/6.01 thf(fact_10161_Rat_Opositive_Orsp,axiom,
% 5.64/6.01 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.64/6.01 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Rat.positive.rsp
% 5.64/6.01 thf(fact_10162_and__not__num_Opelims,axiom,
% 5.64/6.01 ! [X2: num,Xa2: num,Y4: option_num] :
% 5.64/6.01 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4 = none_num )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ one ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4 = none_num )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.64/6.01 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.64/6.01 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ~ ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % and_not_num.pelims
% 5.64/6.01 thf(fact_10163_and__num_Opelims,axiom,
% 5.64/6.01 ! [X2: num,Xa2: num,Y4: option_num] :
% 5.64/6.01 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ one ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4 = none_num )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ one ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4 = none_num )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ one ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ~ ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.64/6.01 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.64/6.01 @ ( bit_un7362597486090784418nd_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % and_num.pelims
% 5.64/6.01 thf(fact_10164_xor__num_Opelims,axiom,
% 5.64/6.01 ! [X2: num,Xa2: num,Y4: option_num] :
% 5.64/6.01 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4 = none_num )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( bit1 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( bit0 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( bit1 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( bit0 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.64/6.01 => ~ ! [M4: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ! [N3: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M4 @ N3 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % xor_num.pelims
% 5.64/6.01 thf(fact_10165_plus__rat_Orsp,axiom,
% 5.64/6.01 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.64/6.01 @ ^ [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 ) ) )
% 5.64/6.01 @ ^ [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 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % plus_rat.rsp
% 5.64/6.01 thf(fact_10166_times__rat_Orsp,axiom,
% 5.64/6.01 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.64/6.01 @ ^ [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 ) ) )
% 5.64/6.01 @ ^ [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 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % times_rat.rsp
% 5.64/6.01 thf(fact_10167_less__integer_Orsp,axiom,
% 5.64/6.01 ( bNF_re3403563459893282935_int_o
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re5089333283451836215nt_o_o
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ord_less_int
% 5.64/6.01 @ ord_less_int ) ).
% 5.64/6.01
% 5.64/6.01 % less_integer.rsp
% 5.64/6.01 thf(fact_10168_less__natural_Orsp,axiom,
% 5.64/6.01 ( bNF_re578469030762574527_nat_o
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re4705727531993890431at_o_o
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ord_less_nat
% 5.64/6.01 @ ord_less_nat ) ).
% 5.64/6.01
% 5.64/6.01 % less_natural.rsp
% 5.64/6.01 thf(fact_10169_divide__natural_Orsp,axiom,
% 5.64/6.01 ( bNF_re1345281282404953727at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re5653821019739307937at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/6.01 @ divide_divide_nat
% 5.64/6.01 @ divide_divide_nat ) ).
% 5.64/6.01
% 5.64/6.01 % divide_natural.rsp
% 5.64/6.01 thf(fact_10170_divide__integer_Orsp,axiom,
% 5.64/6.01 ( bNF_re711492959462206631nt_int
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re4712519889275205905nt_int
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/6.01 @ divide_divide_int
% 5.64/6.01 @ divide_divide_int ) ).
% 5.64/6.01
% 5.64/6.01 % divide_integer.rsp
% 5.64/6.01 thf(fact_10171_times__integer_Orsp,axiom,
% 5.64/6.01 ( bNF_re711492959462206631nt_int
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re4712519889275205905nt_int
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: int,Z3: int] : ( Y6 = Z3 ) )
% 5.64/6.01 @ times_times_int
% 5.64/6.01 @ times_times_int ) ).
% 5.64/6.01
% 5.64/6.01 % times_integer.rsp
% 5.64/6.01 thf(fact_10172_times__natural_Orsp,axiom,
% 5.64/6.01 ( bNF_re1345281282404953727at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re5653821019739307937at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/6.01 @ times_times_nat
% 5.64/6.01 @ times_times_nat ) ).
% 5.64/6.01
% 5.64/6.01 % times_natural.rsp
% 5.64/6.01 thf(fact_10173_Suc_Orsp,axiom,
% 5.64/6.01 ( bNF_re5653821019739307937at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ suc
% 5.64/6.01 @ suc ) ).
% 5.64/6.01
% 5.64/6.01 % Suc.rsp
% 5.64/6.01 thf(fact_10174_plus__natural_Orsp,axiom,
% 5.64/6.01 ( bNF_re1345281282404953727at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re5653821019739307937at_nat
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 ) )
% 5.64/6.01 @ plus_plus_nat
% 5.64/6.01 @ plus_plus_nat ) ).
% 5.64/6.01
% 5.64/6.01 % plus_natural.rsp
% 5.64/6.01 thf(fact_10175_less__eq__natural_Orsp,axiom,
% 5.64/6.01 ( bNF_re578469030762574527_nat_o
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ( bNF_re4705727531993890431at_o_o
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ord_less_eq_nat
% 5.64/6.01 @ ord_less_eq_nat ) ).
% 5.64/6.01
% 5.64/6.01 % less_eq_natural.rsp
% 5.64/6.01 thf(fact_10176_or__not__num__neg_Opelims,axiom,
% 5.64/6.01 ! [X2: num,Xa2: num,Y4: num] :
% 5.64/6.01 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.64/6.01 = Y4 )
% 5.64/6.01 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X2 @ Xa2 ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4 = one )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [M4: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.64/6.01 => ( ( ( X2 = one )
% 5.64/6.01 => ! [M4: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.64/6.01 => ( ! [N3: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bit0 @ one ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [N3: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ! [M4: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.64/6.01 => ( ! [N3: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit0 @ N3 ) )
% 5.64/6.01 => ! [M4: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.64/6.01 => ( ! [N3: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ( ( Xa2 = one )
% 5.64/6.01 => ( ( Y4 = one )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.64/6.01 => ( ! [N3: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ! [M4: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit0 @ M4 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.64/6.01 => ~ ! [N3: num] :
% 5.64/6.01 ( ( X2
% 5.64/6.01 = ( bit1 @ N3 ) )
% 5.64/6.01 => ! [M4: num] :
% 5.64/6.01 ( ( Xa2
% 5.64/6.01 = ( bit1 @ M4 ) )
% 5.64/6.01 => ( ( Y4
% 5.64/6.01 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.64/6.01 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % or_not_num_neg.pelims
% 5.64/6.01 thf(fact_10177_plus__rat_Otransfer,axiom,
% 5.64/6.01 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.64/6.01 @ ^ [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 ) ) )
% 5.64/6.01 @ plus_plus_rat ) ).
% 5.64/6.01
% 5.64/6.01 % plus_rat.transfer
% 5.64/6.01 thf(fact_10178_Rat_Opositive_Otransfer,axiom,
% 5.64/6.01 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 )
% 5.64/6.01 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) )
% 5.64/6.01 @ positive ) ).
% 5.64/6.01
% 5.64/6.01 % Rat.positive.transfer
% 5.64/6.01 thf(fact_10179_times__rat_Otransfer,axiom,
% 5.64/6.01 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.64/6.01 @ ^ [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 ) ) )
% 5.64/6.01 @ times_times_rat ) ).
% 5.64/6.01
% 5.64/6.01 % times_rat.transfer
% 5.64/6.01 thf(fact_10180_times__int_Otransfer,axiom,
% 5.64/6.01 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 5.64/6.01 @ times_times_int ) ).
% 5.64/6.01
% 5.64/6.01 % times_int.transfer
% 5.64/6.01 thf(fact_10181_minus__int_Otransfer,axiom,
% 5.64/6.01 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 5.64/6.01 @ minus_minus_int ) ).
% 5.64/6.01
% 5.64/6.01 % minus_int.transfer
% 5.64/6.01 thf(fact_10182_zero__int_Otransfer,axiom,
% 5.64/6.01 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.64/6.01
% 5.64/6.01 % zero_int.transfer
% 5.64/6.01 thf(fact_10183_int__transfer,axiom,
% 5.64/6.01 ( bNF_re6830278522597306478at_int
% 5.64/6.01 @ ^ [Y6: nat,Z3: nat] : ( Y6 = Z3 )
% 5.64/6.01 @ pcr_int
% 5.64/6.01 @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 5.64/6.01 @ semiri1314217659103216013at_int ) ).
% 5.64/6.01
% 5.64/6.01 % int_transfer
% 5.64/6.01 thf(fact_10184_uminus__int_Otransfer,axiom,
% 5.64/6.01 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.64/6.01 @ ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 5.64/6.01 @ uminus_uminus_int ) ).
% 5.64/6.01
% 5.64/6.01 % uminus_int.transfer
% 5.64/6.01 thf(fact_10185_one__int_Otransfer,axiom,
% 5.64/6.01 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.64/6.01
% 5.64/6.01 % one_int.transfer
% 5.64/6.01 thf(fact_10186_less__int_Otransfer,axiom,
% 5.64/6.01 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.64/6.01 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.64/6.01 @ ord_less_int ) ).
% 5.64/6.01
% 5.64/6.01 % less_int.transfer
% 5.64/6.01 thf(fact_10187_less__eq__int_Otransfer,axiom,
% 5.64/6.01 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.64/6.01 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.64/6.01 @ ord_less_eq_int ) ).
% 5.64/6.01
% 5.64/6.01 % less_eq_int.transfer
% 5.64/6.01 thf(fact_10188_plus__int_Otransfer,axiom,
% 5.64/6.01 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.64/6.01 @ plus_plus_int ) ).
% 5.64/6.01
% 5.64/6.01 % plus_int.transfer
% 5.64/6.01 thf(fact_10189_times__int_Orsp,axiom,
% 5.64/6.01 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y @ U2 ) ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % times_int.rsp
% 5.64/6.01 thf(fact_10190_intrel__iff,axiom,
% 5.64/6.01 ! [X2: nat,Y4: nat,U: nat,V: nat] :
% 5.64/6.01 ( ( intrel @ ( product_Pair_nat_nat @ X2 @ Y4 ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.64/6.01 = ( ( plus_plus_nat @ X2 @ V )
% 5.64/6.01 = ( plus_plus_nat @ U @ Y4 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % intrel_iff
% 5.64/6.01 thf(fact_10191_uminus__int_Orsp,axiom,
% 5.64/6.01 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.64/6.01 @ ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) )
% 5.64/6.01 @ ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] : ( product_Pair_nat_nat @ Y @ X ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % uminus_int.rsp
% 5.64/6.01 thf(fact_10192_zero__int_Orsp,axiom,
% 5.64/6.01 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.64/6.01
% 5.64/6.01 % zero_int.rsp
% 5.64/6.01 thf(fact_10193_one__int_Orsp,axiom,
% 5.64/6.01 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.64/6.01
% 5.64/6.01 % one_int.rsp
% 5.64/6.01 thf(fact_10194_intrel__def,axiom,
% 5.64/6.01 ( intrel
% 5.64/6.01 = ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] :
% 5.64/6.01 ( ( plus_plus_nat @ X @ V4 )
% 5.64/6.01 = ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % intrel_def
% 5.64/6.01 thf(fact_10195_less__int_Orsp,axiom,
% 5.64/6.01 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.64/6.01 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.64/6.01 @ ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % less_int.rsp
% 5.64/6.01 thf(fact_10196_less__eq__int_Orsp,axiom,
% 5.64/6.01 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.64/6.01 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.64/6.01 @ ^ [Y6: $o,Z3: $o] : ( Y6 = Z3 ) )
% 5.64/6.01 @ ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) )
% 5.64/6.01 @ ( produc8739625826339149834_nat_o
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc6081775807080527818_nat_o
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % less_eq_int.rsp
% 5.64/6.01 thf(fact_10197_plus__int_Orsp,axiom,
% 5.64/6.01 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y @ V4 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % plus_int.rsp
% 5.64/6.01 thf(fact_10198_minus__int_Orsp,axiom,
% 5.64/6.01 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) )
% 5.64/6.01 @ ( produc27273713700761075at_nat
% 5.64/6.01 @ ^ [X: nat,Y: nat] :
% 5.64/6.01 ( produc2626176000494625587at_nat
% 5.64/6.01 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y @ U2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % minus_int.rsp
% 5.64/6.01 thf(fact_10199_rcis__inverse,axiom,
% 5.64/6.01 ! [R2: real,A: real] :
% 5.64/6.01 ( ( invers8013647133539491842omplex @ ( rcis @ R2 @ A ) )
% 5.64/6.01 = ( rcis @ ( divide_divide_real @ one_one_real @ R2 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % rcis_inverse
% 5.64/6.01 thf(fact_10200_Re__rcis,axiom,
% 5.64/6.01 ! [R2: real,A: real] :
% 5.64/6.01 ( ( re @ ( rcis @ R2 @ A ) )
% 5.64/6.01 = ( times_times_real @ R2 @ ( cos_real @ A ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Re_rcis
% 5.64/6.01 thf(fact_10201_Im__rcis,axiom,
% 5.64/6.01 ! [R2: real,A: real] :
% 5.64/6.01 ( ( im @ ( rcis @ R2 @ A ) )
% 5.64/6.01 = ( times_times_real @ R2 @ ( sin_real @ A ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % Im_rcis
% 5.64/6.01 thf(fact_10202_rcis__mult,axiom,
% 5.64/6.01 ! [R1: real,A: real,R22: real,B: real] :
% 5.64/6.01 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.64/6.01 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % rcis_mult
% 5.64/6.01 thf(fact_10203_rcis__divide,axiom,
% 5.64/6.01 ! [R1: real,A: real,R22: real,B: real] :
% 5.64/6.01 ( ( divide1717551699836669952omplex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 5.64/6.01 = ( rcis @ ( divide_divide_real @ R1 @ R22 ) @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % rcis_divide
% 5.64/6.01 thf(fact_10204_rcis__def,axiom,
% 5.64/6.01 ( rcis
% 5.64/6.01 = ( ^ [R5: real,A3: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R5 ) @ ( cis @ A3 ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % rcis_def
% 5.64/6.01 thf(fact_10205_DeMoivre2,axiom,
% 5.64/6.01 ! [R2: real,A: real,N: nat] :
% 5.64/6.01 ( ( power_power_complex @ ( rcis @ R2 @ A ) @ N )
% 5.64/6.01 = ( rcis @ ( power_power_real @ R2 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % DeMoivre2
% 5.64/6.01 thf(fact_10206_cauchyD,axiom,
% 5.64/6.01 ! [X8: nat > rat,R2: rat] :
% 5.64/6.01 ( ( cauchy @ X8 )
% 5.64/6.01 => ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.64/6.01 => ? [K3: nat] :
% 5.64/6.01 ! [M5: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K3 @ M5 )
% 5.64/6.01 => ! [N7: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K3 @ N7 )
% 5.64/6.01 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M5 ) @ ( X8 @ N7 ) ) ) @ R2 ) ) ) ) ) ).
% 5.64/6.01
% 5.64/6.01 % cauchyD
% 5.64/6.01 thf(fact_10207_cauchyI,axiom,
% 5.64/6.01 ! [X8: nat > rat] :
% 5.64/6.01 ( ! [R3: rat] :
% 5.64/6.01 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.64/6.01 => ? [K4: nat] :
% 5.64/6.01 ! [M4: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K4 @ M4 )
% 5.64/6.01 => ! [N3: nat] :
% 5.64/6.01 ( ( ord_less_eq_nat @ K4 @ N3 )
% 5.64/6.01 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M4 ) @ ( X8 @ N3 ) ) ) @ R3 ) ) ) )
% 5.64/6.01 => ( cauchy @ X8 ) ) ).
% 5.64/6.01
% 5.64/6.01 % cauchyI
% 5.64/6.01
% 5.64/6.01 % Helper facts (42)
% 5.64/6.01 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.64/6.01 ! [X2: int,Y4: int] :
% 5.64/6.01 ( ( if_int @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.64/6.01 ! [X2: int,Y4: int] :
% 5.64/6.01 ( ( if_int @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.64/6.01 ! [X2: nat,Y4: nat] :
% 5.64/6.01 ( ( if_nat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.64/6.01 ! [X2: nat,Y4: nat] :
% 5.64/6.01 ( ( if_nat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.64/6.01 ! [X2: num,Y4: num] :
% 5.64/6.01 ( ( if_num @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.64/6.01 ! [X2: num,Y4: num] :
% 5.64/6.01 ( ( if_num @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.64/6.01 ! [X2: rat,Y4: rat] :
% 5.64/6.01 ( ( if_rat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.64/6.01 ! [X2: rat,Y4: rat] :
% 5.64/6.01 ( ( if_rat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.64/6.01 ! [X2: real,Y4: real] :
% 5.64/6.01 ( ( if_real @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.64/6.01 ! [X2: real,Y4: real] :
% 5.64/6.01 ( ( if_real @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.64/6.01 ! [P: real > $o] :
% 5.64/6.01 ( ( P @ ( fChoice_real @ P ) )
% 5.64/6.01 = ( ? [X5: real] : ( P @ X5 ) ) ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.64/6.01 ! [X2: complex,Y4: complex] :
% 5.64/6.01 ( ( if_complex @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.64/6.01 ! [X2: complex,Y4: complex] :
% 5.64/6.01 ( ( if_complex @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.64/6.01 ! [X2: extended_enat,Y4: extended_enat] :
% 5.64/6.01 ( ( if_Extended_enat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.64/6.01 ! [X2: extended_enat,Y4: extended_enat] :
% 5.64/6.01 ( ( if_Extended_enat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.64/6.01 ! [X2: code_integer,Y4: code_integer] :
% 5.64/6.01 ( ( if_Code_integer @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.64/6.01 ! [X2: code_integer,Y4: code_integer] :
% 5.64/6.01 ( ( if_Code_integer @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: set_int,Y4: set_int] :
% 5.64/6.01 ( ( if_set_int @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: set_int,Y4: set_int] :
% 5.64/6.01 ( ( if_set_int @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: set_nat,Y4: set_nat] :
% 5.64/6.01 ( ( if_set_nat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: set_nat,Y4: set_nat] :
% 5.64/6.01 ( ( if_set_nat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Y4: vEBT_VEBT] :
% 5.64/6.01 ( ( if_VEBT_VEBT @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.64/6.01 ! [X2: vEBT_VEBT,Y4: vEBT_VEBT] :
% 5.64/6.01 ( ( if_VEBT_VEBT @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: list_int,Y4: list_int] :
% 5.64/6.01 ( ( if_list_int @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: list_int,Y4: list_int] :
% 5.64/6.01 ( ( if_list_int @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: list_nat,Y4: list_nat] :
% 5.64/6.01 ( ( if_list_nat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: list_nat,Y4: list_nat] :
% 5.64/6.01 ( ( if_list_nat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: int > int,Y4: int > int] :
% 5.64/6.01 ( ( if_int_int @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: int > int,Y4: int > int] :
% 5.64/6.01 ( ( if_int_int @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: option_nat,Y4: option_nat] :
% 5.64/6.01 ( ( if_option_nat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: option_nat,Y4: option_nat] :
% 5.64/6.01 ( ( if_option_nat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.64/6.01 ! [X2: option_num,Y4: option_num] :
% 5.64/6.01 ( ( if_option_num @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.64/6.01 ! [X2: option_num,Y4: option_num] :
% 5.64/6.01 ( ( if_option_num @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: product_prod_int_int,Y4: product_prod_int_int] :
% 5.64/6.01 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.64/6.01 ! [X2: product_prod_int_int,Y4: product_prod_int_int] :
% 5.64/6.01 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.64/6.01 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y4 )
% 5.64/6.01 = Y4 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.64/6.01 ! [X2: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.64/6.01 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y4 )
% 5.64/6.01 = X2 ) ).
% 5.64/6.01
% 5.64/6.01 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 7.01/7.29 ! [X2: produc6271795597528267376eger_o,Y4: produc6271795597528267376eger_o] :
% 7.01/7.29 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y4 )
% 7.01/7.29 = Y4 ) ).
% 7.01/7.29
% 7.01/7.29 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 7.01/7.29 ! [X2: produc6271795597528267376eger_o,Y4: produc6271795597528267376eger_o] :
% 7.01/7.29 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y4 )
% 7.01/7.29 = X2 ) ).
% 7.01/7.29
% 7.01/7.29 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 7.01/7.29 ! [P: $o] :
% 7.01/7.29 ( ( P = $true )
% 7.01/7.29 | ( P = $false ) ) ).
% 7.01/7.29
% 7.01/7.29 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 7.01/7.29 ! [X2: produc8923325533196201883nteger,Y4: produc8923325533196201883nteger] :
% 7.01/7.29 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y4 )
% 7.01/7.29 = Y4 ) ).
% 7.01/7.29
% 7.01/7.29 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 7.01/7.29 ! [X2: produc8923325533196201883nteger,Y4: produc8923325533196201883nteger] :
% 7.01/7.29 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y4 )
% 7.01/7.29 = X2 ) ).
% 7.01/7.29
% 7.01/7.29 % Conjectures (1)
% 7.01/7.29 thf(conj_0,conjecture,
% 7.01/7.29 ord_less_eq_nat @ ( vEBT_T_m_e_m_b_e_r2 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ( plus_plus_nat @ one_one_nat @ ( vEBT_VEBT_height @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) ) ) ).
% 7.01/7.29
% 7.01/7.29 %------------------------------------------------------------------------------
% 7.01/7.29 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.6cCLW8s8y9/cvc5---1.0.5_11516.p...
% 7.01/7.29 (declare-sort $$unsorted 0)
% 7.01/7.29 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 7.01/7.29 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 7.01/7.29 (declare-sort tptp.produc1193250871479095198on_num 0)
% 7.01/7.29 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 7.01/7.29 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 7.01/7.29 (declare-sort tptp.produc3368934014287244435at_num 0)
% 7.01/7.29 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 7.01/7.29 (declare-sort tptp.produc7036089656553540234on_num 0)
% 7.01/7.29 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 7.01/7.29 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 7.01/7.29 (declare-sort tptp.produc3447558737645232053on_num 0)
% 7.01/7.29 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 7.01/7.29 (declare-sort tptp.produc2963631642982155120at_num 0)
% 7.01/7.29 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 7.01/7.29 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 7.01/7.29 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 7.01/7.29 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 7.01/7.29 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 7.01/7.29 (declare-sort tptp.produc8923325533196201883nteger 0)
% 7.01/7.29 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 7.01/7.29 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 7.01/7.29 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 7.01/7.29 (declare-sort tptp.set_Pr448751882837621926eger_o 0)
% 7.01/7.29 (declare-sort tptp.option4927543243414619207at_nat 0)
% 7.01/7.29 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 7.01/7.29 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 7.01/7.29 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 7.01/7.29 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 7.01/7.29 (declare-sort tptp.set_Pr8218934625190621173um_num 0)
% 7.01/7.29 (declare-sort tptp.set_Pr6200539531224447659at_num 0)
% 7.01/7.29 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 7.01/7.29 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 7.01/7.29 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 7.01/7.29 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 7.01/7.29 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 7.01/7.29 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 7.01/7.29 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 7.01/7.29 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 7.01/7.29 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 7.01/7.29 (declare-sort tptp.product_prod_num_num 0)
% 7.01/7.29 (declare-sort tptp.product_prod_nat_num 0)
% 7.01/7.29 (declare-sort tptp.product_prod_nat_nat 0)
% 7.01/7.29 (declare-sort tptp.product_prod_int_int 0)
% 7.01/7.29 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 7.01/7.29 (declare-sort tptp.set_list_complex 0)
% 7.01/7.29 (declare-sort tptp.list_VEBT_VEBT 0)
% 7.01/7.29 (declare-sort tptp.set_list_nat 0)
% 7.01/7.29 (declare-sort tptp.set_list_int 0)
% 7.01/7.29 (declare-sort tptp.product_prod_o_nat 0)
% 7.01/7.29 (declare-sort tptp.product_prod_o_int 0)
% 7.01/7.29 (declare-sort tptp.list_Code_integer 0)
% 7.01/7.29 (declare-sort tptp.set_VEBT_VEBT 0)
% 7.01/7.29 (declare-sort tptp.set_set_nat 0)
% 7.01/7.29 (declare-sort tptp.set_Code_integer 0)
% 7.01/7.29 (declare-sort tptp.set_Product_unit 0)
% 7.01/7.29 (declare-sort tptp.list_complex 0)
% 7.01/7.29 (declare-sort tptp.set_list_o 0)
% 7.01/7.29 (declare-sort tptp.product_prod_o_o 0)
% 7.01/7.29 (declare-sort tptp.set_complex 0)
% 7.01/7.29 (declare-sort tptp.filter_real 0)
% 7.01/7.29 (declare-sort tptp.option_num 0)
% 7.01/7.29 (declare-sort tptp.option_nat 0)
% 7.01/7.29 (declare-sort tptp.filter_nat 0)
% 7.01/7.29 (declare-sort tptp.set_char 0)
% 7.01/7.29 (declare-sort tptp.list_real 0)
% 7.01/7.29 (declare-sort tptp.set_real 0)
% 7.01/7.29 (declare-sort tptp.list_num 0)
% 7.01/7.29 (declare-sort tptp.list_nat 0)
% 7.01/7.29 (declare-sort tptp.list_int 0)
% 7.01/7.29 (declare-sort tptp.vEBT_VEBT 0)
% 7.01/7.29 (declare-sort tptp.set_rat 0)
% 7.01/7.29 (declare-sort tptp.set_num 0)
% 7.01/7.29 (declare-sort tptp.set_nat 0)
% 7.01/7.29 (declare-sort tptp.set_int 0)
% 7.01/7.29 (declare-sort tptp.code_integer 0)
% 7.01/7.29 (declare-sort tptp.extended_enat 0)
% 7.01/7.29 (declare-sort tptp.list_o 0)
% 7.01/7.29 (declare-sort tptp.complex 0)
% 7.01/7.29 (declare-sort tptp.set_o 0)
% 7.01/7.29 (declare-sort tptp.char 0)
% 7.01/7.29 (declare-sort tptp.real 0)
% 7.01/7.29 (declare-sort tptp.rat 0)
% 7.01/7.29 (declare-sort tptp.num 0)
% 7.01/7.29 (declare-sort tptp.nat 0)
% 7.01/7.29 (declare-sort tptp.int 0)
% 7.01/7.29 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 7.01/7.29 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 7.01/7.29 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 7.01/7.29 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 7.01/7.29 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 7.01/7.29 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 7.01/7.29 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.29 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.bNF_re6830278522597306478at_int ((-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.product_prod_nat_nat) (-> tptp.nat tptp.int)) Bool)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.01/7.29 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 7.01/7.29 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 7.01/7.29 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 7.01/7.29 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 7.01/7.29 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 7.01/7.29 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 7.01/7.29 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 7.01/7.29 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.01/7.29 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.01/7.29 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 7.01/7.29 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 7.01/7.29 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 7.01/7.29 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 7.01/7.29 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 7.01/7.29 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 7.01/7.29 (declare-fun tptp.im (tptp.complex) tptp.real)
% 7.01/7.29 (declare-fun tptp.re (tptp.complex) tptp.real)
% 7.01/7.29 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.imaginary_unit () tptp.complex)
% 7.01/7.29 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 7.01/7.29 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 7.01/7.29 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 7.01/7.29 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 7.01/7.29 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 7.01/7.29 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 7.01/7.29 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 7.01/7.29 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 7.01/7.29 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 7.01/7.29 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 7.01/7.29 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 7.01/7.29 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.01/7.29 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.01/7.29 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 7.01/7.29 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 7.01/7.29 (declare-fun tptp.at_top_real () tptp.filter_real)
% 7.01/7.29 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 7.01/7.29 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 7.01/7.29 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 7.01/7.29 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 7.01/7.29 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 7.01/7.29 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 7.01/7.29 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 7.01/7.29 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 7.01/7.29 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 7.01/7.29 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 7.01/7.29 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 7.01/7.29 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 7.01/7.29 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 7.01/7.29 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 7.01/7.29 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 7.01/7.29 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 7.01/7.29 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 7.01/7.29 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 7.01/7.29 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 7.01/7.29 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 7.01/7.29 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 7.01/7.29 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 7.01/7.29 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 7.01/7.29 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 7.01/7.29 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 7.01/7.29 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.id_o (Bool) Bool)
% 7.01/7.29 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 7.01/7.29 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 7.01/7.29 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 7.01/7.29 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 7.01/7.29 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.01/7.29 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.01/7.29 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 7.01/7.29 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.01/7.29 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.29 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.01/7.29 (declare-fun tptp.minus_5127226145743854075T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.one_one_complex () tptp.complex)
% 7.01/7.29 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.one_one_int () tptp.int)
% 7.01/7.29 (declare-fun tptp.one_one_nat () tptp.nat)
% 7.01/7.29 (declare-fun tptp.one_one_rat () tptp.rat)
% 7.01/7.29 (declare-fun tptp.one_one_real () tptp.real)
% 7.01/7.29 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 7.01/7.29 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.zero_zero_int () tptp.int)
% 7.01/7.29 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 7.01/7.29 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 7.01/7.29 (declare-fun tptp.zero_zero_real () tptp.real)
% 7.01/7.29 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups769130701875090982BT_int ((-> tptp.vEBT_VEBT tptp.int) tptp.set_VEBT_VEBT) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups771621172384141258BT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups136491112297645522BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups2240296850493347238T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups858564598930262913ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 7.01/7.29 (declare-fun tptp.groups4694064378042380927al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 7.01/7.29 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups5726676334696518183BT_rat ((-> tptp.vEBT_VEBT tptp.rat) tptp.set_VEBT_VEBT) tptp.rat)
% 7.01/7.29 (declare-fun tptp.groups2703838992350267259T_real ((-> tptp.vEBT_VEBT tptp.real) tptp.set_VEBT_VEBT) tptp.real)
% 7.01/7.29 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 7.01/7.29 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 7.01/7.29 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 7.01/7.29 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 7.01/7.29 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.01/7.29 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 7.01/7.29 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.01/7.29 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.01/7.29 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 7.01/7.29 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 7.01/7.29 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 7.01/7.29 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.01/7.29 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 7.01/7.29 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 7.01/7.29 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 7.01/7.29 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 7.01/7.29 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 7.01/7.29 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 7.01/7.29 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 7.01/7.29 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.29 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 7.01/7.29 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 7.01/7.29 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 7.01/7.29 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.nil_int () tptp.list_int)
% 7.01/7.29 (declare-fun tptp.nil_nat () tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 7.01/7.29 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 7.01/7.29 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 7.01/7.29 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.29 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 7.01/7.29 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 7.01/7.29 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 7.01/7.29 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.list_u6180841689913720943at_nat (tptp.list_P6011104703257516679at_nat tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 7.01/7.29 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 7.01/7.29 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 7.01/7.29 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 7.01/7.29 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 7.01/7.29 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 7.01/7.29 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 7.01/7.29 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 7.01/7.29 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 7.01/7.29 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 7.01/7.29 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 7.01/7.29 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 7.01/7.29 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 7.01/7.29 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 7.01/7.29 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 7.01/7.29 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 7.01/7.29 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 7.01/7.29 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 7.01/7.29 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 7.01/7.29 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 7.01/7.29 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 7.01/7.29 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 7.01/7.29 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 7.01/7.29 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 7.01/7.29 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 7.01/7.29 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 7.01/7.29 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 7.01/7.29 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 7.01/7.29 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 7.01/7.29 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 7.01/7.29 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 7.01/7.29 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 7.01/7.29 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 7.01/7.29 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 7.01/7.29 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.01/7.29 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 7.01/7.29 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 7.01/7.29 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 7.01/7.29 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 7.01/7.29 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 7.01/7.29 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 7.01/7.29 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 7.01/7.29 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.inc (tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 7.01/7.29 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 7.01/7.29 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 7.01/7.29 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 7.01/7.29 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 7.01/7.29 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.one () tptp.num)
% 7.01/7.29 (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)
% 7.01/7.29 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 7.01/7.29 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 7.01/7.29 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 7.01/7.29 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 7.01/7.29 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 7.01/7.29 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 7.01/7.29 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 7.01/7.29 (declare-fun tptp.none_nat () tptp.option_nat)
% 7.01/7.29 (declare-fun tptp.none_num () tptp.option_num)
% 7.01/7.29 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 7.01/7.29 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 7.01/7.29 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 7.01/7.29 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 7.01/7.29 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 7.01/7.29 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 7.01/7.29 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 7.01/7.29 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 7.01/7.29 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 7.01/7.29 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 7.01/7.29 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 7.01/7.29 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.bot_bo4731626569425807221er_o_o (tptp.code_integer Bool) Bool)
% 7.01/7.29 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 7.01/7.29 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 7.01/7.29 (declare-fun tptp.bot_bot_nat_num_o (tptp.nat tptp.num) Bool)
% 7.01/7.29 (declare-fun tptp.bot_bot_num_num_o (tptp.num tptp.num) Bool)
% 7.01/7.29 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 7.01/7.29 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 7.01/7.29 (declare-fun tptp.bot_bo5379713665208646970eger_o () tptp.set_Pr448751882837621926eger_o)
% 7.01/7.29 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 7.01/7.29 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.29 (declare-fun tptp.bot_bo7038385379056416535at_num () tptp.set_Pr6200539531224447659at_num)
% 7.01/7.29 (declare-fun tptp.bot_bo9056780473022590049um_num () tptp.set_Pr8218934625190621173um_num)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 7.01/7.29 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 7.01/7.29 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 7.01/7.29 (declare-fun tptp.ord_less_complex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 7.01/7.29 (declare-fun tptp.ord_le549003669493604880_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 7.01/7.29 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 7.01/7.29 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 7.01/7.29 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 7.01/7.29 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 7.01/7.29 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le3480810397992357184T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le2162486998276636481er_o_o ((-> tptp.code_integer Bool Bool) (-> tptp.code_integer Bool Bool)) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le3404735783095501756_num_o ((-> tptp.nat tptp.num Bool) (-> tptp.nat tptp.num Bool)) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le6124364862034508274_num_o ((-> tptp.num tptp.num Bool) (-> tptp.num tptp.num Bool)) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le8980329558974975238eger_o (tptp.set_Pr448751882837621926eger_o tptp.set_Pr448751882837621926eger_o) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le8085105155179020875at_num (tptp.set_Pr6200539531224447659at_num tptp.set_Pr6200539531224447659at_num) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le880128212290418581um_num (tptp.set_Pr8218934625190621173um_num tptp.set_Pr8218934625190621173um_num) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 7.01/7.30 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.30 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 7.01/7.30 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 7.01/7.30 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 7.01/7.30 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 7.01/7.30 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 7.01/7.30 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.01/7.30 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.01/7.30 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 7.01/7.30 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 7.01/7.30 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 7.01/7.30 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 7.01/7.30 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 7.01/7.30 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 7.01/7.30 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 7.01/7.30 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 7.01/7.30 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 7.01/7.30 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 7.01/7.30 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 7.01/7.30 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 7.01/7.30 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 7.01/7.30 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 7.01/7.30 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 7.01/7.30 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 7.01/7.30 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 7.01/7.30 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 7.01/7.30 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 7.01/7.30 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 7.01/7.30 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 7.01/7.30 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 7.01/7.30 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 7.01/7.30 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 7.01/7.30 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 7.01/7.30 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 7.01/7.30 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 7.01/7.30 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 7.01/7.30 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 7.01/7.30 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 7.01/7.30 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 7.01/7.30 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 7.01/7.30 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 7.01/7.30 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 7.01/7.30 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 7.01/7.30 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.30 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.01/7.30 (declare-fun tptp.produc7828578312038201481er_o_o ((-> tptp.code_integer Bool Bool) tptp.produc6271795597528267376eger_o) Bool)
% 7.01/7.30 (declare-fun tptp.produc1043322548047392435omplex ((-> tptp.code_integer Bool tptp.set_complex) tptp.produc6271795597528267376eger_o) tptp.set_complex)
% 7.01/7.30 (declare-fun tptp.produc1253318751659547953et_int ((-> tptp.code_integer Bool tptp.set_int) tptp.produc6271795597528267376eger_o) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.produc5431169771168744661et_nat ((-> tptp.code_integer Bool tptp.set_nat) tptp.produc6271795597528267376eger_o) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.produc242741666403216561t_real ((-> tptp.code_integer Bool tptp.set_real) tptp.produc6271795597528267376eger_o) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 7.01/7.30 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 7.01/7.30 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 7.01/7.30 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 7.01/7.30 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 7.01/7.30 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 7.01/7.30 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 7.01/7.30 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.01/7.30 (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)
% 7.01/7.30 (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)
% 7.01/7.30 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 7.01/7.30 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 7.01/7.30 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 7.01/7.30 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 7.01/7.30 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 7.01/7.30 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 7.01/7.30 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 7.01/7.30 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 7.01/7.30 (declare-fun tptp.produc6231982587499038204omplex ((-> tptp.nat tptp.num tptp.set_complex) tptp.product_prod_nat_num) tptp.set_complex)
% 7.01/7.30 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 7.01/7.30 (declare-fun tptp.produc2866383454006189126omplex ((-> tptp.num tptp.num tptp.set_complex) tptp.product_prod_num_num) tptp.set_complex)
% 7.01/7.30 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.produc8508995932063986495nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 7.01/7.30 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 7.01/7.30 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 7.01/7.30 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 7.01/7.30 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 7.01/7.30 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 7.01/7.30 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 7.01/7.30 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 7.01/7.30 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 7.01/7.30 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 7.01/7.30 (declare-fun tptp.positive (tptp.rat) Bool)
% 7.01/7.30 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 7.01/7.30 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 7.01/7.30 (declare-fun tptp.cauchy ((-> tptp.nat tptp.rat)) Bool)
% 7.01/7.30 (declare-fun tptp.vanishes ((-> tptp.nat tptp.rat)) Bool)
% 7.01/7.30 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 7.01/7.30 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 7.01/7.30 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 7.01/7.30 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 7.01/7.30 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 7.01/7.30 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 7.01/7.30 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 7.01/7.30 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 7.01/7.30 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 7.01/7.30 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 7.01/7.30 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 7.01/7.30 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 7.01/7.30 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 7.01/7.30 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 7.01/7.30 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 7.01/7.30 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 7.01/7.30 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 7.01/7.30 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 7.01/7.30 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 7.01/7.30 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 7.01/7.30 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 7.01/7.30 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 7.01/7.30 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 7.01/7.30 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.01/7.30 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 7.01/7.30 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 7.01/7.30 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 7.01/7.30 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 7.01/7.30 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 7.01/7.30 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 7.01/7.30 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 7.01/7.30 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 7.01/7.30 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 7.01/7.30 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 7.01/7.30 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 7.01/7.30 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.30 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 7.01/7.30 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 7.01/7.30 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 7.01/7.30 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.image_VEBT_VEBT_nat ((-> tptp.vEBT_VEBT tptp.nat) tptp.set_VEBT_VEBT) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 7.01/7.30 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 7.01/7.30 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.30 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 7.01/7.30 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.vimage_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 7.01/7.30 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 7.01/7.30 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 7.01/7.30 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 7.01/7.30 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 7.01/7.30 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 7.01/7.30 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 7.01/7.30 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 7.01/7.30 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 7.01/7.30 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 7.01/7.30 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 7.01/7.30 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 7.01/7.30 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 7.01/7.30 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 7.01/7.30 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 7.01/7.30 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 7.01/7.30 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 7.01/7.30 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 7.01/7.30 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 7.01/7.30 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 7.01/7.30 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 7.01/7.30 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 7.01/7.30 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 7.01/7.30 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 7.01/7.30 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 7.01/7.30 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 7.01/7.30 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.pi () tptp.real)
% 7.01/7.30 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 7.01/7.30 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 7.01/7.30 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 7.01/7.30 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.30 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_T_m_e_m_b_e_r (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_T_m_e_m_b_e_r2 (tptp.vEBT_VEBT tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_T8099345112685741742_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_T5837161174952499735_r_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_height (tptp.vEBT_VEBT) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_height_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 7.01/7.30 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 7.01/7.30 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 7.01/7.30 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 7.01/7.30 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 7.01/7.30 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 7.01/7.30 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 7.01/7.30 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 7.01/7.30 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 7.01/7.30 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.01/7.30 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 7.01/7.30 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 7.01/7.30 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 7.01/7.30 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 7.01/7.30 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 7.01/7.30 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 7.01/7.30 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 7.01/7.30 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 7.01/7.30 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 7.01/7.30 (declare-fun tptp.member1379723562493234055eger_o (tptp.produc6271795597528267376eger_o tptp.set_Pr448751882837621926eger_o) Bool)
% 7.01/7.30 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 7.01/7.30 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 7.01/7.30 (declare-fun tptp.member9148766508732265716at_num (tptp.product_prod_nat_num tptp.set_Pr6200539531224447659at_num) Bool)
% 7.01/7.30 (declare-fun tptp.member7279096912039735102um_num (tptp.product_prod_num_num tptp.set_Pr8218934625190621173um_num) Bool)
% 7.01/7.30 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 7.01/7.30 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 7.01/7.30 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 7.01/7.30 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 7.01/7.30 (declare-fun tptp.deg () tptp.nat)
% 7.01/7.30 (declare-fun tptp.m () tptp.nat)
% 7.01/7.30 (declare-fun tptp.ma () tptp.nat)
% 7.01/7.30 (declare-fun tptp.mi () tptp.nat)
% 7.01/7.30 (declare-fun tptp.na () tptp.nat)
% 7.01/7.30 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 7.01/7.30 (declare-fun tptp.xa () tptp.nat)
% 7.01/7.30 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 7.01/7.30 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((Summary tptp.vEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height Summary))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 tptp.summary) X2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height tptp.summary)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT T) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))))))
% 7.01/7.30 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 7.01/7.30 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 7.01/7.30 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y2)) (= X22 Y2))))
% 7.01/7.30 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y2)) (= X22 Y2))))
% 7.01/7.30 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y2)) (= X22 Y2))))
% 7.01/7.30 (assert (forall ((X1 tptp.code_integer) (X22 Bool) (Y1 tptp.code_integer) (Y2 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X22) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 7.01/7.30 (assert (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y2 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 7.01/7.30 (assert (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y2 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X22) (@ (@ tptp.product_Pair_nat_num Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 7.01/7.30 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 7.01/7.30 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 7.01/7.30 (assert (forall ((A tptp.code_integer) (B Bool) (A2 tptp.code_integer) (B2 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A2) B2)) (and (= A A2) (= B B2)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (A2 tptp.num) (B2 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A2) B2)) (and (= A A2) (= B B2)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.num) (A2 tptp.nat) (B2 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A2) B2)) (and (= A A2) (= B B2)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (and (= A A2) (= B B2)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (and (= A A2) (= B B2)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 7.01/7.30 (assert (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (and (@ _let_1 tptp.na) (@ _let_1 tptp.m))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 7.01/7.30 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 7.01/7.30 (assert (=> (= tptp.mi tptp.ma) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))))
% 7.01/7.30 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X3) tptp.na) (forall ((Xa tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X3) Xa)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height X3))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex)) (= (= tptp.one_one_complex X2) (= X2 tptp.one_one_complex))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real B3) A3))))
% 7.01/7.30 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat B3) A3))))
% 7.01/7.30 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.plus_plus_nat B3) A3))))
% 7.01/7.30 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int B3) A3))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 7.01/7.30 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 7.01/7.30 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 7.01/7.30 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 7.01/7.30 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 7.01/7.30 (assert (forall ((A4 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A4) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 7.01/7.30 (assert (forall ((A4 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 7.01/7.30 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A4) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 7.01/7.30 (assert (forall ((A4 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A4) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (= K L)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 7.01/7.30 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 7.01/7.30 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 7.01/7.30 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 7.01/7.30 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A4))) A4)))
% 7.01/7.30 (assert (forall ((A4 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A4))) A4)))
% 7.01/7.30 (assert (forall ((A4 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A4))) A4)))
% 7.01/7.30 (assert (forall ((A4 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A4))) A4)))
% 7.01/7.30 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A4))) A4)))
% 7.01/7.30 (assert (forall ((A4 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A4))) A4)))
% 7.01/7.30 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X4 tptp.complex)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X4 tptp.list_nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 7.01/7.30 (assert (forall ((A tptp.code_integer) (B Bool) (A2 tptp.code_integer) (B2 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A2) B2)) (not (=> (= A A2) (= B (not B2)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (A2 tptp.num) (B2 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.num) (A2 tptp.nat) (B2 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A5) B5))) (@ P P2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P2 tptp.product_prod_num_num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A5) B5))) (@ P P2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P2 tptp.product_prod_nat_num)) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A5) B5))) (@ P P2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A5) B5))) (@ P P2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P2 tptp.product_prod_int_int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A5) B5))) (@ P P2))))
% 7.01/7.30 (assert (forall ((P2 tptp.produc6271795597528267376eger_o)) (exists ((X4 tptp.code_integer) (Y3 Bool)) (= P2 (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)))))
% 7.01/7.30 (assert (forall ((P2 tptp.product_prod_num_num)) (exists ((X4 tptp.num) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_num_num X4) Y3)))))
% 7.01/7.30 (assert (forall ((P2 tptp.product_prod_nat_num)) (exists ((X4 tptp.nat) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_nat_num X4) Y3)))))
% 7.01/7.30 (assert (forall ((P2 tptp.product_prod_nat_nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (= P2 (@ (@ tptp.product_Pair_nat_nat X4) Y3)))))
% 7.01/7.30 (assert (forall ((P2 tptp.product_prod_int_int)) (exists ((X4 tptp.int) (Y3 tptp.int)) (= P2 (@ (@ tptp.product_Pair_int_int X4) Y3)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.produc6271795597528267376eger_o)) (not (forall ((A5 tptp.code_integer) (B5 Bool)) (not (= Y4 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.product_prod_num_num)) (not (forall ((A5 tptp.num) (B5 tptp.num)) (not (= Y4 (@ (@ tptp.product_Pair_num_num A5) B5)))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.product_prod_nat_num)) (not (forall ((A5 tptp.nat) (B5 tptp.num)) (not (= Y4 (@ (@ tptp.product_Pair_nat_num A5) B5)))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.product_prod_nat_nat)) (not (forall ((A5 tptp.nat) (B5 tptp.nat)) (not (= Y4 (@ (@ tptp.product_Pair_nat_nat A5) B5)))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.product_prod_int_int)) (not (forall ((A5 tptp.int) (B5 tptp.int)) (not (= Y4 (@ (@ tptp.product_Pair_int_int A5) B5)))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X4)))))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (exists ((C2 tptp.nat)) (= B3 (@ (@ tptp.plus_plus_nat A3) C2))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M2) K2))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 7.01/7.30 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList 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) TreeList) Summary))) (=> (or (= X2 Mi) (= X2 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 7.01/7.30 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 7.01/7.30 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 7.01/7.30 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N) (= Deg N))))
% 7.01/7.30 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList2) S))))))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 7.01/7.30 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 7.01/7.30 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList 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) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 7.01/7.30 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y4)) (= X2 Y4))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M5)) N3) (@ P M5))) (@ P N3))) (@ P N))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((N3 tptp.nat)) (@ (@ R N3) (@ tptp.suc N3))) (@ (@ R M) N)))))))
% 7.01/7.30 (assert (forall ((A4 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A4 (@ _let_1 A)) (= (@ tptp.suc A4) (@ _let_1 (@ tptp.suc A)))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_set_nat (@ F N4)) (@ F N))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_rat (@ F N4)) (@ F N))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_num (@ F N4)) (@ F N))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_int (@ F N4)) (@ F N))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_real (@ F N4)) (@ F N))))))
% 7.01/7.30 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 7.01/7.30 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 7.01/7.30 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height _let_1))))))
% 7.01/7.30 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 7.01/7.30 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.01/7.30 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 7.01/7.30 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 7.01/7.30 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X2))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 7.01/7.30 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 7.01/7.30 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 7.01/7.30 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 7.01/7.30 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 7.01/7.30 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 7.01/7.30 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y4) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X2)) (@ tptp.some_nat Y4)) (@ tptp.some_nat Z)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_12)))))
% 7.01/7.30 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 7.01/7.30 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 7.01/7.30 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.01/7.30 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) X2)))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) X2)))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) X2)))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) X2)))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X2) Y4) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X2)) (@ tptp.some_nat Y4)) (@ tptp.some_nat Z)))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 7.01/7.30 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat X2) Maxi))))))
% 7.01/7.30 (assert (forall ((Tree tptp.vEBT_VEBT) (X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 7.01/7.30 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X2)) X2)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y4) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y4)) X2))))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y4) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X2)) Y4) (or (@ (@ tptp.vEBT_vebt_member T) Y4) (= X2 Y4)))))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.member_nat X2) (@ tptp.vEBT_set_vebt T))))))
% 7.01/7.30 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 7.01/7.30 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 7.01/7.30 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 7.01/7.30 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 7.01/7.30 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 7.01/7.30 (assert (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I2)))))
% 7.01/7.30 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 7.01/7.30 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 7.01/7.30 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_12))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_12))))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X2) X_12))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z2) (@ (@ tptp.ord_less_real Z2) Y4))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X2) Z2) (@ (@ tptp.ord_less_rat Z2) Y4))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X4) (@ P Y5))) (@ P X4))) (@ P A))))
% 7.01/7.30 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y4) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y4) X2)) (= (not (@ (@ tptp.ord_less_rat X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y4) X2)) (= (not (@ (@ tptp.ord_less_num X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y4) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y4) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y4)) (=> (not (= X2 Y4)) (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y4)) (=> (not (= X2 Y4)) (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y4)) (=> (not (= X2 Y4)) (@ (@ tptp.ord_less_num Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y4)) (=> (not (= X2 Y4)) (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y4)) (=> (not (= X2 Y4)) (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 7.01/7.30 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 7.01/7.30 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P4 N2) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N2) (not (@ P4 M2)))))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B 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) B))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B 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) B))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B 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) B))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B 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) B))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B 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) B))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y4)) (or (@ (@ tptp.ord_less_real Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y4)) (or (@ (@ tptp.ord_less_rat Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y4)) (or (@ (@ tptp.ord_less_num Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y4)) (or (@ (@ tptp.ord_less_nat Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y4)) (or (@ (@ tptp.ord_less_int Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_real X2) Y4)) (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_rat X2) Y4)) (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_num X2) Y4)) (@ (@ tptp.ord_less_num Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_nat X2) Y4)) (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_int X2) Y4)) (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (not (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (not (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (not (@ (@ tptp.ord_less_num Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (not (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (not (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (not (= X2 Y4)) (or (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (not (= X2 Y4)) (or (@ (@ tptp.ord_less_rat X2) Y4) (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (not (= X2 Y4)) (or (@ (@ tptp.ord_less_num X2) Y4) (@ (@ tptp.ord_less_num Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (not (= X2 Y4)) (or (@ (@ tptp.ord_less_nat X2) Y4) (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (not (= X2 Y4)) (or (@ (@ tptp.ord_less_int X2) Y4) (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_real Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_rat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_num Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_nat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (not (@ (@ tptp.ord_less_rat X2) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num)) (not (@ (@ tptp.ord_less_num X2) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (not (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (not (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (not (@ (@ tptp.ord_less_num Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (not (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (not (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y4) (=> (@ (@ tptp.ord_less_real Y4) X2) P))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (=> (@ (@ tptp.ord_less_rat Y4) X2) P))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X2) Y4) (=> (@ (@ tptp.ord_less_num Y4) X2) P))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (=> (@ (@ tptp.ord_less_nat Y4) X2) P))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y4) (=> (@ (@ tptp.ord_less_int Y4) X2) P))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y4) (= X2 Y4) (@ (@ tptp.ord_less_real Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y4) (= X2 Y4) (@ (@ tptp.ord_less_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y4) (= X2 Y4) (@ (@ tptp.ord_less_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y4) (= X2 Y4) (@ (@ tptp.ord_less_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y4) (= X2 Y4) (@ (@ tptp.ord_less_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (not (= Y4 X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (not (= Y4 X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (not (= Y4 X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (not (= Y4 X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (not (= Y4 X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (not (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (not (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (not (@ (@ tptp.ord_less_num Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (not (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (not (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_nat X2) Y4)) (@ (@ tptp.ord_less_nat Y4) X2)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N3) (not (@ P M5)))))) (@ P N))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N3) (@ P M5))) (@ P N3))) (@ P N))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 7.01/7.30 (assert (forall ((S2 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T) (not (= S2 T)))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_real (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_num (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_int (@ F N)) (@ F N4))))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (or (@ (@ tptp.ord_less_set_nat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (or (@ (@ tptp.ord_less_rat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y4) (or (@ (@ tptp.ord_less_num X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y4) (or (@ (@ tptp.ord_less_nat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y4) (or (@ (@ tptp.ord_less_int X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (or (@ (@ tptp.ord_less_real X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y4) (@ (@ tptp.ord_less_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y4) (@ (@ tptp.ord_less_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y4) (@ (@ tptp.ord_less_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y4) (@ (@ tptp.ord_less_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_real Y4) X2))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y3) (@ (@ tptp.ord_less_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (=> (@ (@ tptp.ord_less_set_nat Y4) Z) (@ (@ tptp.ord_less_set_nat X2) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (=> (@ (@ tptp.ord_less_rat Y4) Z) (@ (@ tptp.ord_less_rat X2) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y4) (=> (@ (@ tptp.ord_less_num Y4) Z) (@ (@ tptp.ord_less_num X2) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y4) (=> (@ (@ tptp.ord_less_nat Y4) Z) (@ (@ tptp.ord_less_nat X2) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ (@ tptp.ord_less_int X2) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (=> (@ (@ tptp.ord_less_real Y4) Z) (@ (@ tptp.ord_less_real X2) Z)))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (@ (@ tptp.ord_less_set_nat A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_nat A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X2) Y4) (@ (@ tptp.ord_less_eq_set_nat X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (@ (@ tptp.ord_less_eq_rat X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y4) (@ (@ tptp.ord_less_eq_num X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y4) (@ (@ tptp.ord_less_eq_nat X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y4) (@ (@ tptp.ord_less_eq_int X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_eq_real X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X2) Y4)) (@ (@ tptp.ord_less_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X2) Y4)) (@ (@ tptp.ord_less_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y4)) (@ (@ tptp.ord_less_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y4)) (@ (@ tptp.ord_less_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X2) Y4)) (@ (@ tptp.ord_less_real Y4) X2))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (not (= X Y))))))
% 7.01/7.30 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (not (= X Y))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (not (= X Y))))))
% 7.01/7.30 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (not (= X Y))))))
% 7.01/7.30 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_num (lambda ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 7.01/7.30 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat B) A))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (@ (@ tptp.ord_less_eq_set_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 7.01/7.30 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (@ (@ tptp.ord_less_eq_set_nat A3) B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A3) (not (@ (@ tptp.ord_less_eq_rat A3) B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (not (@ (@ tptp.ord_less_eq_num A3) B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (@ (@ tptp.ord_less_eq_int A3) B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (not (@ (@ tptp.ord_less_eq_real A3) B3))))))
% 7.01/7.30 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) B) (@ (@ tptp.ord_less_set_nat C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (= tptp.ord_less_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_set_nat (lambda ((B3 tptp.set_nat) (A3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B3) A3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B3) A3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B3) A3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B3) A3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B3) A3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B3) A3) (= A3 B3)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y4) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) W2) (=> (@ (@ tptp.ord_less_rat W2) Y4) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y4) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W2) (=> (@ (@ tptp.ord_less_real W2) Y4) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y4) Z)))))
% 7.01/7.30 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X2) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X2) (@ (@ tptp.ord_less_eq_rat Y4) W2)))) (@ (@ tptp.ord_less_eq_rat Y4) Z)))))
% 7.01/7.30 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X2) (@ (@ tptp.ord_less_eq_real Y4) W2)))) (@ (@ tptp.ord_less_eq_real Y4) Z)))))
% 7.01/7.30 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (@ (@ tptp.ord_less_eq_set_nat B3) A3))))))
% 7.01/7.30 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B3) (not (@ (@ tptp.ord_less_eq_rat B3) A3))))))
% 7.01/7.30 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (not (@ (@ tptp.ord_less_eq_num B3) A3))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (@ (@ tptp.ord_less_eq_nat B3) A3))))))
% 7.01/7.30 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (@ (@ tptp.ord_less_eq_int B3) A3))))))
% 7.01/7.30 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (not (@ (@ tptp.ord_less_eq_real B3) A3))))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 7.01/7.30 (assert (= tptp.ord_less_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (not (= A3 B3))))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A3) B3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B3 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B3) (= A3 B3)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B3) (= A3 B3)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y4) X2)) (@ (@ tptp.ord_less_rat X2) Y4))))
% 7.01/7.30 (assert (forall ((Y4 tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y4) X2)) (@ (@ tptp.ord_less_num X2) Y4))))
% 7.01/7.30 (assert (forall ((Y4 tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y4) X2)) (@ (@ tptp.ord_less_nat X2) Y4))))
% 7.01/7.30 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y4) X2)) (@ (@ tptp.ord_less_int X2) Y4))))
% 7.01/7.30 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y4) X2)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.rat) (Z tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat X4) Z))) (@ (@ tptp.ord_less_eq_rat Y4) Z))))
% 7.01/7.30 (assert (forall ((Y4 tptp.real) (Z tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y4) (@ (@ tptp.ord_less_eq_real X4) Z))) (@ (@ tptp.ord_less_eq_real Y4) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.rat) (Y4 tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (@ (@ tptp.ord_less_eq_rat Y4) X4))) (@ (@ tptp.ord_less_eq_rat Y4) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.real) (Y4 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (@ (@ tptp.ord_less_eq_real Y4) X4))) (@ (@ tptp.ord_less_eq_real Y4) Z))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (= (not (@ (@ tptp.ord_less_set_nat X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (= (not (@ (@ tptp.ord_less_rat X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y4) (= (not (@ (@ tptp.ord_less_num X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y4) (= (not (@ (@ tptp.ord_less_nat X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y4) (= (not (@ (@ tptp.ord_less_int X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (= (not (@ (@ tptp.ord_less_real X2) Y4)) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X2) Y4)) (= (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y4)) (= (@ (@ tptp.ord_less_eq_rat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y4)) (= (@ (@ tptp.ord_less_eq_num X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y4)) (= (@ (@ tptp.ord_less_eq_nat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y4)) (= (@ (@ tptp.ord_less_eq_int X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y4)) (= (@ (@ tptp.ord_less_eq_real X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (not (@ (@ tptp.ord_less_set_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X2))))
% 7.01/7.30 (assert (forall ((Y4 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X2) (not (@ (@ tptp.ord_less_set_nat X2) Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X2) (not (@ (@ tptp.ord_less_rat X2) Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X2) (not (@ (@ tptp.ord_less_num X2) Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X2) (not (@ (@ tptp.ord_less_nat X2) Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X2) (not (@ (@ tptp.ord_less_int X2) Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X2) (not (@ (@ tptp.ord_less_real X2) Y4)))))
% 7.01/7.30 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 7.01/7.30 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B2) A2)) (@ (@ tptp.ord_less_num A2) B2))))
% 7.01/7.30 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B2) A2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 7.01/7.30 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B2) A2)) (@ (@ tptp.ord_less_int A2) B2))))
% 7.01/7.30 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B2) A2)) (@ (@ tptp.ord_less_real A2) B2))))
% 7.01/7.30 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Y4 tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X2) (@ tptp.size_s6755466524823107622T_VEBT Y4))) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.list_o) (Y4 tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X2) (@ tptp.size_size_list_o Y4))) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.list_nat) (Y4 tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y4))) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.list_int) (Y4 tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X2) (@ tptp.size_size_list_int Y4))) (not (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y4))) (not (= X2 Y4)))))
% 7.01/7.30 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 7.01/7.30 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 7.01/7.30 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 7.01/7.30 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 7.01/7.30 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K3) (=> (@ _let_1 J2) (=> (@ (@ P J2) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M6 tptp.nat)) (and (= M (@ tptp.suc M6)) (@ (@ tptp.ord_less_nat N) M6))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P N) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P N) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P I4)))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.01/7.30 (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))))))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M2) N2) (= M2 N2)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (not (= M2 N2))))))
% 7.01/7.30 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 7.01/7.30 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 7.01/7.30 (assert (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))
% 7.01/7.30 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))
% 7.01/7.30 (assert (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q2 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q2)))))))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M2) K2)))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K3)))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X2) (= (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X2) (= (@ (@ tptp.ord_less_eq_rat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X2) (= (@ (@ tptp.ord_less_eq_num X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X2) (= (@ (@ tptp.ord_less_eq_real X2) Y4) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X2) Y4)) (@ (@ tptp.ord_less_eq_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X2) Y4)) (@ (@ tptp.ord_less_eq_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y4)) (@ (@ tptp.ord_less_eq_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y4)) (@ (@ tptp.ord_less_eq_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real X2) Y4)) (@ (@ tptp.ord_less_eq_real Y4) X2))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real A) (@ F C)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y4) (@ (@ tptp.ord_less_eq_num Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y4) (@ (@ tptp.ord_less_eq_int Y4) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_eq_real Y4) X2))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (or (= A B) (not (@ (@ tptp.ord_less_eq_real A) B)) (not (@ (@ tptp.ord_less_eq_real B) A)))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (= X2 Y4) (@ (@ tptp.ord_less_eq_set_nat X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (= X2 Y4) (@ (@ tptp.ord_less_eq_rat X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (= X2 Y4) (@ (@ tptp.ord_less_eq_num X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (= X2 Y4) (@ (@ tptp.ord_less_eq_nat X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (= X2 Y4) (@ (@ tptp.ord_less_eq_int X2) Y4))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (= X2 Y4) (@ (@ tptp.ord_less_eq_real X2) Y4))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_real (@ F A)) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X4 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_real B) C) (=> (forall ((X4 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y3) (@ (@ tptp.ord_less_eq_num (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_nat B3) A3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A3 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B3) (@ (@ tptp.ord_less_eq_rat B3) A3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B3) (@ (@ tptp.ord_less_eq_num B3) A3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B3) (@ (@ tptp.ord_less_eq_nat B3) A3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B3) (@ (@ tptp.ord_less_eq_int B3) A3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B3) (@ (@ tptp.ord_less_eq_real B3) A3)))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 7.01/7.30 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (= A B)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B3) A3) (@ (@ tptp.ord_less_eq_set_nat A3) B3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A3 tptp.rat) (B3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B3) A3) (@ (@ tptp.ord_less_eq_rat A3) B3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((A3 tptp.num) (B3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B3) A3) (@ (@ tptp.ord_less_eq_num A3) B3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B3) A3) (@ (@ tptp.ord_less_eq_nat A3) B3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A3 tptp.int) (B3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B3) A3) (@ (@ tptp.ord_less_eq_int A3) B3)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) (lambda ((A3 tptp.real) (B3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B3) A3) (@ (@ tptp.ord_less_eq_real A3) B3)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B 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) B)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B 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) B)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B 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) B)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B 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) B)))))
% 7.01/7.30 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) Z) (@ _let_1 Z))))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y4) (=> (@ (@ tptp.ord_less_eq_num Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y4) (=> (@ (@ tptp.ord_less_eq_nat Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X2) (= X2 Y4)))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_eq_real A) C)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.set_nat) (Z3 tptp.set_nat)) (= Y6 Z3)) (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)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((X tptp.rat) (Y tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.num) (Z3 tptp.num)) (= Y6 Z3)) (lambda ((X tptp.num) (Y tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((X tptp.int) (Y tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X)))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) (lambda ((X tptp.real) (Y tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real Y) X)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_num Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ _let_1 Y4))) (let ((_let_3 (@ tptp.ord_less_eq_real Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_real Y4))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y4))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 7.01/7.30 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real B) A) (not (= B A))))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 7.01/7.30 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) A)))
% 7.01/7.30 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X2))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList 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 X2) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Mi))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ tptp.some_nat Ma))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_nat X2) Y4))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X)) (@ tptp.some_nat Y)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Y4)) (@ (@ tptp.ord_less_nat Y4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Y4)) (@ (@ tptp.ord_less_nat Y4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_nat X2) Y4))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) N))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ P (@ (@ tptp.nth_real Xs2) N))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (@ P X4))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X2) (@ (@ tptp.ord_less_eq_nat Mini) X2))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X2)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.01/7.30 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y4) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat X2) Y4) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat X2) Z4)) (@ (@ tptp.ord_less_eq_nat Y4) Z4)))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (X2 tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Y4) (and (@ (@ tptp.vEBT_vebt_member T) Y4) (@ (@ tptp.ord_less_nat Y4) X2) (forall ((Z4 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z4) (@ (@ tptp.ord_less_nat Z4) X2)) (@ (@ tptp.ord_less_eq_nat Z4) Y4)))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Px)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X2) Sx)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X2) Sx)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N5)))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 7.01/7.30 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 7.01/7.30 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 7.01/7.30 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 7.01/7.30 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat _let_1) (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.times_times_nat _let_1) N))))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 7.01/7.30 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low X3) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X3) (@ (@ tptp.ord_less_eq_nat X3) tptp.ma)))))))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X2) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X2) tptp.none_nat))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) N)) (@ tptp.set_Pr5648618587558075414at_nat Xs2)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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 ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) N))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_o Xs2) N))))))
% 7.01/7.30 (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 ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_nat Xs2) N))))))
% 7.01/7.30 (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 ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (@ P X4))) (@ P (@ (@ tptp.nth_int Xs2) N))))))
% 7.01/7.30 (assert (forall ((X2 tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s5460976970255530739at_nat Xs2)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Xs2 tptp.list_complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs2)) (= (@ (@ tptp.nth_complex Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Xs2 tptp.list_real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_real Xs2)) (= (@ (@ tptp.nth_real Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((X2 Bool) (Xs2 tptp.list_o)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Xs2 tptp.list_int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I4) X2))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs2) I3)))) (=> (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ P X2)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_complex) (P (-> tptp.complex Bool)) (X2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ P (@ (@ tptp.nth_complex Xs2) I3)))) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs2)) (@ P X2)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_real) (P (-> tptp.real Bool)) (X2 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 X2) (@ tptp.set_real2 Xs2)) (@ P X2)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I3)))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ P X2)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool)) (X2 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 X2) (@ tptp.set_o2 Xs2)) (@ P X2)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_nat) (P (-> tptp.nat Bool)) (X2 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 X2) (@ tptp.set_nat2 Xs2)) (@ P X2)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_int) (P (-> tptp.int Bool)) (X2 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 X2) (@ tptp.set_int2 Xs2)) (@ P X2)))))
% 7.01/7.30 (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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs2) I4)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs2)) (@ P X))) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs2)) (@ P (@ (@ tptp.nth_o Xs2) I4)))))))
% 7.01/7.30 (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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs2)) (@ P (@ (@ tptp.nth_nat Xs2) I4)))))))
% 7.01/7.30 (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 ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs2)) (@ P (@ (@ tptp.nth_int Xs2) I4)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X2) D)) (@ (@ tptp.vEBT_VEBT_low X2) D)) D) X2)))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y4) _let_1)) X2)) N) Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y4) _let_1)) X2)) N) X2)))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 7.01/7.30 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (forall ((Y tptp.product_prod_nat_nat)) (not (= X2 (@ tptp.some_P7363390416028606310at_nat Y)))) (= X2 tptp.none_P5556105721700978146at_nat))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_nat)) (= (forall ((Y tptp.nat)) (not (= X2 (@ tptp.some_nat Y)))) (= X2 tptp.none_nat))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_num)) (= (forall ((Y tptp.num)) (not (= X2 (@ tptp.some_num Y)))) (= X2 tptp.none_num))))
% 7.01/7.30 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (not (= X2 tptp.none_P5556105721700978146at_nat)) (exists ((Y tptp.product_prod_nat_nat)) (= X2 (@ tptp.some_P7363390416028606310at_nat Y))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_nat)) (= (not (= X2 tptp.none_nat)) (exists ((Y tptp.nat)) (= X2 (@ tptp.some_nat Y))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_num)) (= (not (= X2 tptp.none_num)) (exists ((Y tptp.num)) (= X2 (@ tptp.some_num Y))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 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))) L2))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList 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) X2) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ 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) TreeList) Summary)) X2) tptp.none_nat)))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_VEBT_high X2) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) tptp.none_nat)))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 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 X2) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X2 Mi) (= X2 Ma) (and (@ (@ tptp.ord_less_nat X2) Ma) (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))))))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2))))))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M5 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M5) N3) (@ P M5))) (@ P N3))) (@ P N))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 7.01/7.30 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.times_times_real B3) A3))))
% 7.01/7.30 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.times_times_rat B3) A3))))
% 7.01/7.30 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.times_times_nat B3) A3))))
% 7.01/7.30 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.times_times_int B3) A3))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.30 (assert (forall ((X2 tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uu) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv))))) (=> (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat Uw) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A5)) (@ tptp.some_P7363390416028606310at_nat B5)))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uu) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv))))) (=> (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat Uw) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat)) (not (= X2 (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A5)) (@ tptp.some_nat B5)))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.produc1193250871479095198on_num)) (=> (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uu) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv))))) (=> (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num Uw) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A5 tptp.num) (B5 tptp.num)) (not (= X2 (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A5)) (@ tptp.some_num B5)))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv tptp.option4927543243414619207at_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uu) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv))))) (=> (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat Uw) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X4 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat)) (not (= X2 (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X4)) (@ tptp.some_P7363390416028606310at_nat Y3)))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu (-> tptp.nat tptp.nat Bool)) (Uv tptp.option_nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uu) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv))))) (=> (forall ((Uw (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat Uw) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X4 tptp.nat) (Y3 tptp.nat)) (not (= X2 (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X4)) (@ tptp.some_nat Y3)))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.produc7036089656553540234on_num)) (=> (forall ((Uu (-> tptp.num tptp.num Bool)) (Uv tptp.option_num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uu) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv))))) (=> (forall ((Uw (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num Uw) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X4 tptp.num) (Y3 tptp.num)) (not (= X2 (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X4)) (@ tptp.some_num Y3)))))))))))
% 7.01/7.30 (assert (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu2) tptp.none_P5556105721700978146at_nat) Uv2) tptp.none_P5556105721700978146at_nat)))
% 7.01/7.30 (assert (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu2) tptp.none_num) Uv2) tptp.none_num)))
% 7.01/7.30 (assert (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu2) tptp.none_nat) Uv2) tptp.none_nat)))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) N))) (let ((_let_2 (@ tptp.times_times_complex Y4))) (=> (= (@ (@ tptp.times_times_complex X2) Y4) (@ _let_2 X2)) (= (@ (@ tptp.times_times_complex _let_1) Y4) (@ _let_2 _let_1)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) N))) (let ((_let_2 (@ tptp.times_times_real Y4))) (=> (= (@ (@ tptp.times_times_real X2) Y4) (@ _let_2 X2)) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ _let_2 _let_1)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) N))) (let ((_let_2 (@ tptp.times_times_rat Y4))) (=> (= (@ (@ tptp.times_times_rat X2) Y4) (@ _let_2 X2)) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ _let_2 _let_1)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X2) N))) (let ((_let_2 (@ tptp.times_times_nat Y4))) (=> (= (@ (@ tptp.times_times_nat X2) Y4) (@ _let_2 X2)) (= (@ (@ tptp.times_times_nat _let_1) Y4) (@ _let_2 _let_1)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X2) N))) (let ((_let_2 (@ tptp.times_times_int Y4))) (=> (= (@ (@ tptp.times_times_int X2) Y4) (@ _let_2 X2)) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ _let_2 _let_1)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y4 (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y4 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y4 tptp.none_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.nat)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y4 (@ tptp.some_nat B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y4 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y4 tptp.none_num) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.num)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y4 (@ tptp.some_num B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_nat A5)) (=> (= Y4 (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y4 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y4 tptp.none_nat) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= X2 (@ tptp.some_nat A5)) (=> (= Y4 (@ tptp.some_nat B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y4 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_nat) _let_1) (=> (=> (= Y4 tptp.none_num) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= X2 (@ tptp.some_nat A5)) (=> (= Y4 (@ tptp.some_num B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_num A5)) (=> (= Y4 (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y4 tptp.option_nat)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y4 tptp.none_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.nat)) (=> (= X2 (@ tptp.some_num A5)) (=> (= Y4 (@ tptp.some_nat B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y4 tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y4))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y4 tptp.none_num) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= X2 (@ tptp.some_num A5)) (=> (= Y4 (@ tptp.some_num B5)) (@ (@ P X2) Y4)))) _let_1))))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (forall ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (and (@ P4 tptp.none_nat) (forall ((X tptp.nat)) (@ P4 (@ tptp.some_nat X)))))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (exists ((X6 tptp.option_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_nat Bool))) (or (@ P4 tptp.none_nat) (exists ((X tptp.nat)) (@ P4 (@ tptp.some_nat X)))))))
% 7.01/7.30 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.option4927543243414619207at_nat)) (=> (not (= Y4 tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y4 (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.option_nat)) (=> (not (= Y4 tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y4 (@ tptp.some_nat X23))))))))
% 7.01/7.30 (assert (forall ((Y4 tptp.option_num)) (=> (not (= Y4 tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y4 (@ tptp.some_num X23))))))))
% 7.01/7.30 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 7.01/7.30 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 7.01/7.30 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 7.01/7.30 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 7.01/7.30 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 7.01/7.30 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L))))))
% 7.01/7.30 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 7.01/7.30 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 7.01/7.30 (assert (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw2) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 7.01/7.30 (assert (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw2) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 7.01/7.30 (assert (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw2) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 7.01/7.30 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y4 tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y4 tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X2) Xa2) Xb) Y4) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A5 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A5)) (forall ((B5 tptp.product_prod_nat_nat)) (=> (= Xb (@ tptp.some_P7363390416028606310at_nat B5)) (not (= Y4 (@ tptp.some_P7363390416028606310at_nat (@ (@ X2 A5) B5)))))))))))))))
% 7.01/7.30 (assert (forall ((X2 (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X2) Xa2) Xb) Y4) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A5 tptp.num)) (=> (= Xa2 (@ tptp.some_num A5)) (forall ((B5 tptp.num)) (=> (= Xb (@ tptp.some_num B5)) (not (= Y4 (@ tptp.some_num (@ (@ X2 A5) B5)))))))))))))))
% 7.01/7.30 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y4 tptp.option_nat)) (let ((_let_1 (not (= Y4 tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X2) Xa2) Xb) Y4) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A5 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A5)) (forall ((B5 tptp.nat)) (=> (= Xb (@ tptp.some_nat B5)) (not (= Y4 (@ tptp.some_nat (@ (@ X2 A5) B5)))))))))))))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X2) Y4) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y4) N)) tptp.one_one_complex))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X2) Y4) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y4) N)) tptp.one_one_real))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X2) Y4) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y4) N)) tptp.one_one_rat))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X2) Y4) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y4) N)) tptp.one_one_nat))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X2) Y4) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y4) N)) tptp.one_one_int))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) B4) (forall ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ _let_1 B4)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_complex) (B4 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) B4) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 Xs2)) (@ _let_1 B4)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_real) (B4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) B4) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 Xs2)) (@ _let_1 B4)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) B4) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs2)) (@ _let_1 B4)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) B4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 Xs2)) (@ _let_1 B4)))))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) B4) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 Xs2)) (@ _let_1 B4)))))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys))) (not (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys))) (not (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys))) (not (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 7.01/7.30 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X2) X2)) X2)) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X2) X2)) X2)) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X2) X2)) X2)) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.power_power_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X2) X2)) X2)) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X2) X2)) X2)) X2))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y4)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y4) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y4)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y4)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X2) Y4)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X2)) Y4))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X2) Y4)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y4) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.list_o Bool)) (Xs2 tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs2 tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 7.01/7.30 (assert (forall ((P (-> tptp.list_int Bool)) (Xs2 tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs2))))
% 7.01/7.30 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 7.01/7.30 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X4) N))) (and (@ (@ tptp.ord_less_nat Mi) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 7.01/7.30 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 7.01/7.30 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I3) (@ (@ tptp.nth_VEBT_VEBT Ys) I3)))) (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I3) (@ (@ tptp.nth_o Ys) I3)))) (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((Xs2 tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I3) (@ (@ tptp.nth_int Ys) I3)))) (= Xs2 Ys)))))
% 7.01/7.30 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.vEBT_VEBT)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_VEBT_VEBT Xs) I4)))))))))
% 7.01/7.30 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 Bool)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs) I4)))))))))
% 7.01/7.30 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.nat)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs) I4)))))))))
% 7.01/7.30 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X5 tptp.int)) (@ (@ P I4) X5)))) (exists ((Xs tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_int Xs) I4)))))))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.list_VEBT_VEBT) (Z3 tptp.list_VEBT_VEBT)) (= Y6 Z3)) (lambda ((Xs tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys3) I4))))))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.list_o) (Z3 tptp.list_o)) (= Y6 Z3)) (lambda ((Xs tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys3) I4))))))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.list_nat) (Z3 tptp.list_nat)) (= Y6 Z3)) (lambda ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 7.01/7.30 (assert (= (lambda ((Y6 tptp.list_int) (Z3 tptp.list_int)) (= Y6 Z3)) (lambda ((Xs tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys3) I4))))))))
% 7.01/7.30 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X) N2))) (@ (@ tptp.vEBT_VEBT_low X) N2)))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))))))))))
% 7.01/7.30 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N) (=> (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))))))))))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList 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) TreeList) 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)))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y4)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))))))
% 7.01/7.30 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 7.01/7.30 (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))))))))
% 7.01/7.30 (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))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y4)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (Q3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M) N) Q3))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X2) Y4) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X2)) (@ tptp.some_nat Y4)) (@ tptp.some_nat Z)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 7.01/7.30 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 7.01/7.30 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 7.01/7.30 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 7.01/7.30 (assert (forall ((A4 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A4) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 7.01/7.30 (assert (forall ((A4 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A4) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 7.01/7.30 (assert (forall ((A4 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A4 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A4) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 7.01/7.30 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 7.01/7.30 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 7.01/7.30 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y4)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y4) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) A)) B))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y4)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y4) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) A)) B))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y4)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y4) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) A)) B))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L)))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L)))))))
% 7.01/7.30 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 7.01/7.30 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 7.01/7.30 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 7.01/7.30 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 7.01/7.30 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 7.01/7.30 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) _let_2))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 7.01/7.30 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 7.01/7.30 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) tptp.none_nat)))
% 7.01/7.30 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) tptp.none_nat)))
% 7.01/7.30 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X2) tptp.one_one_nat)))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y4)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y4) X2)) _let_1)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y4)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y4) X2)) _let_1)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y4)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y4) X2)) _let_1)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y4)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y4) X2)) _let_1)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y4)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y4) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y4)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y4)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y4) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y4)))))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y4)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y4) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y4)))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 7.01/7.30 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q3)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q3)))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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)))
% 7.01/7.30 (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)))
% 7.01/7.30 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 7.01/7.30 (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))))
% 7.01/7.30 (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))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X2))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X2))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 7.01/7.30 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2))) _let_1) TreeList) Summary)))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.30 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))))
% 7.01/7.30 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.power_power_real X2) N3))))))
% 7.01/7.30 (assert (forall ((Z tptp.extended_enat) (Y4 tptp.extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y4) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y4) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y4)) Z))))))
% 7.01/7.30 (assert (forall ((X3 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X3))))
% 7.01/7.30 (assert (forall ((X3 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X3))))
% 7.01/7.30 (assert (forall ((X3 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X3) X_12))))
% 7.01/7.30 (assert (forall ((X3 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X3) X_12))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_real X2) Y4)) (@ (@ tptp.ord_less_real Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_rat X2) Y4)) (@ (@ tptp.ord_less_rat Y4) X2)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (not (= X2 Y4)) (=> (not (@ (@ tptp.ord_less_int X2) Y4)) (@ (@ tptp.ord_less_int Y4) X2)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 7.01/7.30 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex Y4) W)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y4) W)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y4) W)))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) W)) (@ (@ tptp.times_times_complex Y4) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) W)) (@ (@ tptp.times_times_real Y4) Z)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) W)) (@ (@ tptp.times_times_rat Y4) Z)))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 7.01/7.30 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 7.01/7.30 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 7.01/7.30 (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)))))))))
% 7.01/7.30 (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)))))))))
% 7.01/7.30 (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)))))))))
% 7.01/7.30 (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)))))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.minus_minus_real X2) Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y4) Y4)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) Y4)) (@ (@ tptp.minus_minus_rat X2) Y4)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y4) Y4)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) Y4)) (@ (@ tptp.minus_minus_int X2) Y4)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 7.01/7.30 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 7.01/7.30 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))
% 7.01/7.30 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 7.01/7.30 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))
% 7.01/7.30 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT 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_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList 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 X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT 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_low X2) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X2) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (Ma tptp.nat) (TreeList 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 X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT 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_low X2) _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) X2) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ 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)))))))))))))))
% 7.01/7.30 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X2 tptp.nat) (TreeList 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 X2) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT 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_low X2) _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) X2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ 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)))))))))))))))))))))
% 7.01/7.30 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 7.01/7.30 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.none_nat)))
% 7.01/7.30 (assert (forall ((L tptp.num) (R2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q3) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (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))))))))))
% 7.01/7.30 (assert (forall ((L tptp.num) (R2 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q3) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (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))))))))))
% 7.01/7.30 (assert (forall ((L tptp.num) (R2 tptp.code_integer) (Q3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q3) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (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))))))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X2)))) tptp.bot_bot_set_nat)))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X2) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X2) Y)))) tptp.bot_bot_set_nat)))))
% 7.01/7.30 (assert (forall ((C tptp.real)) (= (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C)) (@ tptp.times_times_real C))))
% 7.01/7.30 (assert (forall ((C tptp.rat)) (= (lambda ((X tptp.rat)) (@ (@ tptp.times_times_rat X) C)) (@ tptp.times_times_rat C))))
% 7.01/7.30 (assert (forall ((C tptp.nat)) (= (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C)) (@ tptp.times_times_nat C))))
% 7.01/7.30 (assert (forall ((C tptp.int)) (= (lambda ((X tptp.int)) (@ (@ tptp.times_times_int X) C)) (@ tptp.times_times_int C))))
% 7.01/7.30 (assert (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)))
% 7.01/7.30 (assert (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)))
% 7.01/7.30 (assert (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)))
% 7.01/7.30 (assert (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)))
% 7.01/7.30 (assert (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_int)))
% 7.01/7.30 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)))
% 7.01/7.30 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 7.01/7.30 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 7.01/7.30 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 7.01/7.30 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 7.01/7.30 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 7.01/7.30 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 7.01/7.30 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 7.01/7.30 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 7.01/7.30 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 7.01/7.30 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 7.01/7.30 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 7.01/7.30 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 7.01/7.30 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 7.01/7.30 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 7.01/7.30 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 7.01/7.30 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (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 X2) _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) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat X2) 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 TreeList))) (@ (@ (@ 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))))))))))))))))))
% 7.01/7.30 (assert (forall ((Ma tptp.nat) (X2 tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList))) (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 X2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList) Summary)) X2))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X2))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X2)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 7.01/7.30 (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 ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat X) Z4) (@ (@ tptp.ord_less_eq_nat Y) Z4))))))))
% 7.01/7.30 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.member_nat Y) Xs) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z4 tptp.nat)) (=> (@ (@ tptp.member_nat Z4) Xs) (=> (@ (@ tptp.ord_less_nat Z4) X) (@ (@ tptp.ord_less_eq_nat Z4) Y))))))))
% 7.01/7.30 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 7.01/7.30 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X2) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (=> (not (= X2 Mi)) (=> (not (= X2 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))))))))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ tptp.ord_less_nat X2))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_4 Mi)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi) X2) (@ _let_4 Ma))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) tptp.zero_zero_nat)) tptp.zero_zero_nat)))))))))))))
% 7.01/7.30 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 7.01/7.30 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 7.01/7.30 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.option_nat)) (let ((_let_1 (not (= Y4 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y4) (=> (forall ((Uu Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uu) B5)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y4 tptp.none_nat))))))) (=> (=> (exists ((Uv Bool) (Uw Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uv) Uw))) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _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 Xa2) _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 Xa2) Mi2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y4 (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y4 (@ (@ (@ 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))))))))))))))))))))))))))))
% 7.01/7.30 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.option_nat)) (let ((_let_1 (not (= Y4 tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y4) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A5 Bool)) (=> (exists ((Uw Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) Uw))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y4 tptp.none_nat))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va2)))) (not (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y4 tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT 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 Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList2) Summary2)) (not (and (=> _let_11 (= Y4 (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y4 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 7.01/7.30 (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)))))
% 7.01/7.30 (assert (forall ((Uw2 tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux) Uy))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X2))))
% 7.01/7.30 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X2))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.01/7.30 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 7.01/7.30 (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)))))))
% 7.01/7.30 (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))))))
% 7.01/7.30 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B3 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B3))))))
% 7.01/7.30 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X) (@ (@ tptp.vEBT_VEBT_membermima T2) X)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 7.01/7.30 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X2) (@ (@ tptp.vEBT_VEBT_membermima Tree) X2))))))
% 7.01/7.30 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 7.01/7.30 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 7.01/7.30 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 7.01/7.30 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 7.01/7.30 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 7.01/7.30 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y4)) (and (= X2 tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))
% 7.01/7.30 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y4) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 7.01/7.30 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 7.01/7.30 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 7.01/7.30 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 7.01/7.30 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 7.01/7.30 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 7.01/7.30 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 7.01/7.30 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 7.01/7.30 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 7.01/7.30 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 7.01/7.30 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 7.01/7.30 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 7.01/7.30 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 7.01/7.30 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 7.01/7.30 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 7.01/7.31 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 7.01/7.31 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.01/7.31 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.01/7.31 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y4) Y4)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y4) Y4)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))
% 7.01/7.31 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 7.01/7.31 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 7.01/7.31 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 7.01/7.31 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 7.01/7.31 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 7.01/7.31 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 7.01/7.31 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 7.01/7.31 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X2) M) _let_1) (or (= M tptp.zero_zero_nat) (= X2 _let_1))))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X2) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 7.01/7.31 (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)))))))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 7.01/7.31 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 7.01/7.31 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.31 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 7.01/7.31 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.01/7.31 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 7.01/7.31 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.01/7.31 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.01/7.31 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y4) _let_1)) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_nat X2) _let_1) (@ (@ tptp.power_power_nat Y4) _let_1)) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y4) _let_1)) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y4) _let_1)) (= X2 Y4))))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 7.01/7.31 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 7.01/7.31 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 7.01/7.31 (assert (forall ((X2 tptp.complex)) (= (= tptp.zero_zero_complex X2) (= X2 tptp.zero_zero_complex))))
% 7.01/7.31 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat)) (= (= tptp.zero_zero_rat X2) (= X2 tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2))))
% 7.01/7.31 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 7.01/7.31 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q2 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q2))))))
% 7.01/7.31 (assert (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux))))
% 7.01/7.31 (assert (forall ((Uu2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu2) true)))))
% 7.01/7.31 (assert (forall ((Uv2 Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv2)))))
% 7.01/7.31 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 7.01/7.31 (assert (forall ((N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((N tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X4)))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S)) X4)))))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A4 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A4) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B4) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A4) N)) (@ (@ tptp.divide_divide_nat B4) N))))))))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B2) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B2) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A2) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B2) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B2) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B2) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A2) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B2) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A2) B2)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (D3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y4 (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y4 (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 7.01/7.31 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X2))) (let ((_let_4 (= X2 tptp.one_one_nat))) (let ((_let_5 (= X2 tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 7.01/7.31 (assert (forall ((Uu2 Bool) (Uv2 Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat) tptp.none_nat)))
% 7.01/7.31 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.01/7.31 (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)))))))))
% 7.01/7.31 (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)))))))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (= A B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 7.01/7.31 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 7.01/7.31 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 7.01/7.31 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 7.01/7.31 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 7.01/7.31 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 7.01/7.31 (assert (= (lambda ((Y6 tptp.complex) (Z3 tptp.complex)) (= Y6 Z3)) (lambda ((A3 tptp.complex) (B3 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B3) tptp.zero_zero_complex))))
% 7.01/7.31 (assert (= (lambda ((Y6 tptp.real) (Z3 tptp.real)) (= Y6 Z3)) (lambda ((A3 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B3) tptp.zero_zero_real))))
% 7.01/7.31 (assert (= (lambda ((Y6 tptp.rat) (Z3 tptp.rat)) (= Y6 Z3)) (lambda ((A3 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B3) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B3) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (@ (@ P X4) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X4) Y3) (@ (@ P (@ tptp.suc X4)) (@ tptp.suc Y3)))) (@ (@ P M) N))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (=> (not (= X2 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X2 (@ tptp.suc (@ tptp.suc Va2))))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.nat)) (=> (not (= Y4 tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y4 (@ tptp.suc Nat3))))))))
% 7.01/7.31 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 7.01/7.31 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M5 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N3) (not (@ P M5))))))) (@ P N)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P J3))))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 7.01/7.31 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 7.01/7.31 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 7.01/7.31 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 7.01/7.31 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 7.01/7.31 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X2) (or (= X2 Mi) (= X2 Ma)))))
% 7.01/7.31 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C)))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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 ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P2) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P2))))) (@ P M)))))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 7.01/7.31 (assert (= tptp.modulo_modulo_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M2) N2)) M2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y4) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X2) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y4) (@ _let_1 Q22))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu) true)))) (=> (forall ((Uw tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 7.01/7.31 (assert (forall ((A Bool) (Uw2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw2)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 7.01/7.31 (assert (forall ((B Bool) (Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu2) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 7.01/7.31 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 7.01/7.31 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 7.01/7.31 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X2) Y4) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y4) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X2) Y4) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X2) Y4) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X2) Y4) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_rat X2) Y4) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_nat X2) Y4) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y4 tptp.zero_zero_nat))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_int X2) Y4) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (= (@ (@ tptp.plus_plus_real X2) Y4) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y4)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X2) Y4)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) Y4)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y4) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 7.01/7.31 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B3)) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B3)) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y4)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y4)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y4)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y4)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y4)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y4)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 7.01/7.31 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B3)) tptp.zero_zero_real))))
% 7.01/7.31 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B3)) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B3)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y4)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y4)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y4)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y4)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y4)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y4)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (forall ((Uv Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv)))) (=> (forall ((Uu Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y4) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W) Y4)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y4) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W) Y4)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y4) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W) Y4)))))))
% 7.01/7.31 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 7.01/7.31 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux2) Uy2)))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.01/7.31 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M2 tptp.nat)) (= N (@ tptp.suc M2))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N) (@ P (@ tptp.suc I4))))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K3) (not (@ P I2)))) (@ P K3)))))))
% 7.01/7.31 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K3) (= (@ (@ tptp.plus_plus_nat I) K3) J))))))
% 7.01/7.31 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.01/7.31 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 7.01/7.31 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.vEBT_Leaf A) B)) X2) tptp.one_one_nat)))
% 7.01/7.31 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2))))
% 7.01/7.31 (assert (forall ((A4 tptp.nat) (B4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A4) 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))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S)) X4)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S)) X4)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2)) X4)))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X4)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2)) X4)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2)) X4)))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X4)))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X4)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X4)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2)) X4)))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (B5 Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) B5)) tptp.zero_zero_nat)))) (=> (forall ((Uv Bool) (Uw Bool) (N3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N3))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2)) X4))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu Bool) (Uv Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (Uw Bool)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) Uw)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B5 Bool) (Va2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc (@ tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve)) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X4 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2)) X4)))))))))))))
% 7.01/7.31 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 7.01/7.31 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 7.01/7.31 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 7.01/7.31 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X2) N) (@ (@ tptp.modulo_modulo_nat Y4) N)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X2) (exists ((Q2 tptp.nat)) (= X2 (@ (@ tptp.plus_plus_nat Y4) (@ (@ tptp.times_times_nat N) Q2))))))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q3) S))))))))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q3) S))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 Bool)) (let ((_let_1 (not Y4))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y4) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv))) Y4) (=> (=> (exists ((Uu Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) true))) Y4) (=> (=> (exists ((Uw tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y4))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.nat) (N tptp.nat)) (= A4 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A4) N)) N)) (@ (@ tptp.modulo_modulo_nat A4) N)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q3)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q3))) (@ _let_1 N)))))))
% 7.01/7.31 (assert (= tptp.modulo_modulo_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M2) N2)) N2)))))
% 7.01/7.31 (assert (forall ((Uv2 Bool) (Uw2 Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N)) tptp.none_nat)))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y4) E2)))) (@ (@ tptp.ord_less_eq_rat X2) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y4) E2)))) (@ (@ tptp.ord_less_eq_real X2) Y4))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y4) W))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (X2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y4) W))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat X2) Y4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y4) W))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y4) W))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y4) W)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y4) W)))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y4)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y4)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y4)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y4)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y4)) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y4)) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Y4)) X2)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Y4)) X2)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Y4)) X2)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_rat Y4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y4) X2)) X2)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_int Y4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y4) X2)) X2)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y4) X2)) X2)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y4) Y4)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y4) Y4)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y4) Y4))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y4) Y4))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y4 tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y4 tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4))) tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y4) Y4))) tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y4) Y4))) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y4) Y4))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y4) Y4))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int))))))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.31 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real Z) Y4)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.times_times_rat Z) Y4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y4)) X2) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y4)) X2) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.01/7.31 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y4))) (@ (@ tptp.times_times_complex Y4) Z)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y4))) Y4)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y4)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y4))) Y4)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y4)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y4))) Y4)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X2 tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y4))) Y4)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y4))) Y4)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y4))) Y4)))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y4) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real Y4) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat Y4) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Z)) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y4 tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y4))) (@ (@ tptp.times_times_complex Y4) Z)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z)))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z)))))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y4) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real Y4) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat Y4) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Z)) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2))))
% 7.01/7.31 (assert (forall ((M tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 7.01/7.31 (assert (forall ((M tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 7.01/7.31 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 7.01/7.31 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) K3) (not (@ P I2)))) (@ P (@ tptp.suc K3))))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 7.01/7.31 (assert (forall ((X2 tptp.product_prod_nat_nat) (Xs2 tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs2)))))
% 7.01/7.31 (assert (forall ((X2 tptp.complex) (Xs2 tptp.list_complex)) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs2)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Xs2 tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs2)))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs2)))))
% 7.01/7.31 (assert (forall ((X2 Bool) (Xs2 tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs2)))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs2)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Xs2 tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs2)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P D2)))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P D2)))))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q3)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q3))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X2)) Y4)))) (@ (@ tptp.ord_less_eq_rat X2) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z2) (=> (@ (@ tptp.ord_less_real Z2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z2) X2)) Y4)))) (@ (@ tptp.ord_less_eq_real X2) Y4))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.31 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 7.01/7.31 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.times_times_rat Z) Y4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.times_times_real Z) Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y4)) Z)))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y4)) X2) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y4)) X2) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y4 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X2) A) (=> (@ (@ tptp.ord_less_eq_rat Y4) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y4))) A)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (A tptp.int) (Y4 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X2) A) (=> (@ (@ tptp.ord_less_eq_int Y4) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y4))) A)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (A tptp.real) (Y4 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X2) A) (=> (@ (@ tptp.ord_less_eq_real Y4) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y4))) A)))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z))) tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z))) tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y4))) (@ (@ tptp.times_times_real Y4) Z))) tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y4 tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y4)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y4))) (@ (@ tptp.times_times_rat Y4) Z))) tptp.zero_zero_rat))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y4) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y4 tptp.none_nat)))))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (not (= Y4 tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y4 (@ tptp.some_nat Mi2)))))))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y4) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y4 tptp.none_nat)))))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (not (= Y4 tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y4 (@ tptp.some_nat Ma2)))))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (N5 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N5)) (@ _let_1 N))))))))
% 7.01/7.31 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 7.01/7.31 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 7.01/7.31 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.01/7.31 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.31 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (= tptp.divide_divide_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M2) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (= tptp.plus_plus_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) N2))))))
% 7.01/7.31 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q3)) N)))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I4)) J3)) (@ P I4))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ 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) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y4) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y4 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) Y4) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S))) (= Y4 (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 7.01/7.31 (assert (= tptp.times_times_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)) N2))))))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve2) tptp.none_nat)))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve2)) Vf2) tptp.none_nat)))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) tptp.one_one_nat)))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y4) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv))) Y4) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y4) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y4 (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (= Y4 (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (= Y4 (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (A tptp.rat) (Y4 tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X2) A) (=> (@ (@ tptp.ord_less_rat Y4) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X2)) (@ (@ tptp.times_times_rat V) Y4))) A)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (A tptp.int) (Y4 tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X2) A) (=> (@ (@ tptp.ord_less_int Y4) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X2)) (@ (@ tptp.times_times_int V) Y4))) A)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (A tptp.real) (Y4 tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X2) A) (=> (@ (@ tptp.ord_less_real Y4) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X2)) (@ (@ tptp.times_times_real V) Y4))) A)))))))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.01/7.31 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 7.01/7.31 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 7.01/7.31 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S2))) V))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X2) _let_2) (@ (@ tptp.power_power_rat Y4) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X2) _let_2) (@ (@ tptp.power_power_nat Y4) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X2) _let_2) (@ (@ tptp.power_power_int Y4) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X2) _let_2) (@ (@ tptp.power_power_real Y4) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= X2 Y4))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_eq_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4) (@ (@ tptp.ord_less_eq_nat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_eq_int X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_eq_real X2) Y4))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))))))))
% 7.01/7.31 (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))))))))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 7.01/7.31 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M2 tptp.nat)) (@ (@ (@ tptp.if_complex (= M2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.31 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M2 tptp.nat)) (@ (@ (@ tptp.if_real (= M2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.31 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M2 tptp.nat)) (@ (@ (@ tptp.if_rat (= M2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.31 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.31 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M2 tptp.nat)) (@ (@ (@ tptp.if_int (= M2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2) tptp.none_nat)))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2) tptp.none_nat)))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) tptp.one_one_nat)))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (@ (@ tptp.ord_less_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y4) (@ (@ tptp.ord_less_nat X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (@ (@ tptp.ord_less_int X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (@ (@ tptp.ord_less_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y4 tptp.zero_zero_rat))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y4 tptp.zero_zero_int))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y4 tptp.zero_zero_real))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) tptp.zero_zero_real)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) tptp.zero_zero_rat)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y4 tptp.zero_zero_real)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y4 tptp.zero_zero_rat)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y4 tptp.zero_zero_int)))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ 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) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y4) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y4 (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) Y4) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y4) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y4) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2))) (= Y4 (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X2) N)) (@ _let_1 M)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X2) N)) (@ _let_1 N)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (not (= Y4 tptp.one_one_nat)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa2) Y4) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) _let_1) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ tptp.ord_less_nat Xa2))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2))) (not (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_3 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_3 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((U tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X2) Y4)) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y4)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 7.01/7.31 (assert (forall ((U tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X2) Y4)) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 7.01/7.31 (assert (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A1) A22) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A22 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (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))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (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))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2)))) (=> (=> _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 Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A22 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2)))) (=> (=> _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 Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I2)) (@ (@ tptp.vEBT_VEBT_low X3) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))))))))))))))))))))))
% 7.01/7.31 (assert (= tptp.vEBT_invar_vebt (lambda ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (or (and (exists ((A3 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A3) B3))) (= A23 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_1)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N2)) (= A23 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N2))) (and (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A23) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A23 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I4)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A23)) (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I4)) (@ (@ tptp.vEBT_VEBT_low X) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))
% 7.01/7.31 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X2))))
% 7.01/7.31 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) B5))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y4 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)) (=> (= X2 (@ (@ tptp.vEBT_Leaf Uv) Uw)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv) Uw)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y4 (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y4 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ 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) Xa2))))))))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (Uw Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) Uw))) (=> (= X2 _let_2) (=> (= Xa2 _let_1) (=> (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y4 tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (=> (= Xa2 _let_1) (=> (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y4 tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X2 _let_2) (=> (and (=> _let_12 (= Y4 (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y4 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 7.01/7.31 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 7.01/7.31 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 7.01/7.31 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 7.01/7.31 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 7.01/7.31 (assert (forall ((X2 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X2) X2))) (= X2 tptp.zero_zero_real))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A4 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A4) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B4) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A4) N)) (@ (@ tptp.divide_divide_int B4) N))))))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A4) 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))))))
% 7.01/7.31 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 7.01/7.31 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 7.01/7.31 (assert (forall ((A4 tptp.int) (N tptp.int)) (= A4 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A4) N)) N)) (@ (@ tptp.modulo_modulo_int A4) N)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X2) K)) X2)))))
% 7.01/7.31 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K) L)))))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L)) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B2)) (@ _let_1 B))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q3))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q3))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B2 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B2))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A2) B))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 7.01/7.31 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 7.01/7.31 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N) (@ P M2))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N) (@ P M2))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) N3)) Y4))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real X4) N) A) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5) (= (@ (@ tptp.power_power_real Y5) N) A)) (= Y5 X4)))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 7.01/7.31 (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)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y4 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X2 _let_1) (=> (= Y4 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y4 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y4 tptp.one_one_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.ord_less_nat Xa2))) (=> (= X2 _let_2) (=> (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_5 Mi2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (and (@ (@ tptp.ord_less_nat Mi2) Xa2) (@ _let_5 Ma2))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ tptp.vEBT_T_m_e_m_b_e_r2 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) tptp.zero_zero_nat)) tptp.zero_zero_nat))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T8099345112685741742_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y4 (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) Xa2))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X2 _let_2) (=> (= Y4 (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_1) (=> (= Y4 (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) Xa2))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y4 (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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))) (=> (= X2 _let_1) (=> (= Y4 (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y4 (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y4 (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))))
% 7.01/7.31 (assert (forall ((B2 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 B2) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 Q5)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (Q3 tptp.int) (R2 tptp.int) (B2 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 B2) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B2) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q3) Q5)))))))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((B tptp.int) (Q3 tptp.int) (R2 tptp.int) (B2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q5) Q3))))))))))
% 7.01/7.31 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 7.01/7.31 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q3))))))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q3)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q3) Q5)))))))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L) _let_1))))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q2 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q2))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))))
% 7.01/7.31 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 7.01/7.31 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (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))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (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))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 7.01/7.31 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 7.01/7.31 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 7.01/7.31 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 7.01/7.31 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 7.01/7.31 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B) D))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 7.01/7.31 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 7.01/7.31 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 7.01/7.31 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))))))))
% 7.01/7.31 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) (@ (@ tptp.times_times_int K) D))))))))))
% 7.01/7.31 (assert (forall ((I tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 7.01/7.31 (assert (forall ((I tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 7.01/7.31 (assert (forall ((I tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 7.01/7.31 (assert (forall ((I tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 7.01/7.31 (assert (forall ((I tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 7.01/7.31 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 7.01/7.31 (assert (forall ((L tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 7.01/7.31 (assert (forall ((L tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 7.01/7.31 (assert (forall ((L tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 7.01/7.31 (assert (forall ((L tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 7.01/7.31 (assert (forall ((L tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (not (@ (@ tptp.ord_less_real X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (not (@ (@ tptp.ord_less_rat X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (not (@ (@ tptp.ord_less_num X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (not (@ (@ tptp.ord_less_nat X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (not (@ (@ tptp.ord_less_int X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (@ (@ tptp.ord_less_real T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (@ (@ tptp.ord_less_rat T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (@ (@ tptp.ord_less_num T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (@ (@ tptp.ord_less_nat T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (@ (@ tptp.ord_less_int T) X3))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (and (@ P X3) (@ Q X3)) (and (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ Q X4) (@ Q6 X4))))) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (= (or (@ P X3) (@ Q X3)) (or (@ P6 X3) (@ Q6 X3))))))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (not (= X3 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X3))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (not (@ (@ tptp.ord_less_real T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (not (@ (@ tptp.ord_less_rat T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (not (@ (@ tptp.ord_less_num T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (not (@ (@ tptp.ord_less_nat T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (not (@ (@ tptp.ord_less_int T) X3)))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M7 tptp.nat)) (=> (@ P X2) (=> (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M7))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M4)))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.num)) (not (= X2 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X2 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))))
% 7.01/7.31 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))))) (= (exists ((X5 tptp.int)) (@ P X5)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X))))))))
% 7.01/7.31 (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 ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ 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) Xa3))))))) (=> (= X3 T) (= (@ (@ tptp.minus_minus_int X3) D4) T))))))))
% 7.01/7.31 (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 ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ 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) Xa3))))))) (=> (not (= X3 T)) (not (= (@ (@ tptp.minus_minus_int X3) D4) T)))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ 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) Xa3))))))) (=> (@ (@ tptp.ord_less_int X3) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X3) D4)) T)))))))
% 7.01/7.31 (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 ((X3 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 ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.minus_minus_int X3) D4))))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X3 T) (= (@ (@ tptp.plus_plus_int X3) D4) T))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X3 T)) (not (= (@ (@ tptp.plus_plus_int X3) D4) T)))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X3) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X3) D4)) T))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (A4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 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 ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.plus_plus_int X3) D4)))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ 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) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X3) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X3) D4)) T)))))))
% 7.01/7.31 (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 ((X3 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 ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.minus_minus_int X3) D4))))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (T tptp.int) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X3) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X3) D4)) T))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (A4 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 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 ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A4) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.plus_plus_int X3) D4)))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A4) (not (= X4 (@ (@ tptp.minus_minus_int Xb3) Xa))))))) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P6 X4) (@ P6 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X5 tptp.int)) (@ P X5)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 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) A4) (@ P (@ (@ tptp.minus_minus_int Y) X))))))))))))))
% 7.01/7.31 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P6 X4))))) (=> (forall ((X4 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B4) (not (= X4 (@ (@ tptp.plus_plus_int Xb3) Xa))))))) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P6 X4) (@ P6 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X5 tptp.int)) (@ P X5)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 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))))))))))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (not (@ (@ tptp.ord_less_eq_rat T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (not (@ (@ tptp.ord_less_eq_num T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (not (@ (@ tptp.ord_less_eq_int T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (not (@ (@ tptp.ord_less_eq_real T) X3)))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z2) (@ (@ tptp.ord_less_eq_rat X3) T))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z2) (@ (@ tptp.ord_less_eq_num X3) T))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z2) (@ (@ tptp.ord_less_eq_nat X3) T))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z2) (@ (@ tptp.ord_less_eq_int X3) T))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z2) (@ (@ tptp.ord_less_eq_real X3) T))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (@ (@ tptp.ord_less_eq_rat T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (@ (@ tptp.ord_less_eq_num T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (@ (@ tptp.ord_less_eq_nat T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (@ (@ tptp.ord_less_eq_int T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (@ (@ tptp.ord_less_eq_real T) X3))))))
% 7.01/7.31 (assert (forall ((T tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X3) (not (@ (@ tptp.ord_less_eq_rat X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.num)) (exists ((Z2 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X3) (not (@ (@ tptp.ord_less_eq_num X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X3) (not (@ (@ tptp.ord_less_eq_nat X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X3) (not (@ (@ tptp.ord_less_eq_int X3) T)))))))
% 7.01/7.31 (assert (forall ((T tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X3) (not (@ (@ tptp.ord_less_eq_real X3) T)))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X4 tptp.real) (K3 tptp.real)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X4 tptp.rat) (K3 tptp.rat)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ Q X4) (@ Q (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 7.01/7.31 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (= (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_nat B) D) (or (@ (@ tptp.ord_less_set_nat C) A) (@ (@ tptp.ord_less_set_nat B) D)))) (@ _let_1 D))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 7.01/7.31 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 7.01/7.31 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P1 X4) (@ P1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (@ P X4) (@ P1 X4))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 7.01/7.31 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X4 tptp.int) (K3 tptp.int)) (= (@ P6 X4) (@ P6 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (@ P X4) (@ P6 X4))))) (=> (exists ((X_1 tptp.int)) (@ P6 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X4) (@ (@ tptp.ord_less_eq_real X4) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D5)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_rat X2) Y4))))))
% 7.01/7.31 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_int X2) Y4))))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4))))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y4) Z)) (@ (@ tptp.ord_less_eq_rat X2) Y4)))))
% 7.01/7.31 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y4) Z)) (@ (@ tptp.ord_less_eq_int X2) Y4)))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y4) Z)) (@ (@ tptp.ord_less_eq_real X2) Y4)))))
% 7.01/7.31 (assert (forall ((Q3 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R2)) (= R2 tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((Q3 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R2)) (= R2 tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (Q3 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 Q3))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ 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) Ys)) N) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs2) Ys)) N) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs2) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs2) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.vEBT_Leaf A) B)) X2) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= X2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_o Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ tptp.size_size_list_int Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_o Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_nat Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs2)) (@ tptp.size_size_list_int Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs2) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs2)) (@ tptp.size_size_list_o Ys)))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R2)) (= (@ (@ tptp.divide_divide_int K) L) Q3))))
% 7.01/7.31 (assert (forall ((L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q3) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int))))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L)) (@ (@ tptp.modulo_modulo_int K) L)))))
% 7.01/7.31 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q3)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q3 tptp.zero_zero_int)))))))))))
% 7.01/7.31 (assert (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.01/7.31 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y4) Z)) (@ (@ tptp.ord_less_real X2) Y4)))))
% 7.01/7.31 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y4) Z)) (@ (@ tptp.ord_less_rat X2) Y4)))))
% 7.01/7.31 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y4) Z)) (@ (@ tptp.ord_less_int X2) Y4)))))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.01/7.31 (assert (forall ((B tptp.int) (A tptp.int) (Q3 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 Q3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 7.01/7.31 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (not (= Y4 _let_1)))) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa2) Y4) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= Y4 (@ (@ tptp.plus_plus_nat _let_1) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))))) (=> (=> (exists ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) _let_2) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) _let_2) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList2) Summary2))) (not (= Y4 (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_5 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_5 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3)))) tptp.one_one_nat)))))))))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (not (= A4 B4)) (@ (@ tptp.ord_less_set_nat A4) B4)))))
% 7.01/7.31 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_3) _let_2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high X2) _let_4))) (let ((_let_6 (@ tptp.plus_plus_nat tptp.one_one_nat))) (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_3) TreeList) Summary)) X2) (@ (@ tptp.plus_plus_nat _let_2) (@ (@ (@ tptp.if_nat (= X2 Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (= X2 Ma)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)) tptp.one_one_nat) (@ _let_6 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma) X2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_1)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList))) (@ _let_6 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_5)) (@ (@ tptp.vEBT_VEBT_low X2) _let_4)))) tptp.one_one_nat)))))))))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.nat)) (=> (= (@ (@ tptp.vEBT_T_m_e_m_b_e_r X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y4 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ (@ tptp.if_nat (= Xa2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X2 _let_1) (=> (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (= Y4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ tptp.bit0 tptp.one))) (let ((_let_4 (@ tptp.numeral_numeral_nat _let_3))) (let ((_let_5 (@ (@ tptp.divide_divide_nat _let_1) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_5))) (let ((_let_7 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (= X2 _let_2) (=> (= Y4 (@ (@ tptp.plus_plus_nat _let_4) (@ (@ (@ tptp.if_nat (= Xa2 Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (= Xa2 Ma2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)) tptp.one_one_nat) (@ _let_7 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat Ma2) Xa2)) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit0 _let_3)))) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ _let_7 (@ (@ tptp.vEBT_T_m_e_m_b_e_r (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_5)))) tptp.one_one_nat))))))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_T5837161174952499735_r_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 7.01/7.31 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (A4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X2) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A4) Z) (=> (@ tptp.finite_finite_nat A4) (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A4) X2) X_12)))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Z tptp.nat) (A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X2) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A4) Z) (=> (@ tptp.finite_finite_nat B4) (=> (= A4 B4) (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A4) X2) X_12))))))))
% 7.01/7.31 (assert (forall ((A Bool) (B Bool)) (= (@ tptp.vEBT_VEBT_height (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat)))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs2) A) X_12))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (@ (@ tptp.ord_less_nat A) X3))))))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs2) A) X_12))) (=> (@ tptp.finite_finite_nat Xs2) (not (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (@ (@ tptp.ord_less_nat X3) A))))))))
% 7.01/7.31 (assert (forall ((X32 tptp.num) (Y32 tptp.num)) (= (= (@ tptp.bit1 X32) (@ tptp.bit1 Y32)) (= X32 Y32))))
% 7.01/7.31 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 7.01/7.31 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 7.01/7.31 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 7.01/7.31 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs2))))
% 7.01/7.31 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 7.01/7.31 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 7.01/7.31 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 7.01/7.31 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 7.01/7.31 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 7.01/7.31 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N6) (@ (@ tptp.ord_less_nat X) M2)))))))
% 7.01/7.31 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N5) (@ (@ tptp.ord_less_nat X4) N))) (@ tptp.finite_finite_nat N5))))
% 7.01/7.31 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N6) (@ (@ tptp.ord_less_eq_nat X) M2)))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A4)))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A4)))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A4)))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A4) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A4)))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ P K2) (@ (@ tptp.ord_less_nat K2) I)))))))
% 7.01/7.31 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (= (@ tptp.size_s3451745648224563538omplex Xs) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (= (@ tptp.size_size_list_o Xs) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (= (@ tptp.size_size_list_int Xs) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (= (@ tptp.size_size_list_nat Xs) N))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.product_prod_num_num)) (=> (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N3))))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N3))))) (not (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N3))))))))))))))))
% 7.01/7.31 (assert (forall ((Y4 tptp.num)) (=> (not (= Y4 tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y4 (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y4 (@ tptp.bit1 X33)))))))))
% 7.01/7.31 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 7.01/7.31 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A4) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs)) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A4) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A4) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) N))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A4) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) N))))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (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))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ 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)))))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (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))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A4) B4) (exists ((B5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B5) (@ (@ tptp.minus_1356011639430497352at_nat B4) A4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_complex) (B4 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A4) B4) (exists ((B5 tptp.complex)) (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B4) A4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real) (B4 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A4) B4) (exists ((B5 tptp.real)) (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B4) A4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A4) B4) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B4) A4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A4) B4) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B4) A4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (B4 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_less_set_complex A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A4) B4) (=> (@ _let_1 A4) (@ _let_1 B4))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat))))
% 7.01/7.31 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int))))
% 7.01/7.31 (assert (forall ((N tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((Q3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ 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 Q3)) tptp.zero_zero_int)))))
% 7.01/7.31 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.31 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le549003669493604880_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6))))))
% 7.01/7.31 (assert (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B6 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) B6))))))
% 7.01/7.31 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B6 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) B6))))))
% 7.01/7.31 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 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) B6))))))
% 7.01/7.31 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 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) B6))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A4) tptp.bot_bot_set_nat))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A4) tptp.bot_bot_set_int))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A4) tptp.bot_bot_set_real))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A4) B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A4))))))
% 7.01/7.31 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (= A6 B6))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A4) B4) (@ (@ tptp.ord_less_eq_set_nat A4) B4))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A4))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C4) (@ _let_1 C4))))))
% 7.01/7.31 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B6) (not (@ (@ tptp.ord_less_eq_set_nat B6) A6))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (B4 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A4) B4) (=> (@ (@ tptp.ord_less_set_nat B4) C4) (@ (@ tptp.ord_less_set_nat A4) C4)))))
% 7.01/7.31 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B6) (= A6 B6)))))
% 7.01/7.31 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf A5) B5)))) (not (forall ((Uu tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu) Deg2) TreeList2) Summary2))))))))
% 7.01/7.31 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.vEBT_T_m_e_m_b_e_r T) X2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.vEBT_VEBT_height T))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 tptp.one)))))))))
% 7.01/7.31 (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))))))))
% 7.01/7.31 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 7.01/7.31 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z4 tptp.real)) (= (@ (@ tptp.power_power_real Z4) N) tptp.one_one_real)))))))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 7.01/7.31 (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)))))))))))))
% 7.01/7.31 (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)))))))))))))
% 7.01/7.31 (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)))))))))))))
% 7.01/7.31 (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)))))))))))))
% 7.01/7.31 (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)))))))))))))
% 7.01/7.31 (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)))))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y4 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y4 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y4 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y4 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_complex (@ X2 I4)) (@ Y4 I4)) tptp.one_one_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y4 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y4 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y4 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y4 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.times_times_real (@ X2 I4)) (@ Y4 I4)) tptp.one_one_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (Y4 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X2 I4)) (@ Y4 I4)) tptp.one_one_rat))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (Y4 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X2 I4)) (@ Y4 I4)) tptp.one_one_rat))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.complex)) (Y4 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.complex)) (Y4 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.complex)) (Y4 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.complex)) (Y4 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_complex (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_complex))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.real)) (Y4 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.real)) (Y4 (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.real)) (Y4 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (Y4 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ X2 I4) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I4 tptp.complex)) (and (@ (@ tptp.member_complex I4) I5) (not (= (@ (@ tptp.plus_plus_real (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_real))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (Y4 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I4 tptp.real)) (and (@ (@ tptp.member_real I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_rat))))))))))
% 7.01/7.31 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (Y4 (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X2 I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y4 I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X2 I4)) (@ Y4 I4)) tptp.zero_zero_rat))))))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 7.01/7.31 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 7.01/7.31 (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))))
% 7.01/7.31 (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))))
% 7.01/7.31 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 7.01/7.31 (assert (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M7) (exists ((N3 tptp.nat)) (forall ((X3 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X3)) N3)))))))
% 7.01/7.31 (assert (forall ((M7 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M7) (exists ((N3 tptp.nat)) (forall ((X3 tptp.list_o)) (=> (@ (@ tptp.member_list_o X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X3)) N3)))))))
% 7.01/7.31 (assert (forall ((M7 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M7) (exists ((N3 tptp.nat)) (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X3)) N3)))))))
% 7.01/7.31 (assert (forall ((M7 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M7) (exists ((N3 tptp.nat)) (forall ((X3 tptp.list_int)) (=> (@ (@ tptp.member_list_int X3) M7) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X3)) N3)))))))
% 7.01/7.31 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 7.01/7.31 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 7.01/7.31 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 7.01/7.31 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 7.01/7.31 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (@ (@ tptp.ord_less_eq_set_nat X4) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A4) (@ (@ tptp.ord_less_eq_rat X4) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A4) (@ (@ tptp.ord_less_eq_num X4) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_nat X4) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_int X4) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real A) A4) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_real X4) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (@ (@ tptp.member_set_nat A) A4) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (@ (@ tptp.ord_less_eq_set_nat A) X4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A4) (=> (@ (@ tptp.member_rat A) A4) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A4) (@ (@ tptp.ord_less_eq_rat A) X4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A4) (=> (@ (@ tptp.member_num A) A4) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A4) (@ (@ tptp.ord_less_eq_num A) X4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (@ (@ tptp.member_nat A) A4) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_nat A) X4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int A) A4) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_int A) X4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A4) (=> (@ (@ tptp.member_real A) A4) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_real A) X4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((B7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B7) A7) (@ P B7))) (@ P A7)))) (@ P A4)))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((B7 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B7) A7) (@ P B7))) (@ P A7)))) (@ P A4)))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (forall ((B7 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex B7) A7) (@ P B7))) (@ P A7)))) (@ P A4)))))
% 7.01/7.31 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M2))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M2) (@ tptp.bit0 N2)))))))
% 7.01/7.31 (assert (= tptp.unique5052692396658037445od_int (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M2))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M2) (@ tptp.bit0 N2)))))))
% 7.01/7.31 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M2) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M2) (@ tptp.bit0 N2)))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real X4) Xa) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A4) (=> (not (= A4 tptp.bot_bot_set_set_nat)) (exists ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A4) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A4) (=> (not (= A4 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) A4) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A4) (=> (@ (@ tptp.ord_less_eq_rat Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_num)) (=> (@ tptp.finite_finite_num A4) (=> (not (= A4 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) A4) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A4) (=> (@ (@ tptp.ord_less_eq_num Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A4) (=> (@ (@ tptp.ord_less_eq_nat Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_int)) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A4) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A4) (=> (@ (@ tptp.ord_less_eq_int Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (forall ((A4 tptp.set_real)) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) A4) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A4) (=> (@ (@ tptp.ord_less_eq_real Xa) X4) (= X4 Xa))))))))))
% 7.01/7.31 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 7.01/7.31 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))))))
% 7.01/7.31 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 7.01/7.31 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 7.01/7.31 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 7.01/7.31 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 7.01/7.31 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 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 TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X2) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _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)))))))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X2) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 7.01/7.31 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M4) N3)) (@ (@ P M4) N3)))) (@ (@ P M) N)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X2)) I) Y4) (@ _let_1 Y4)))))
% 7.01/7.31 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X2) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X2) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X2) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X2) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X2) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X2) tptp.bot_bot_set_nat) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X2) tptp.bot_bot_set_int) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X2) tptp.bot_bot_set_real) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat X2) tptp.bot_bot_nat) X2)))
% 7.01/7.31 (assert (forall ((X2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) tptp.bot_bo4199563552545308370d_enat) X2)))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) (@ tptp.size_size_list_o Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) (@ tptp.size_size_list_nat Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) (@ tptp.size_size_list_int Xs2))))
% 7.01/7.31 (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)))))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 7.01/7.31 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 7.01/7.31 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 7.01/7.31 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 7.01/7.31 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (not (= I J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) J) (@ (@ tptp.nth_int Xs2) J)))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (not (= I J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) J) (@ (@ tptp.nth_nat Xs2) J)))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (not (= I J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) J) (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs2) I) (@ (@ tptp.nth_int Xs2) I)) Xs2)))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs2) I) (@ (@ tptp.nth_nat Xs2) I)) Xs2)))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ (@ tptp.nth_VEBT_VEBT Xs2) I)) Xs2)))
% 7.01/7.31 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.31 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.31 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.31 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.31 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 7.01/7.31 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X2))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) I) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2) Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_o) (I tptp.nat) (X2 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) I) (= (@ (@ (@ tptp.list_update_o Xs2) I) X2) Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) I) (= (@ (@ (@ tptp.list_update_nat Xs2) I) X2) Xs2))))
% 7.01/7.31 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) I) (= (@ (@ (@ tptp.list_update_int Xs2) I) X2) Xs2))))
% 7.01/7.31 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 7.01/7.31 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.31 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 7.01/7.31 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 7.01/7.31 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) I) X2))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) I) X2))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) I) X2))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) I) X2))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs2))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_VEBT_VEBT2 Xs2))))))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs2))) (let ((_let_2 (@ tptp.size_size_list_o Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_o2 Xs2))))))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs2))) (let ((_let_2 (@ tptp.size_size_list_nat Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_nat2 Xs2))))))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs2))) (let ((_let_2 (@ tptp.size_size_list_int Xs2))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs2) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_int2 Xs2))))))))
% 7.01/7.31 (assert (forall ((I tptp.nat) (I6 tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (X7 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs2))) (=> (not (= I I6)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X2)) I6) X7) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I6) X7)) I) X2))))))
% 7.01/7.31 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3)) B3) A3))))
% 7.01/7.31 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) B3) A3))))
% 7.01/7.31 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B3)) B3) A3))))
% 7.01/7.31 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B3)) B3) A3))))
% 7.01/7.31 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) B3) A3))))
% 7.01/7.31 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) B3) A3))))
% 7.01/7.31 (assert (= tptp.ord_max_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B3)) B3) A3))))
% 7.01/7.31 (assert (forall ((Y4 tptp.extended_enat) (X2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y4) X2) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((Y4 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) X2) (= (@ (@ tptp.ord_max_set_nat X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X2) (= (@ (@ tptp.ord_max_rat X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((Y4 tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y4) X2) (= (@ (@ tptp.ord_max_num X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((Y4 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y4) X2) (= (@ (@ tptp.ord_max_nat X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y4) X2) (= (@ (@ tptp.ord_max_int X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X2) (= (@ (@ tptp.ord_max_real X2) Y4) X2))))
% 7.01/7.31 (assert (forall ((X2 tptp.extended_enat) (Y4 tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X2) Y4) (= (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (= (@ (@ tptp.ord_max_set_nat X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (= (@ (@ tptp.ord_max_rat X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y4) (= (@ (@ tptp.ord_max_num X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y4) (= (@ (@ tptp.ord_max_nat X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y4) (= (@ (@ tptp.ord_max_int X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (= (@ (@ tptp.ord_max_real X2) Y4) Y4))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X2) Y4)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X2) Z)) (@ (@ tptp.plus_plus_real Y4) Z)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X2) Y4)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X2) Z)) (@ (@ tptp.plus_plus_rat Y4) Z)))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X2) Y4)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X2) Z)) (@ (@ tptp.plus_plus_nat Y4) Z)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X2) Y4)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X2) Z)) (@ (@ tptp.plus_plus_int Y4) Z)))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X2))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y4) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y4)) (@ _let_1 Z))))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y4) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y4)) (@ _let_1 Z))))))
% 7.01/7.31 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y4) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y4)) (@ _let_1 Z))))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y4) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y4)) (@ _let_1 Z))))))
% 7.01/7.31 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X2) Y4)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X2) Z)) (@ (@ tptp.minus_minus_real Y4) Z)))))
% 7.01/7.31 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X2) Y4)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X2) Z)) (@ (@ tptp.minus_minus_rat Y4) Z)))))
% 7.01/7.31 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X2) Y4)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X2) Z)) (@ (@ tptp.minus_minus_int Y4) Z)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q3)) (@ (@ tptp.plus_plus_nat N) Q3)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q3))))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N) Q3)))))
% 7.01/7.31 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q3))))))
% 7.01/7.31 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B3)) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_max_set_nat (lambda ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A3) B3)) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B3)) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B3 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B3)) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B3)) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B3)) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_max_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_eq_real A3) B3)) B3) A3))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (A4 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (I tptp.nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs2)) A4) (=> (@ (@ tptp.member8440522571783428010at_nat X2) A4) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) I) X2))) A4)))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_complex) (A4 tptp.set_complex) (X2 tptp.complex) (I tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A4) (=> (@ (@ tptp.member_complex X2) A4) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) I) X2))) A4)))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_real) (A4 tptp.set_real) (X2 tptp.real) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs2)) A4) (=> (@ (@ tptp.member_real X2) A4) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I) X2))) A4)))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_int) (A4 tptp.set_int) (X2 tptp.int) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A4) (=> (@ (@ tptp.member_int X2) A4) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I) X2))) A4)))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (I tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A4) (=> (@ (@ tptp.member_VEBT_VEBT X2) A4) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2))) A4)))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_nat) (A4 tptp.set_nat) (X2 tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A4) (=> (@ (@ tptp.member_nat X2) A4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I) X2))) A4)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_P6011104703257516679at_nat) (X2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s5460976970255530739at_nat Xs2)) (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ (@ tptp.list_u6180841689913720943at_nat Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_complex) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs2)) (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs2)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs2)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs2)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs2)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) N) X2))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I) X2)))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (= (@ (@ (@ tptp.list_update_o Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_o Xs2) I) X2)))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (= (= (@ (@ (@ tptp.list_update_nat Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_nat Xs2) I) X2)))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (= (= (@ (@ (@ tptp.list_update_int Xs2) I) X2) Xs2) (= (@ (@ tptp.nth_int Xs2) I) X2)))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_VEBT_VEBT) (J tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs2) J)))))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_o) (X2 Bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs2) I) X2)) J) (and (=> _let_1 X2) (=> (not _let_1) (@ (@ tptp.nth_o Xs2) J))))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_nat) (J tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_nat Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs2) J)))))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (Xs2 tptp.list_int) (J tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs2) I) X2)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_int Xs2)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs2) J)))))))))
% 7.01/7.32 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 7.01/7.32 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 7.01/7.32 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 7.01/7.32 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B 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) B))))))
% 7.01/7.32 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) 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 X2) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X2) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X2) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _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)))))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y4) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (not (and (=> _let_4 (= Y4 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y4 (@ _let_1 true))) (=> (not _let_3) (= Y4 _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S))) (=> (= X2 _let_1) (not (= Y4 _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X2 _let_1) (not (= Y4 _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (not (= Y4 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT 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 Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (=> (and (=> _let_4 (= Y4 (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y4 (@ _let_1 true))) (=> (not _let_3) (= Y4 _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts) S))) (=> (= X2 _let_1) (=> (= Y4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts) S))) (=> (= X2 _let_1) (=> (= Y4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X2 _let_2) (=> (= Y4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y4 (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT 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 Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.extended_enat) (Y4 tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y4)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X2) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y4) Z)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X2) Y4)) Z) (and (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y4) Z)))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X2) Y4)) Z) (and (@ (@ tptp.ord_less_rat X2) Z) (@ (@ tptp.ord_less_rat Y4) Z)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (Y4 tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X2) Y4)) Z) (and (@ (@ tptp.ord_less_num X2) Z) (@ (@ tptp.ord_less_num Y4) Z)))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X2) Y4)) Z) (and (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y4) Z)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X2) Y4)) Z) (and (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_int Y4) Z)))))
% 7.01/7.32 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 7.01/7.32 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 7.01/7.32 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B) C)) A) (and (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real C) A)))))
% 7.01/7.32 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q3) tptp.zero_z5237406670263579293d_enat) Q3)))
% 7.01/7.32 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q3) Q3)))
% 7.01/7.32 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (D tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) A) (=> (@ (@ tptp.ord_less_eq_real D) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real C) D)) (@ (@ tptp.ord_max_real A) B))))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= A (@ (@ tptp.ord_max_real A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A (@ (@ tptp.ord_max_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_real B) A) (not (@ (@ tptp.ord_less_eq_real C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 7.01/7.32 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.ord_max_real B) C)) A)))))
% 7.01/7.32 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B3)))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (= A3 (@ (@ tptp.ord_max_rat A3) B3)))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A3 tptp.num)) (= A3 (@ (@ tptp.ord_max_num A3) B3)))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B3)))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B3)))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (= A3 (@ (@ tptp.ord_max_real A3) B3)))))
% 7.01/7.32 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.ord_max_real A) B))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 7.01/7.32 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.ord_max_real A) B))))
% 7.01/7.32 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y4 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_num (lambda ((B3 tptp.num) (A3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_int (lambda ((B3 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_real (lambda ((B3 tptp.real) (A3 tptp.real)) (= (@ (@ tptp.ord_max_real A3) B3) A3))))
% 7.01/7.32 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B3) B3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B3) B3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B3) B3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B3) B3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B3) B3))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B3 tptp.real)) (= (@ (@ tptp.ord_max_real A3) B3) B3))))
% 7.01/7.32 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 7.01/7.32 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B3 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B3)) (not (= A3 B3))))))
% 7.01/7.32 (assert (= tptp.ord_less_real (lambda ((B3 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B3)) (not (= A3 B3))))))
% 7.01/7.32 (assert (= tptp.ord_less_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B3)) (not (= A3 B3))))))
% 7.01/7.32 (assert (= tptp.ord_less_num (lambda ((B3 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B3)) (not (= A3 B3))))))
% 7.01/7.32 (assert (= tptp.ord_less_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B3)) (not (= A3 B3))))))
% 7.01/7.32 (assert (= tptp.ord_less_int (lambda ((B3 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B3)) (not (= A3 B3))))))
% 7.01/7.32 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 7.01/7.32 (assert (forall ((Z tptp.extended_enat) (X2 tptp.extended_enat) (Y4 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y4)) (or (@ _let_1 X2) (@ _let_1 Y4))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L)))))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 7.01/7.32 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q4) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((H2 (-> Bool Bool)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> Bool tptp.int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> tptp.int Bool)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> tptp.product_prod_int_int Bool)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> tptp.product_prod_int_int tptp.int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> Bool tptp.product_prod_int_int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> tptp.int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> tptp.product_prod_int_int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 7.01/7.32 (assert (forall ((H2 (-> (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat Bool)) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (= (@ H2 (@ (@ tptp.produc8739625826339149834_nat_o F) Prod)) (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X15 tptp.nat) (X24 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ H2 (@ (@ F X15) X24)) __flatten_var_0))) Prod))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B8 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B8) C5)) (@ (@ tptp.dvd_dvd_nat B8) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B8 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B8) C5)) (@ (@ tptp.dvd_dvd_int B8) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 7.01/7.32 (assert (forall ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X4) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X4) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 7.01/7.32 (assert (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X4) Y3)) (=> (@ (@ tptp.dvd_dvd_int X4) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 7.01/7.32 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B3 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K2 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B3) K2))))))
% 7.01/7.32 (assert (= tptp.dvd_dvd_real (lambda ((B3 tptp.real) (A3 tptp.real)) (exists ((K2 tptp.real)) (= A3 (@ (@ tptp.times_times_real B3) K2))))))
% 7.01/7.32 (assert (= tptp.dvd_dvd_rat (lambda ((B3 tptp.rat) (A3 tptp.rat)) (exists ((K2 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B3) K2))))))
% 7.01/7.32 (assert (= tptp.dvd_dvd_nat (lambda ((B3 tptp.nat) (A3 tptp.nat)) (exists ((K2 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B3) K2))))))
% 7.01/7.32 (assert (= tptp.dvd_dvd_int (lambda ((B3 tptp.int) (A3 tptp.int)) (exists ((K2 tptp.int)) (= A3 (@ (@ tptp.times_times_int B3) K2))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K3))))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K3))))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K3 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K3))))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K3))))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K3))))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 7.01/7.32 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 7.01/7.32 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 7.01/7.32 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))))
% 7.01/7.32 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y4) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y4) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y4) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y4) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y4) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y4) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y4) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y4) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y4) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y4) N)))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 7.01/7.32 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 7.01/7.32 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 7.01/7.32 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 7.01/7.32 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ Q (@ (@ P X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y)) __flatten_var_0))) F)))
% 7.01/7.32 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y)) __flatten_var_0))) F)))
% 7.01/7.32 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 7.01/7.32 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 7.01/7.32 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X tptp.int) (Y tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y)))) F)))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X4) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X4) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_int_int X4) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_int_int X4) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (= (@ (@ F X4) Y3) (@ G (@ (@ tptp.product_Pair_int_int X4) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L)) R2)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) A)))) (@ tptp.collect_complex (lambda ((C2 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C2) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B 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) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 7.01/7.32 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 7.01/7.32 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.01/7.32 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2)))) (=> (@ (@ tptp.ord_less_real Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2)))) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2)))) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2)))) (=> (@ (@ tptp.ord_less_int Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2))))) (=> (@ (@ tptp.ord_less_real Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2))))) (=> (@ (@ tptp.ord_less_rat Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2))))) (=> (@ (@ tptp.ord_less_nat Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2))))) (=> (@ (@ tptp.ord_less_int Z2) X3) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2)))) (=> (@ (@ tptp.ord_less_real X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2)))) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2)))) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2)))) (=> (@ (@ tptp.ord_less_int X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2))))) (=> (@ (@ tptp.ord_less_real X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2))))) (=> (@ (@ tptp.ord_less_rat X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2))))) (=> (@ (@ tptp.ord_less_nat X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2))))) (=> (@ (@ tptp.ord_less_int X3) Z2) (= _let_1 _let_1)))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N)) (@ (@ tptp.power_8256067586552552935nteger Y4) M))))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N)) (@ (@ tptp.power_power_nat Y4) M))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y4) M))))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y4) M))))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y4) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y4) M))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X2) (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) D)) (= (@ _let_2 X2) (@ (@ tptp.plus_plus_nat (@ _let_1 Y4)) D))) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X4) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X4)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X4)) (@ _let_1 Y3)) D3)))))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (D tptp.int) (X2 tptp.int) (T tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X2) _let_1) (@ (@ tptp.divide_divide_nat Y4) _let_1)) (=> (= (@ _let_2 X2) (@ _let_2 Y4)) (= X2 Y4)))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X))) (exists ((X tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X) tptp.zero_zero_complex)) (@ P X))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X3 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X3) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 7.01/7.32 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X3) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 7.01/7.32 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X3) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X3) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 7.01/7.32 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X3 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X3) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 7.01/7.32 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X3) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 7.01/7.32 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X3) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 7.01/7.32 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X3) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 7.01/7.32 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 7.01/7.32 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 7.01/7.32 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (M tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M) N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 7.01/7.32 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M4 tptp.nat)) (not (= X2 (@ (@ tptp.product_Pair_nat_nat K3) M4)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 7.01/7.32 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 7.01/7.32 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 7.01/7.32 (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)))))))))))))))
% 7.01/7.32 (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)))))))))))))))
% 7.01/7.32 (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)))))))))))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 7.01/7.32 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 7.01/7.32 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 7.01/7.32 (assert (= (lambda ((Y6 tptp.code_integer) (Z3 tptp.code_integer)) (= Y6 Z3)) (lambda ((A3 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 A3) (@ _let_2 B3)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B3) _let_1))))))))
% 7.01/7.32 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A3 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 A3) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B3) _let_1))))))))
% 7.01/7.32 (assert (= (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)) (lambda ((A3 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 A3) (@ _let_2 B3)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B3) _let_1))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X2))) (=> (not (= X2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (not (= X2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X2) (@ (@ tptp.power_8256067586552552935nteger X2) N)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X2) (@ (@ tptp.power_power_rat X2) N)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X2) (@ (@ tptp.power_power_nat X2) N)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X2) (@ (@ tptp.power_power_real X2) N)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X2) (@ (@ tptp.power_power_int X2) N)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X2 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X2) (@ (@ tptp.power_power_complex X2) N)))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((Q3 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 Q3))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q3)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q3)))))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X2 (@ tptp.suc N3))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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)))))))))))))
% 7.01/7.32 (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)))))))))))))
% 7.01/7.32 (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)))))))))))))
% 7.01/7.32 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 7.01/7.32 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 7.01/7.32 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 7.01/7.32 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X4) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 7.01/7.32 (assert (forall ((X8 tptp.set_rat)) (=> (not (= X8 tptp.bot_bot_set_rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) X8) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X8) (@ (@ tptp.ord_less_rat X4) Xa))))) (not (@ tptp.finite_finite_rat X8))))))
% 7.01/7.32 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X4) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 7.01/7.32 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X4) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 7.01/7.32 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X4) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 7.01/7.32 (assert (forall ((S3 tptp.set_real)) (=> (@ tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) S3) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S3) (@ (@ tptp.ord_less_real Xa) X4))))))))))
% 7.01/7.32 (assert (forall ((S3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S3) (=> (not (= S3 tptp.bot_bot_set_rat)) (exists ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) S3) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S3) (@ (@ tptp.ord_less_rat Xa) X4))))))))))
% 7.01/7.32 (assert (forall ((S3 tptp.set_num)) (=> (@ tptp.finite_finite_num S3) (=> (not (= S3 tptp.bot_bot_set_num)) (exists ((X4 tptp.num)) (and (@ (@ tptp.member_num X4) S3) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S3) (@ (@ tptp.ord_less_num Xa) X4))))))))))
% 7.01/7.32 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (=> (not (= S3 tptp.bot_bot_set_nat)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S3) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S3) (@ (@ tptp.ord_less_nat Xa) X4))))))))))
% 7.01/7.32 (assert (forall ((S3 tptp.set_int)) (=> (@ tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S3) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S3) (@ (@ tptp.ord_less_int Xa) X4))))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y4 (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y4) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (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.dvd_dvd_nat _let_1) _let_2))) (=> (= X2 _let_2) (not (and (=> _let_8 (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 7.01/7.32 (assert (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M2) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M2) N2)) N2))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((X2 (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X2) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((X2 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X2) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X2)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X2)) I))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I))))))
% 7.01/7.32 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc7828578312038201481er_o_o C) P2))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc5703948589228662326_num_o C) P2))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc4927758841916487424_num_o C) P2))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc6081775807080527818_nat_o C) P2))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc4947309494688390418_int_o C) P2))))
% 7.01/7.32 (assert (forall ((F (-> tptp.code_integer Bool Bool)) (A tptp.code_integer) (B Bool)) (=> (@ (@ F A) B) (@ (@ tptp.produc7828578312038201481er_o_o F) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))
% 7.01/7.32 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 7.01/7.32 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A5) B5)) (@ (@ tptp.member_int Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A5) B5)) (@ (@ tptp.member_int Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex))) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1043322548047392435omplex C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc242741666403216561t_real C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc5431169771168744661et_nat C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1253318751659547953et_int C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2866383454006189126omplex C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8296048397933160132t_real C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1361121860356118632et_nat C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6406642877701697732et_int C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6231982587499038204omplex C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1435849484188172666t_real C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 7.01/7.32 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A5) B5) P2) (@ (@ (@ C A5) B5) X2))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) X2))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (=> P Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 7.01/7.32 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 7.01/7.32 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 7.01/7.32 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 7.01/7.32 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 7.01/7.32 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 7.01/7.32 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 7.01/7.32 (assert (forall ((M tptp.nat) (X2 tptp.vEBT_VEBT) (N tptp.nat) (Y4 tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X2) (@ (@ tptp.replicate_VEBT_VEBT N) Y4)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X2 Y4))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) N)))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X2)) N)))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X2)) N)))
% 7.01/7.32 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X2)) N)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 7.01/7.32 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.product_prod_nat_nat) (N tptp.nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X2) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N) Y4))) (and (= X2 Y4) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y4))) (and (= X2 Y4) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y4))) (and (= X2 Y4) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y4 tptp.int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y4))) (and (= X2 Y4) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (N tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y4))) (and (= X2 Y4) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.vEBT_VEBT) (N tptp.nat) (Y4 tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y4))) (and (= X2 Y4) (not (= N tptp.zero_zero_nat))))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X2)) I) X2))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X2)) I) X2))))
% 7.01/7.32 (assert (forall ((I tptp.nat) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X2)) I) X2))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 7.01/7.32 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 7.01/7.32 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 7.01/7.32 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 7.01/7.32 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X2)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)) (not (forall ((X4 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)) (not (forall ((X4 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)) (not (forall ((X4 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)) (not (forall ((X4 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X4) Y3)))))))))
% 7.01/7.32 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 7.01/7.32 (assert (forall ((C (-> tptp.code_integer Bool Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.produc7828578312038201481er_o_o C) P2) (not (forall ((X4 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 7.01/7.32 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P2) (not (forall ((X4 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 7.01/7.32 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P2) (not (forall ((X4 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 7.01/7.32 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P2) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 7.01/7.32 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P2 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P2) (not (forall ((X4 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int X4) Y3)) (not (@ (@ C X4) Y3))))))))
% 7.01/7.32 (assert (forall ((F (-> tptp.code_integer Bool Bool)) (A tptp.code_integer) (B Bool)) (=> (@ (@ tptp.produc7828578312038201481er_o_o F) (@ (@ tptp.produc6677183202524767010eger_o A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 7.01/7.32 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) Z) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X4) Y3)) (not (@ (@ (@ C X4) Y3) Z))))))))
% 7.01/7.32 (assert (forall ((R (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R A) B) C))))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 7.01/7.32 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 7.01/7.32 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 7.01/7.32 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 7.01/7.32 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 7.01/7.32 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 7.01/7.32 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs2)) X2) Xs2))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_o) (X2 Bool)) (=> (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs2)) X2) Xs2))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_nat) (X2 tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs2)) X2) Xs2))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_int) (X2 tptp.int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs2)) (= X4 X2))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs2)) X2) Xs2))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_P6011104703257516679at_nat) (N tptp.nat) (X2 tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs2) N) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replic4235873036481779905at_nat N) X2))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_complex) (N tptp.nat) (X2 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs2) N) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_complex N) X2))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_real) (N tptp.nat) (X2 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs2) N) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_real N) X2))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_VEBT_VEBT N) X2))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_o) (N tptp.nat) (X2 Bool)) (=> (= (@ tptp.size_size_list_o Xs2) N) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_o N) X2))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_nat) (N tptp.nat) (X2 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs2) N) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_nat N) X2))))))
% 7.01/7.32 (assert (forall ((Xs2 tptp.list_int) (N tptp.nat) (X2 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs2) N) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs2)) (= Y3 X2))) (= Xs2 (@ (@ tptp.replicate_int N) X2))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (= tptp.divmod_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M2) N2)) (@ (@ tptp.modulo_modulo_nat M2) N2)))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (forall ((X2 (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X2) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.32 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.32 (assert (forall ((X2 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X2) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.32 (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))))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= 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 A3) _let_1))))))))))
% 7.01/7.32 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= 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 A3) _let_1))))))))))
% 7.01/7.32 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((X2 tptp.nat) (Y4 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y4 (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y4) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X2 _let_1) (=> (and (=> _let_8 (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y4 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 7.01/7.32 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z4) (@ (@ tptp.ord_less_int Z6) Z4))))))))
% 7.01/7.32 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z6) Z4))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.set_int) (Y4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X2) Y4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X2) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.set_real) (Y4 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X2) Y4) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X2) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X2) Y4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X2) Y4))))
% 7.01/7.32 (assert (forall ((B tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int B)) B)))
% 7.01/7.32 (assert (forall ((B tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real B)) B)))
% 7.01/7.32 (assert (forall ((B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex B)) B)))
% 7.01/7.32 (assert (forall ((B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat B)) B)))
% 7.01/7.32 (assert (forall ((B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 7.01/7.32 (assert (forall ((P Bool) (Q (-> tptp.int tptp.int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (B3 tptp.int)) (and P (@ (@ Q A3) B3)))) (lambda ((Ab tptp.product_prod_int_int)) (and P (@ (@ tptp.produc4947309494688390418_int_o Q) Ab))))))
% 7.01/7.32 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) (@ tptp.uminus5710092332889474511et_nat Y4)) (@ (@ tptp.ord_less_eq_set_nat Y4) X2))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 7.01/7.32 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.01/7.32 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.01/7.32 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 7.01/7.32 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.01/7.32 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 7.01/7.32 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 7.01/7.32 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 7.01/7.32 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 7.01/7.32 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 7.01/7.32 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 7.01/7.32 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 7.01/7.32 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 7.01/7.32 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 7.01/7.32 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 7.01/7.32 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 7.01/7.32 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 7.01/7.32 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.divide_divide_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X2))))
% 7.01/7.32 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 7.01/7.32 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 7.01/7.32 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 7.01/7.32 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y4)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y4)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y4)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y4)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y4))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y4)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y4)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y4)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y4)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y4)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y4)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y4)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y4)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y4)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y4)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y4)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y4)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (assert (forall ((V tptp.num) (W tptp.num) (Y4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y4)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y4))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 7.01/7.32 (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)))
% 7.01/7.32 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 7.01/7.32 (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))
% 7.01/7.32 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.01/7.32 (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))
% 7.01/7.32 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 7.01/7.32 (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)))
% 7.01/7.32 (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)))
% 7.01/7.32 (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)))
% 7.01/7.32 (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)))
% 7.01/7.32 (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)))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.01/7.32 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.01/7.32 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((A4 (-> tptp.int tptp.int Bool)) (B4 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A4) B4) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A4))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B4))))))
% 7.01/7.32 (assert (forall ((Prod tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((Uu3 tptp.int) (Uv3 tptp.int)) true)) Prod)))
% 7.01/7.32 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y4)) (@ tptp.uminus5710092332889474511et_nat X2)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y4) (@ tptp.uminus5710092332889474511et_nat X2)) (@ (@ tptp.ord_less_eq_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y4)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y4)) X2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) Y4))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A B) (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A B) (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 7.01/7.32 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.01/7.32 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.01/7.32 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 7.01/7.32 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.01/7.32 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((A4 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A4 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 7.01/7.32 (assert (forall ((A4 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A4 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 7.01/7.32 (assert (forall ((A4 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A4 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 7.01/7.32 (assert (forall ((A4 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A4 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 7.01/7.32 (assert (forall ((A4 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A4 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.01/7.32 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 7.01/7.32 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.01/7.32 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.01/7.32 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 7.01/7.32 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.01/7.32 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 7.01/7.32 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 7.01/7.32 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 7.01/7.32 (assert (forall ((W tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X2)) (@ (@ tptp.times_times_int X2) (@ tptp.uminus_uminus_int _let_1))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real X2) (@ tptp.uminus_uminus_real _let_1))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (X2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex X2) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat X2) (@ tptp.uminus_uminus_rat _let_1))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X2)) (@ (@ tptp.times_3573771949741848930nteger X2) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.times_times_int X2) X2) tptp.one_one_int) (or (= X2 tptp.one_one_int) (= X2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.times_times_real X2) X2) tptp.one_one_real) (or (= X2 tptp.one_one_real) (= X2 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X2) X2) tptp.one_one_complex) (or (= X2 tptp.one_one_complex) (= X2 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X2) X2) tptp.one_one_rat) (or (= X2 tptp.one_one_rat) (= X2 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X2) X2) tptp.one_one_Code_integer) (or (= X2 tptp.one_one_Code_integer) (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 7.01/7.32 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B3)))))
% 7.01/7.32 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B3)))))
% 7.01/7.32 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B3 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B3)))))
% 7.01/7.32 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B3)))))
% 7.01/7.32 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B4 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B4 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B4 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B4 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B4 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B4 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 7.01/7.32 (assert (forall ((U tptp.real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X2) X2))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 7.01/7.32 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.01/7.32 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 7.01/7.32 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 7.01/7.32 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 7.01/7.32 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 7.01/7.32 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 7.01/7.32 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 7.01/7.32 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 7.01/7.32 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 7.01/7.32 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 7.01/7.32 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 7.01/7.32 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 7.01/7.32 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 7.01/7.32 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 7.01/7.32 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.01/7.32 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.32 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 7.01/7.32 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ (@ tptp.power_power_int X2) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ (@ tptp.power_power_real X2) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ (@ tptp.power_power_complex X2) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ (@ tptp.power_power_rat X2) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X2) _let_1))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X2) _let_1))))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X2) _let_1))))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X2) _let_1))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y4) (@ tptp.uminus_uminus_real X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X2)) Y4))))
% 7.01/7.32 (assert (= tptp.pred_numeral (lambda ((K2 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) tptp.one_one_nat))))
% 7.01/7.32 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 7.01/7.32 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y4) Z))) Z)))))
% 7.01/7.32 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y4 tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y4) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y4) Z))) Z)))))
% 7.01/7.32 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y4 tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y4) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y4) Z))) Z)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y4) _let_1)) (or (= X2 Y4) (= X2 (@ tptp.uminus_uminus_int Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y4) _let_1)) (or (= X2 Y4) (= X2 (@ tptp.uminus_uminus_real Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X2) _let_1) (@ (@ tptp.power_power_complex Y4) _let_1)) (or (= X2 Y4) (= X2 (@ tptp.uminus1482373934393186551omplex Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y4) _let_1)) (or (= X2 Y4) (= X2 (@ tptp.uminus_uminus_rat Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1)) (or (= X2 Y4) (= X2 (@ tptp.uminus1351360451143612070nteger Y4)))))))
% 7.01/7.32 (assert (forall ((A4 tptp.int) (B4 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) 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 A4) N))))))
% 7.01/7.32 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 7.01/7.32 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 7.01/7.32 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((U tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 7.01/7.32 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 7.01/7.32 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (=> (@ (@ tptp.ord_le3102999989581377725nteger X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 7.01/7.32 (assert (= tptp.ring_1_of_int_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K2) _let_1))))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K2) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 7.01/7.32 (assert (= tptp.ring_1_of_int_real (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 7.01/7.32 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 7.01/7.32 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 7.01/7.32 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 7.01/7.32 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 7.01/7.32 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 7.01/7.32 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 7.01/7.32 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 7.01/7.32 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 7.01/7.32 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 7.01/7.32 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 7.01/7.32 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X2) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X2) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X2) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X2) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 7.01/7.32 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 7.01/7.32 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.01/7.32 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.32 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 7.01/7.32 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.ring_17405671764205052669omplex Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.ring_1_of_int_real Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.ring_1_of_int_rat Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y4) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (= (@ tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 7.01/7.32 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y4)) (= _let_1 Y4)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N) (@ tptp.ring_1_of_int_real Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N) (@ tptp.ring_17405671764205052669omplex Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N) (@ tptp.ring_1_of_int_rat Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y4))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N) (@ tptp.ring_18347121197199848620nteger Y4)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N) Y4))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (= (@ tptp.ring_1_of_int_int Y4) _let_1) (= Y4 _let_1)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y4) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y4) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 7.01/7.32 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)) A))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ (@ tptp.times_times_real Y4) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ (@ tptp.times_times_rat Y4) _let_1)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ (@ tptp.times_times_int Y4) _let_1)))))
% 7.01/7.32 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 7.01/7.32 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M2)) tptp.one_one_real)))))
% 7.01/7.32 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X2) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X2) D))) _let_1))))))
% 7.01/7.32 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2))))))
% 7.01/7.32 (assert (forall ((N tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X2)))) tptp.one_one_real)))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 7.01/7.32 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 7.01/7.32 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 7.01/7.32 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X4) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X4)))))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr448751882837621926eger_o) (S3 tptp.set_Pr448751882837621926eger_o)) (= (@ (@ tptp.ord_le2162486998276636481er_o_o (lambda ((X tptp.code_integer) (Y Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y)) R))) (lambda ((X tptp.code_integer) (Y Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y)) S3))) (@ (@ tptp.ord_le8980329558974975238eger_o R) S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (@ (@ tptp.ord_le6124364862034508274_num_o (lambda ((X tptp.num) (Y tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y)) R))) (lambda ((X tptp.num) (Y tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y)) S3))) (@ (@ tptp.ord_le880128212290418581um_num R) S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (@ (@ tptp.ord_le3404735783095501756_num_o (lambda ((X tptp.nat) (Y tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y)) R))) (lambda ((X tptp.nat) (Y tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y)) S3))) (@ (@ tptp.ord_le8085105155179020875at_num R) S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R))) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) S3))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R))) (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) S3))) (@ (@ tptp.ord_le2843351958646193337nt_int R) S3))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))
% 7.01/7.32 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 7.01/7.32 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 7.01/7.32 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 7.01/7.32 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 7.01/7.32 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y4)) (@ (@ tptp.ord_less_real X2) Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (= (@ tptp.ln_ln_real X2) (@ tptp.ln_ln_real Y4)) (= X2 Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (= (@ tptp.ln_ln_real X2) tptp.zero_zero_real) (= X2 tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (= (@ _let_1 (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X2)) (=> (@ _let_1 X2) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y4))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (= (@ tptp.ln_ln_real X2) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (= X2 tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y4))))))))
% 7.01/7.32 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr448751882837621926eger_o) (S3 tptp.set_Pr448751882837621926eger_o)) (= (= (lambda ((X tptp.code_integer) (Y Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y)) R)) (lambda ((X tptp.code_integer) (Y Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y)) S3))) (= R S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (= (lambda ((X tptp.num) (Y tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y)) R)) (lambda ((X tptp.num) (Y tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y)) S3))) (= R S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (= (lambda ((X tptp.nat) (Y tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y)) R)) (lambda ((X tptp.nat) (Y tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y)) S3))) (= R S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (= (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) R)) (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) S3))) (= R S3))))
% 7.01/7.32 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (= (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) R)) (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) S3))) (= R S3))))
% 7.01/7.32 (assert (= tptp.bot_bo4731626569425807221er_o_o (lambda ((X tptp.code_integer) (Y Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y)) tptp.bot_bo5379713665208646970eger_o))))
% 7.01/7.32 (assert (= tptp.bot_bot_num_num_o (lambda ((X tptp.num) (Y tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y)) tptp.bot_bo9056780473022590049um_num))))
% 7.01/7.32 (assert (= tptp.bot_bot_nat_num_o (lambda ((X tptp.nat) (Y tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y)) tptp.bot_bo7038385379056416535at_num))))
% 7.01/7.32 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) tptp.bot_bo2099793752762293965at_nat))))
% 7.01/7.32 (assert (= tptp.bot_bot_int_int_o (lambda ((X tptp.int) (Y tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y)) tptp.bot_bo1796632182523588997nt_int))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y4))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) Y4)) Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2))) (@ tptp.uminus_uminus_real X2))))))
% 7.01/7.32 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 7.01/7.32 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 7.01/7.32 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((W tptp.real) (Y4 tptp.real) (X2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X2) (= Y4 Z)))))))
% 7.01/7.32 (assert (forall ((W tptp.rat) (Y4 tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X2) (= Y4 Z)))))))
% 7.01/7.32 (assert (forall ((W tptp.nat) (Y4 tptp.nat) (X2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X2))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X2) (= Y4 Z)))))))
% 7.01/7.32 (assert (forall ((W tptp.int) (Y4 tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y4)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y4))) (or (= W X2) (= Y4 Z)))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 7.01/7.32 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 7.01/7.32 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X2))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z2)))))
% 7.01/7.32 (assert (forall ((R2 tptp.set_Pr448751882837621926eger_o) (S2 tptp.set_Pr448751882837621926eger_o)) (=> (forall ((X4 tptp.code_integer) (Y3 Bool)) (let ((_let_1 (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8980329558974975238eger_o R2) S2))))
% 7.01/7.32 (assert (forall ((R2 tptp.set_Pr8218934625190621173um_num) (S2 tptp.set_Pr8218934625190621173um_num)) (=> (forall ((X4 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le880128212290418581um_num R2) S2))))
% 7.01/7.32 (assert (forall ((R2 tptp.set_Pr6200539531224447659at_num) (S2 tptp.set_Pr6200539531224447659at_num)) (=> (forall ((X4 tptp.nat) (Y3 tptp.num)) (let ((_let_1 (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8085105155179020875at_num R2) S2))))
% 7.01/7.32 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2))))
% 7.01/7.32 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X4 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y4))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X2) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X2) Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y4))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X2) _let_1)) (= (@ tptp.archim8280529875227126926d_real X2) Y4)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.01/7.32 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 7.01/7.32 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) (@ tptp.tanh_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X2)) (@ _let_1 X2)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 7.01/7.32 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 7.01/7.32 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 7.01/7.32 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X2))))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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)))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (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))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 7.01/7.32 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (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)))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 7.01/7.32 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 7.01/7.32 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 7.01/7.32 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 7.01/7.32 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 7.01/7.32 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 7.01/7.32 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 7.01/7.33 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 7.01/7.33 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 7.01/7.33 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 7.01/7.33 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 7.01/7.33 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) E2))) (= X2 tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) E2))) (= X2 tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y4)) X2) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y4) X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y4)) X2) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y4) X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y4)) X2) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y4) X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y4)) X2) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y4) X2))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B)))))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B A) (= B (@ tptp.uminus1351360451143612070nteger A)))))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.33 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 7.01/7.33 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 7.01/7.33 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X2)) Y4) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) Y4))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y4) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X2)) Y4) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X2) Y4))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 7.01/7.33 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 7.01/7.33 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 7.01/7.33 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 7.01/7.33 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X2) (@ (@ tptp.ord_le3102999989581377725nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X2) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.plus_plus_int A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real A) R2))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X2) (@ (@ tptp.ord_le6747313008572928689nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X2) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.plus_plus_int A) R2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X2)) (@ tptp.archim7778729529865785530nd_rat Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X2)) (@ tptp.archim8280529875227126926d_real Y4)))))
% 7.01/7.33 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (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 X2) Y5))) D3) (and (@ (@ tptp.ord_less_real A) Y5) (@ (@ tptp.ord_less_real Y5) B))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X2) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X2)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (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 X2) Y5))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y5) (@ (@ tptp.ord_less_eq_real Y5) B))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) X2))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) X2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X2) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X2) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) (@ tptp.abs_abs_Code_integer Y4)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) (@ tptp.abs_abs_rat Y4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X2) tptp.one_one_Code_integer))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X2) tptp.one_one_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X2) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.code_integer) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y4) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y4) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) Y4))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y4) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) Y4))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) Y4))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) Y4))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X2 tptp.code_integer)) (=> (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (@ (@ P X4) (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X2)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X2 tptp.rat)) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ P X4) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X2)) (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X2 tptp.int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ P X4) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X2)) (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ P X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A4)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 7.01/7.33 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 7.01/7.33 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 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 A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.33 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 7.01/7.33 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.33 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X2)) (@ _let_1 X2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A4))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A4))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A4))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 7.01/7.33 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 7.01/7.33 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ tptp.abs_abs_real (@ F I4)))) A4))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q3)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X2)) (@ tptp.arctan Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 7.01/7.33 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 7.01/7.33 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N2)))) A4))))
% 7.01/7.33 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A4 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A4)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N2)))) A4))))
% 7.01/7.33 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N2)))) A4))))
% 7.01/7.33 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N2)))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int (@ F N2)) R2))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.complex tptp.complex)) (A4 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A4)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N2)) R2))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N2)) R2))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A4)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) R2))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int) (G (-> tptp.int tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int G) B4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I4)) (@ G J3)))) B4))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.complex tptp.complex)) (A4 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B4 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A4)) (@ (@ tptp.groups7754918857620584856omplex G) B4)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I4)) (@ G J3)))) B4))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat G) B4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I4)) (@ G J3)))) B4))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A4)) (@ (@ tptp.groups6591440286371151544t_real G) B4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ G J3)))) B4))) A4))))
% 7.01/7.33 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A4)) (@ (@ tptp.groups4538972089207619220nt_int H2) A4)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A4 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A4)) (@ (@ tptp.groups7754918857620584856omplex H2) A4)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A4)) (@ (@ tptp.groups3542108847815614940at_nat H2) A4)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A4)) (@ (@ tptp.groups6591440286371151544t_real H2) A4)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.complex tptp.complex)) (A4 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A4)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) R2))) A4))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A4 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A4)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) R2))) A4))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A4)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A4)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A4)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A4)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A4)) tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A4)) tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) A4)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) A4)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_int (@ F X4)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) A4)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups5690904116761175830ex_int F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1932886352136224148al_int F) A4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups3539618377306564664at_int F) A4)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.real tptp.rat)) (I5 tptp.set_real) (G (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I5) (@ (@ tptp.groups1300246762558778688al_rat G) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.complex tptp.rat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I5) (@ (@ tptp.groups5058264527183730370ex_rat G) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.real tptp.nat)) (I5 tptp.set_real) (G (-> tptp.real tptp.nat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) I5) (@ (@ tptp.groups1935376822645274424al_nat G) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (I tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.complex tptp.nat)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) I5) (@ (@ tptp.groups5693394587270226106ex_nat G) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.real tptp.int)) (I5 tptp.set_real) (G (-> tptp.real tptp.int)) (I tptp.real)) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) I5) (@ (@ tptp.groups1932886352136224148al_int G) I5)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_real I) I5) (=> (@ tptp.finite_finite_real I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I5) (@ (@ tptp.groups3539618377306564664at_int G) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.complex tptp.int)) (I5 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I5) (@ (@ tptp.groups5690904116761175830ex_int G) I5)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_complex I) I5) (=> (@ tptp.finite3207457112153483333omplex I5) (= (@ F I) (@ G I))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))))))))
% 7.01/7.33 (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)))))))))))
% 7.01/7.33 (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)))))))))))
% 7.01/7.33 (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)))))))))))
% 7.01/7.33 (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)))))))))))
% 7.01/7.33 (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)))))))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y4) X2) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X2) Y4)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y4))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A4) tptp.zero_zero_rat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A4) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A4) tptp.zero_zero_rat) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A4) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A4) tptp.zero_zero_rat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A4) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A4) tptp.zero_zero_rat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A4) (= (@ F X) tptp.zero_zero_rat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A4) tptp.zero_zero_nat) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A4) (= (@ F X) tptp.zero_zero_nat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A4) tptp.zero_zero_nat) (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) A4) (= (@ F X) tptp.zero_zero_nat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A4) tptp.zero_zero_nat) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A4) (= (@ F X) tptp.zero_zero_nat))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real A4) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (= (= (@ (@ tptp.groups1932886352136224148al_int F) A4) tptp.zero_zero_int) (forall ((X tptp.real)) (=> (@ (@ tptp.member_real X) A4) (= (@ F X) tptp.zero_zero_int))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (= (= (@ (@ tptp.groups3539618377306564664at_int F) A4) tptp.zero_zero_int) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A4) (= (@ F X) tptp.zero_zero_int))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (= (= (@ (@ tptp.groups5690904116761175830ex_int F) A4) tptp.zero_zero_int) (forall ((X tptp.complex)) (=> (@ (@ tptp.member_complex X) A4) (= (@ F X) tptp.zero_zero_int))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X4)))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S2) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.nat)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) T) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ G X4)))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S2) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) S2)) (@ (@ tptp.groups4541462559716669496nt_nat G) T))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A4)) (@ (@ tptp.groups2906978787729119204at_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A4)) (@ (@ tptp.groups3906332499630173760nt_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_rat (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A4)) (@ (@ tptp.groups5058264527183730370ex_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A4)) (@ (@ tptp.groups5693394587270226106ex_nat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A4) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A4) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A4)) (@ (@ tptp.groups3539618377306564664at_int G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A4)) (@ (@ tptp.groups5690904116761175830ex_int G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A4)) (@ (@ tptp.groups8778361861064173332t_real G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A4) (@ (@ tptp.ord_less_real (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A4)) (@ (@ tptp.groups5808333547571424918x_real G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_int (@ F X4)) (@ G X4)))) (=> (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A4) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A4)) (@ (@ tptp.groups4538972089207619220nt_int G) A4)))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X16) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups2073611262835488442omplex H2) S3)) (@ (@ tptp.groups2073611262835488442omplex G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_complex X16) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups3049146728041665814omplex H2) S3)) (@ (@ tptp.groups3049146728041665814omplex G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X16) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups8778361861064173332t_real H2) S3)) (@ (@ tptp.groups8778361861064173332t_real G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_real X16) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups5808333547571424918x_real H2) S3)) (@ (@ tptp.groups5808333547571424918x_real G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups2906978787729119204at_rat H2) S3)) (@ (@ tptp.groups2906978787729119204at_rat G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups3906332499630173760nt_rat H2) S3)) (@ (@ tptp.groups3906332499630173760nt_rat G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_rat X16) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups5058264527183730370ex_rat H2) S3)) (@ (@ tptp.groups5058264527183730370ex_rat G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X16) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups4541462559716669496nt_nat H2) S3)) (@ (@ tptp.groups4541462559716669496nt_nat G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_nat X16) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups5693394587270226106ex_nat H2) S3)) (@ (@ tptp.groups5693394587270226106ex_nat G) S3))))))))
% 7.01/7.33 (assert (forall ((R (-> tptp.int tptp.int Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X16 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.plus_plus_int X16) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups3539618377306564664at_int H2) S3)) (@ (@ tptp.groups3539618377306564664at_int G) S3))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A4)) (@ (@ tptp.groups5808333547571424918x_real G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A4)) (@ (@ tptp.groups8778361861064173332t_real G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A4)) (@ (@ tptp.groups8097168146408367636l_real G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A4)) (@ (@ tptp.groups5058264527183730370ex_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A4) (=> (not (= A4 tptp.bot_bot_set_nat)) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A4)) (@ (@ tptp.groups2906978787729119204at_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A4)) (@ (@ tptp.groups3906332499630173760nt_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A4)) (@ (@ tptp.groups1300246762558778688al_rat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (= A4 tptp.bot_bot_set_complex)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A4)) (@ (@ tptp.groups5693394587270226106ex_nat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (=> (not (= A4 tptp.bot_bot_set_int)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G) A4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A4) (=> (not (= A4 tptp.bot_bot_set_real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A4)) (@ (@ tptp.groups1935376822645274424al_nat G) A4)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (= tptp.abs_abs_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I4)) I4))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S2) (= (@ F I) tptp.zero_zero_rat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_real I) S2) (= (@ F I) tptp.zero_zero_nat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I) S2) (= (@ F I) tptp.zero_zero_nat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I) S2) (= (@ F I) tptp.zero_zero_nat)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.int)) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) S2) tptp.zero_zero_int) (=> (@ (@ tptp.member_real I) S2) (= (@ F I) tptp.zero_zero_int)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) S2) tptp.zero_zero_int) (=> (@ (@ tptp.member_nat I) S2) (= (@ F I) tptp.zero_zero_int)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) S2) tptp.zero_zero_int) (=> (@ (@ tptp.member_complex I) S2) (= (@ F I) tptp.zero_zero_int)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.rat)) (B4 tptp.rat) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S2) B4) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B4 tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B4) (=> (@ (@ tptp.member_nat I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B4 tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B4) (=> (@ (@ tptp.member_int I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B4 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S2) B4) (=> (@ (@ tptp.member_complex I) S2) (@ (@ tptp.ord_less_eq_rat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.nat)) (B4 tptp.nat) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups1935376822645274424al_nat F) S2) B4) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_nat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (B4 tptp.nat) (I tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) B4) (=> (@ (@ tptp.member_int I) S2) (@ (@ tptp.ord_less_eq_nat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B4 tptp.nat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S2) B4) (=> (@ (@ tptp.member_complex I) S2) (@ (@ tptp.ord_less_eq_nat (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.int)) (B4 tptp.int) (I tptp.real)) (=> (@ tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) S2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int F) S2) B4) (=> (@ (@ tptp.member_real I) S2) (@ (@ tptp.ord_less_eq_int (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (B4 tptp.int) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) S2) B4) (=> (@ (@ tptp.member_nat I) S2) (@ (@ tptp.ord_less_eq_int (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (B4 tptp.int) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) S2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) S2) B4) (=> (@ (@ tptp.member_complex I) S2) (@ (@ tptp.ord_less_eq_int (@ F I)) B4)))))))
% 7.01/7.33 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L))) (@ tptp.abs_abs_int L)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1932886352136224148al_int F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3539618377306564664at_int F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups5690904116761175830ex_int F) I5)))))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I5)))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.33 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.33 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B4) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A4) B4) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B4) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B4) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B4) A4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B4) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A4) B4) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B4) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B4) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B4) A4)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B4) A4)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B4) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B4) A4)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B4) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A4) B4) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B4) A4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A4)) (@ _let_1 B4))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.modulo_modulo_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.33 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L))) (@ _let_2 (@ _let_1 L)))))))
% 7.01/7.33 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 7.01/7.33 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A4) B4) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B4) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A4)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (@ (@ tptp.ord_less_rat (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A4) B4) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B4) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A4)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B4) (=> (@ (@ tptp.ord_le211207098394363844omplex A4) B4) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B4) A4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) B4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_real) (A4 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B4) (=> (@ (@ tptp.ord_less_eq_set_real A4) B4) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B4) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real F))) (=> (@ tptp.finite_finite_int B4) (=> (@ (@ tptp.ord_less_eq_set_int A4) B4) (=> (@ (@ tptp.member_int B) (@ (@ tptp.minus_minus_set_int B4) A4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (@ (@ tptp.ord_less_real (@ _let_1 A4)) (@ _let_1 B4))))))))))
% 7.01/7.33 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I3)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I4 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I3)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I4 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X2) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I3)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I3)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X2) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I4 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I3)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X2) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X2) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_int) (X2 (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X2) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_complex) (X2 (-> tptp.complex tptp.int)) (A (-> tptp.complex tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X2 I3)))) (=> (= (@ (@ tptp.groups5690904116761175830ex_int X2) I5) tptp.one_one_int) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups5690904116761175830ex_int (lambda ((I4 tptp.complex)) (@ (@ tptp.times_times_int (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (assert (forall ((I5 tptp.set_real) (X2 (-> tptp.real tptp.int)) (A (-> tptp.real tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X2 I3)))) (=> (= (@ (@ tptp.groups1932886352136224148al_int X2) I5) tptp.one_one_int) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups1932886352136224148al_int (lambda ((I4 tptp.real)) (@ (@ tptp.times_times_int (@ A I4)) (@ X2 I4)))) I5)) B))) Delta))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (assert (forall ((D tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D))))))
% 7.01/7.33 (assert (forall ((D tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 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 K2) _let_1))) _let_1)))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.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))))))))))
% 7.01/7.33 (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))))))))))
% 7.01/7.33 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X2)) (@ tptp.arctan Y4)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y4)))))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K2 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L)))))
% 7.01/7.33 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L)))))
% 7.01/7.33 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L)))))
% 7.01/7.33 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L)))))
% 7.01/7.33 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L)))))
% 7.01/7.33 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.33 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 7.01/7.33 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 7.01/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 7.01/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2)))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) (@ tptp.uminus_uminus_int tptp.one_one_int)) X2)))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X2) _let_1))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X2) _let_1))))
% 7.01/7.33 (assert (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X2) _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X2) _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 7.01/7.33 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 7.01/7.33 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) tptp.one_one_int) tptp.one_one_int)))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) tptp.one_one_nat) tptp.one_one_nat)))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) tptp.one_one_int)))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) tptp.one_one_nat)))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X2)) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) tptp.zero_zero_int)))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) tptp.zero_zero_int)))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) tptp.zero_zero_nat)))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A4) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4)))) A4) tptp.zero_zero_complex))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A4) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A4) tptp.zero_zero_rat))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A4) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4)))) A4) tptp.zero_zero_real))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4))))))
% 7.01/7.33 (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)))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A4) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I4)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I4))) (@ D I4)))) A4) tptp.zero_zero_complex))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A4) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D I4)))) A4) tptp.zero_zero_rat))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A4) (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A4) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I4)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I4))) (@ D I4)))) A4) tptp.zero_zero_real))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y4))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.33 (assert (forall ((A4 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A4))) (= (@ (@ tptp.times_times_complex _let_1) A4) (@ (@ tptp.times_times_complex A4) _let_1)))))
% 7.01/7.33 (assert (forall ((A4 tptp.real)) (let ((_let_1 (@ tptp.exp_real A4))) (= (@ (@ tptp.times_times_real _let_1) A4) (@ (@ tptp.times_times_real A4) _let_1)))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (X2 tptp.code_integer) (Y4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (@ tptp.bit_se3949692690581998587nteger A))) (=> (= (@ _let_3 X2) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X2) _let_1) (=> (= (@ _let_3 Y4) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y4) _let_1) (= X2 Y4))))))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (X2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (@ tptp.bit_se725231765392027082nd_int A))) (=> (= (@ _let_3 X2) tptp.zero_zero_int) (=> (= (@ _let_2 X2) _let_1) (=> (= (@ _let_3 Y4) tptp.zero_zero_int) (=> (= (@ _let_2 Y4) _let_1) (= X2 Y4))))))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X4 tptp.num)) (=> (@ P X4) (@ P (@ tptp.inc X4)))) (@ P X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X2))) (= (@ _let_1 (@ tptp.inc Y4)) (@ tptp.inc (@ _let_1 Y4))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (exists ((X4 tptp.real)) (= (@ tptp.exp_real X4) Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.suc X4))) (=> (@ (@ tptp.member_nat _let_1) A4) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A4) (@ (@ tptp.groups3542108847815614940at_nat G) A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A4)) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.suc X4))) (=> (@ (@ tptp.member_nat _let_1) A4) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A4) (@ (@ tptp.groups6591440286371151544t_real G) A4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y4)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y4)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X2) Y4) (@ (@ tptp.times_times_complex Y4) X2)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y4)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (= (@ (@ tptp.times_times_real X2) Y4) (@ (@ tptp.times_times_real Y4) X2)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X2) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y4)))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A4) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A4)) (@ (@ tptp.groups977919841031483927at_nat G) A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A4)) (@ (@ tptp.groups5693394587270226106ex_nat G) A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A4)) (@ (@ tptp.groups1935376822645274424al_nat G) A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups4541462559716669496nt_nat G) A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_nat (@ G X4)) (@ F X4)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A4) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups3542108847815614940at_nat G) A4))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.pow X2) tptp.one) X2)))
% 7.01/7.33 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X2)) (@ tptp.bit0 (@ tptp.inc X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X2)) (@ tptp.bit1 X2))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A4) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A4) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A4) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A4) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A4) (@ tptp.suc tptp.zero_zero_nat)) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (= (@ F X) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A4) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A4) (@ tptp.suc N)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A4) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A4) tptp.one_one_nat) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) A4) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.int)) (=> (@ (@ tptp.member_int Y) A4) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A4) tptp.one_one_nat) (exists ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A4) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.complex)) (=> (@ (@ tptp.member_complex Y) A4) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A4) (= (= (@ (@ tptp.groups3542108847815614940at_nat F) A4) tptp.one_one_nat) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (= (@ F X) tptp.one_one_nat) (forall ((Y tptp.nat)) (=> (@ (@ tptp.member_nat Y) A4) (=> (not (= X Y)) (= (@ F Y) tptp.zero_zero_nat))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.plus_plus_num X2) tptp.one) (@ tptp.inc X2))))
% 7.01/7.33 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) K))))
% 7.01/7.33 (assert (forall ((Y4 tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y4) Ya)) Z)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (=> (@ (@ tptp.ord_less_int Y4) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y4)) Z)))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))) tptp.one_one_real)))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2))) tptp.one_one_complex)))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.times_times_num X2))) (= (@ _let_1 (@ tptp.inc Y4)) (@ (@ tptp.plus_plus_num (@ _let_1 Y4)) X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.01/7.33 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 7.01/7.33 (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 ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))) tptp.zero_zero_complex))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1080825931792720795nteger A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 7.01/7.33 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y4)) X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X2)) tptp.one_one_complex))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X2)) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X2)) tptp.one_one_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X2)) tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y4)) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 7.01/7.33 (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.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.01/7.33 (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.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.01/7.33 (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.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.01/7.33 (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.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 7.01/7.33 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.bit_se2000444600071755411sk_int N)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 7.01/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 7.01/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 7.01/7.33 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 7.01/7.33 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 7.01/7.33 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N)) (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N)) (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y4) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X2) Y4)) _let_1)))))))
% 7.01/7.33 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 7.01/7.33 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X2))))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X2))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M2 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_int M2) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S3)))))))
% 7.01/7.33 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X2)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) Y4) (and (=> _let_5 (= Y4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (M tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X2 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 7.01/7.33 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 7.01/7.33 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 7.01/7.33 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 7.01/7.33 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 7.01/7.33 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 7.01/7.33 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 7.01/7.33 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.01/7.33 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X2) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X2) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X2) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X2) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 7.01/7.33 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 7.01/7.33 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 7.01/7.33 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) tptp.zero_zero_nat)))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((Y4 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y4) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y4) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y4) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.nat) (X2 tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y4) _let_1) (= Y4 _let_1)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.nat) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y4) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N)) (= Y4 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N) (@ tptp.semiri681578069525770553at_rat Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) (@ tptp.semiri1314217659103216013at_int Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N) (@ tptp.semiri5074537144036343181t_real Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y4)) (= _let_1 Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N) (@ tptp.semiri8010041392384452111omplex Y4)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) Y4))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 7.01/7.33 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 7.01/7.33 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) tptp.one_one_nat)))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X2)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X2)) N)) (or (@ _let_1 X2) (= N tptp.zero_zero_nat))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_nat X2) _let_1)))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_eq_nat X2) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.01/7.33 (assert (forall ((I tptp.num) (N tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N3)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N3)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y4) (@ (@ tptp.times_times_rat Y4) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y4) (@ (@ tptp.times_times_int Y4) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y4) (@ (@ tptp.times_times_real Y4) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X2))) (= (@ (@ tptp.times_times_nat _let_1) Y4) (@ (@ tptp.times_times_nat Y4) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) Y4) (@ (@ tptp.times_times_complex Y4) _let_1)))))
% 7.01/7.33 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X2)) (@ _let_1 X2)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X2))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 7.01/7.33 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N3))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))) (@ P Z)))))
% 7.01/7.33 (assert (forall ((Z tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))))
% 7.01/7.33 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 7.01/7.33 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 7.01/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X2) Y4)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X2)) (@ tptp.semiri4216267220026989637d_enat Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X2) Y4)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X2) Y4)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.semiri5074537144036343181t_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X2) Y4)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ tptp.semiri1316708129612266289at_nat Y4)))))
% 7.01/7.33 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.01/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y4) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X4 tptp.vEBT_VEBT) (S4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) S4) (@ (@ tptp.ord_less_eq_rat (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool)) (F (-> tptp.vEBT_VEBT tptp.num))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((X4 tptp.vEBT_VEBT) (S4 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT S4) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_VEBT_VEBT X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X4 tptp.complex) (S4 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S4) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_complex X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X4 tptp.nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S4) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_nat X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X4 tptp.int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S4) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_int X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X4 tptp.real) (S4 tptp.set_real)) (=> (@ tptp.finite_finite_real S4) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) S4) (@ (@ tptp.ord_less_eq_num (@ F Y5)) (@ F X4)))) (=> (@ P S4) (@ P (@ (@ tptp.insert_real X4) S4)))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A4) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ (@ tptp.ord_less_real X3) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A4) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) A7) (@ (@ tptp.ord_less_rat X3) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A4) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) A7) (@ (@ tptp.ord_less_num X3) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ (@ tptp.ord_less_nat X3) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A4) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ (@ tptp.ord_less_int X3) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A4) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A7) (@ (@ tptp.ord_less_real B5) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A4) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) A7) (@ (@ tptp.ord_less_rat B5) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A4) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) A7) (@ (@ tptp.ord_less_num B5) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A4) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A7) (@ (@ tptp.ord_less_nat B5) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A4) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A7) (@ (@ tptp.ord_less_int B5) X3))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B5) A7)))))) (@ P A4))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X2) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X2) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A4)))) (let ((_let_4 (@ (@ tptp.member_real X2) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A4)))) (let ((_let_4 (@ (@ tptp.member_int X2) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A4)))) (let ((_let_4 (@ (@ tptp.member_real X2) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A4)))) (let ((_let_4 (@ (@ tptp.member_int X2) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X2)) _let_2)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (forall ((Y5 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y5) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X2)))))))
% 7.01/7.33 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2)))))
% 7.01/7.33 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 7.01/7.33 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z4 tptp.int)) (exists ((N2 tptp.nat)) (= Z4 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((Xs2 tptp.list_real) (I tptp.nat) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs2) I) X2))) (@ (@ tptp.insert_real X2) (@ tptp.set_real2 Xs2)))))
% 7.01/7.33 (assert (forall ((Xs2 tptp.list_int) (I tptp.nat) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs2) I) X2))) (@ (@ tptp.insert_int X2) (@ tptp.set_int2 Xs2)))))
% 7.01/7.33 (assert (forall ((Xs2 tptp.list_VEBT_VEBT) (I tptp.nat) (X2 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs2) I) X2))) (@ (@ tptp.insert_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs2)))))
% 7.01/7.33 (assert (forall ((Xs2 tptp.list_nat) (I tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs2) I) X2))) (@ (@ tptp.insert_nat X2) (@ tptp.set_nat2 Xs2)))))
% 7.01/7.33 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 7.01/7.33 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 7.01/7.33 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 7.01/7.33 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M2)))))
% 7.01/7.33 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M2)) tptp.one_one_real)))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (P (-> tptp.set_VEBT_VEBT Bool))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (=> (@ P tptp.bot_bo8194388402131092736T_VEBT) (=> (forall ((T3 tptp.set_VEBT_VEBT)) (=> (@ (@ tptp.ord_le3480810397992357184T_VEBT T3) S3) (=> (@ P T3) (exists ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) T3)) (@ P (@ (@ tptp.insert_VEBT_VEBT X3) T3))))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T3) S3) (=> (@ P T3) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) (@ (@ tptp.minus_811609699411566653omplex S3) T3)) (@ P (@ (@ tptp.insert_complex X3) T3))))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T3) S3) (=> (@ P T3) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int S3) T3)) (@ P (@ (@ tptp.insert_int X3) T3))))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T3) S3) (=> (@ P T3) (exists ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) (@ (@ tptp.minus_minus_set_real S3) T3)) (@ P (@ (@ tptp.insert_real X3) T3))))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T3) S3) (=> (@ P T3) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat S3) T3)) (@ P (@ (@ tptp.insert_nat X3) T3))))))) (@ P S3))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le3480810397992357184T_VEBT A4))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le3480810397992357184T_VEBT (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ _let_3 tptp.bot_bo8194388402131092736T_VEBT))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le4337996190870823476T_VEBT A4) B4)))))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_Pr1261947904930325089at_nat) (X2 tptp.product_prod_nat_nat) (B4 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert8211810215607154385at_nat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_le7866589430770878221at_nat A4))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A4) (@ _let_3 tptp.bot_bo2099793752762293965at_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le3146513528884898305at_nat A4) B4)))))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_complex X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_complex A4))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_3 tptp.bot_bot_set_complex))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A4) B4)))))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_int X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_int A4))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A4) (@ _let_3 tptp.bot_bot_set_int))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A4) B4)))))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_real X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_real A4))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A4) (@ _let_3 tptp.bot_bot_set_real))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A4) B4)))))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ tptp.insert_nat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_nat A4))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A4) (@ _let_3 tptp.bot_bot_set_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A4) B4)))))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X2)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X2) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X2) D))) _let_1))))))
% 7.01/7.33 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 7.01/7.33 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 7.01/7.33 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X2)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X2)) C))) (= X2 tptp.zero_zero_real)))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (@ (@ tptp.member_VEBT_VEBT X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (@ (@ tptp.member_VEBT_VEBT X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (@ (@ tptp.member_VEBT_VEBT X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (@ (@ tptp.member_VEBT_VEBT X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_1 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (@ (@ tptp.member_complex X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex X2) tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (@ (@ tptp.member_int X2) A4) (= (@ _let_1 A4) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups2240296850493347238T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups136491112297645522BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.nat)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups771621172384141258BT_nat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_nat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_VEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.int)) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.insert_VEBT_VEBT X2))) (let ((_let_2 (@ tptp.groups769130701875090982BT_int G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ _let_1 tptp.bot_bo8194388402131092736T_VEBT))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X2 tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X2))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_int (@ G X2)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A4) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.real)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_real (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat)) (X2 tptp.int)) (let ((_let_1 (@ tptp.insert_int X2))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_2 (@ _let_1 A4)) (@ (@ tptp.plus_plus_rat (@ G X2)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A4) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 7.01/7.33 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y4 tptp.one))))) (let ((_let_3 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y4) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (not (= Y4 _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y4 (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y4 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (=> (exists ((N3 tptp.num)) (= X2 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))))))))))))))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.nat) (Y4 tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X2) Y4))) (and (=> (@ (@ tptp.ord_less_eq_nat Y4) X2) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y4)))) (=> (@ (@ tptp.ord_less_nat X2) Y4) (@ P tptp.zero_zero_int))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X2)))) tptp.one_one_real)))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X2))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.real)) (C (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ (@ tptp.groups2240296850493347238T_real C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups2240296850493347238T_real (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.rat)) (C (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ (@ tptp.groups136491112297645522BT_rat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups136491112297645522BT_rat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.nat)) (C (-> tptp.vEBT_VEBT tptp.nat))) (let ((_let_1 (@ (@ tptp.groups771621172384141258BT_nat C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups771621172384141258BT_nat (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_VEBT_VEBT) (A tptp.vEBT_VEBT) (B (-> tptp.vEBT_VEBT tptp.int)) (C (-> tptp.vEBT_VEBT tptp.int))) (let ((_let_1 (@ (@ tptp.groups769130701875090982BT_int C) (@ (@ tptp.minus_5127226145743854075T_VEBT S3) (@ (@ tptp.insert_VEBT_VEBT A) tptp.bot_bo8194388402131092736T_VEBT))))) (let ((_let_2 (@ (@ tptp.member_VEBT_VEBT A) S3))) (=> (@ tptp.finite5795047828879050333T_VEBT S3) (and (=> _let_2 (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups769130701875090982BT_int (lambda ((K2 tptp.vEBT_VEBT)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ tptp.minus_811609699411566653omplex S3) (@ (@ tptp.insert_complex A) tptp.bot_bot_set_complex))))) (let ((_let_2 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups8778361861064173332t_real C) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups3906332499630173760nt_rat C) (@ (@ tptp.minus_minus_set_int S3) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))) (let ((_let_2 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_2 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S3) _let_1))))))))
% 7.01/7.33 (assert (forall ((I tptp.vEBT_VEBT) (A4 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.rat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A4) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups136491112297645522BT_rat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.complex) (A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.int) (A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.real) (A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A4) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.nat) (A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I) A4) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat A4) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X4)))) (=> (@ tptp.finite_finite_nat A4) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups2906978787729119204at_rat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.vEBT_VEBT) (A4 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.nat))) (=> (@ (@ tptp.member_VEBT_VEBT I) A4) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups771621172384141258BT_nat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.complex) (A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I) A4) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex A4) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (=> (@ tptp.finite3207457112153483333omplex A4) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups5693394587270226106ex_nat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.int) (A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int I) A4) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int A4) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (=> (@ tptp.finite_finite_int A4) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups4541462559716669496nt_nat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.real) (A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ (@ tptp.member_real I) A4) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real A4) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (=> (@ tptp.finite_finite_real A4) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups1935376822645274424al_nat F) A4)))))))
% 7.01/7.33 (assert (forall ((I tptp.vEBT_VEBT) (A4 tptp.set_VEBT_VEBT) (F (-> tptp.vEBT_VEBT tptp.int))) (=> (@ (@ tptp.member_VEBT_VEBT I) A4) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ (@ tptp.minus_5127226145743854075T_VEBT A4) (@ (@ tptp.insert_VEBT_VEBT I) tptp.bot_bo8194388402131092736T_VEBT))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (@ (@ tptp.ord_less_eq_int (@ F I)) (@ (@ tptp.groups769130701875090982BT_int F) A4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) N)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 7.01/7.33 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N7) (@ (@ tptp.member_nat N7) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 7.01/7.33 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M2 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M2 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.member_nat N2) S3)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M2)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 7.01/7.33 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M2)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 7.01/7.33 (assert (forall ((A tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 7.01/7.33 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 7.01/7.33 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X2)))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M2)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M2)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M2)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M2)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M2 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M2)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (forall ((U tptp.real) (Deg tptp.nat) (T tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.log _let_1))) (=> (= U (@ (@ tptp.power_power_real _let_1) Deg)) (=> (@ (@ tptp.vEBT_invar_vebt T) Deg) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.vEBT_VEBT_height T))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ _let_2 (@ _let_2 U))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) 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 X2) _let_1))))))))
% 7.01/7.33 (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)))))))))))))
% 7.01/7.33 (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))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X2) (@ tptp.suminf_real (lambda ((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 X2) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 7.01/7.33 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.01/7.33 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.01/7.33 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 7.01/7.33 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 7.01/7.33 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 7.01/7.33 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 7.01/7.33 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 7.01/7.33 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X2)) (@ tptp.set_ord_lessThan_rat Y4)) (@ (@ tptp.ord_less_eq_rat X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X2)) (@ tptp.set_ord_lessThan_num Y4)) (@ (@ tptp.ord_less_eq_num X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X2)) (@ tptp.set_ord_lessThan_int Y4)) (@ (@ tptp.ord_less_eq_int X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X2)) (@ tptp.set_ord_lessThan_nat Y4)) (@ (@ tptp.ord_less_eq_nat X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X2)) (@ tptp.set_or5984915006950818249n_real Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X2) (= (@ _let_2 (@ (@ tptp.log A) X2)) (@ _let_1 X2))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_real A) X2)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) A))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_real X2) Y4)))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4)))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) A))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real A) X2))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 7.01/7.33 (assert (forall ((A4 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat N) A4)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A4)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A4)))))))
% 7.01/7.33 (assert (= (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)) (lambda ((A3 tptp.nat) (B3 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int A3) (@ tptp.semiri1314217659103216013at_int B3)))))
% 7.01/7.33 (assert (forall ((P Bool) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ (@ tptp.if_nat P) A) B)))) (and (=> P (= _let_1 (@ tptp.semiri1314217659103216013at_int A))) (=> (not P) (= _let_1 (@ tptp.semiri1314217659103216013at_int B)))))))
% 7.01/7.33 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))
% 7.01/7.33 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))
% 7.01/7.33 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))
% 7.01/7.33 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))
% 7.01/7.33 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))
% 7.01/7.33 (assert (= tptp.log (lambda ((A3 tptp.real) (X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real A3)))))
% 7.01/7.33 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 7.01/7.33 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 7.01/7.33 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 7.01/7.33 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 7.01/7.33 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 7.01/7.33 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X4)) (@ P X4))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B))))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) (@ tptp.semiri5074537144036343181t_real N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X2)))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) R2))) _let_1)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) R2))) _let_1)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (N tptp.nat) (R2 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) R2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I4)) R2))) _let_1)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I4)) R2))) _let_1)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.plus_plus_real (@ _let_1 X2)) (@ _let_1 Y4)))))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.minus_minus_real (@ _let_1 X2)) (@ _let_1 Y4)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X2)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X2)))))))))))
% 7.01/7.33 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.01/7.33 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.01/7.33 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_complex Y4) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_complex X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_rat Y4) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_rat X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.power_power_int Y4) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_int X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real Y4) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4)))) (@ (@ tptp.power_power_real X2) I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.power_power_complex Y4) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) P5)) (@ (@ tptp.power_power_complex Y4) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat) (Y4 tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y4) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) P5)) (@ (@ tptp.power_power_rat Y4) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y4) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) P5)) (@ (@ tptp.power_power_int Y4) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) P5)) (@ (@ tptp.power_power_real Y4) (@ (@ tptp.minus_minus_nat N) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.times_times_complex (@ _let_1 X2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.times_times_rat (@ _let_1 X2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X2) N)) (@ (@ tptp.times_times_int (@ _let_1 X2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ F I4)) (@ G I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) tptp.one_one_nat)))) _let_1))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 X2) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.log _let_1) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arctan X2) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X2)) (not (= X2 tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2)) (not (= X2 tptp.zero_zero_complex)))))
% 7.01/7.33 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 7.01/7.33 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 7.01/7.33 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) Y4)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) Y4)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y4)))))
% 7.01/7.33 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 7.01/7.33 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (R2 tptp.real) (Y4 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y4))) (@ (@ tptp.times_times_real R2) S2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (R2 tptp.real) (Y4 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y4))) (@ (@ tptp.times_times_real R2) S2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y4))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y4))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (R2 tptp.real) (Y4 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y4))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (R2 tptp.real) (Y4 tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y4)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y4))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y4))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y4))) E))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y4))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y4))) E))))
% 7.01/7.33 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.01/7.33 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y4))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y4))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y4))) E))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y4))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y4))) E))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 7.01/7.33 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y4) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y4))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y4) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 7.01/7.33 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 7.01/7.33 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X2) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X2) tptp.one_one_real))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ F (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 7.01/7.33 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height T)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M2)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.archim7802044766580827645g_real (@ _let_1 X2)) (@ tptp.archim7802044766580827645g_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))))))
% 7.01/7.33 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 7.01/7.33 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 7.01/7.33 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 7.01/7.33 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) Z))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) Z))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.numeral_numeral_real V)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X2))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X2)) tptp.one_one_int))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2))))
% 7.01/7.33 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 7.01/7.33 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 7.01/7.33 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 7.01/7.33 (assert (forall ((Y4 tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y4) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y4)) (@ tptp.archim2889992004027027881ng_rat X2)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y4) X2) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y4)) (@ tptp.archim7802044766580827645g_real X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y4)) (@ (@ tptp.ord_less_rat X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) A))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) A))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X2) Y4))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X2)) (@ tptp.archim2889992004027027881ng_rat Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X2) Y4))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X2)) (@ tptp.archim7802044766580827645g_real Y4)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 7.01/7.33 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 7.01/7.33 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T) (@ (@ tptp.ord_less_eq_rat T) _let_1)) (@ P I4)))))))
% 7.01/7.33 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T) (@ (@ tptp.ord_less_eq_real T) _let_1)) (@ P I4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X2) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X2) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1))))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X2) Z))))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.archim7802044766580827645g_real X2) Z))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X2)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X2) (@ (@ tptp.ord_less_eq_rat X2) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X2)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real X2) _let_1)))))
% 7.01/7.33 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X2)) Z) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X2)) Z) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 7.01/7.33 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 7.01/7.33 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat P2) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)))))
% 7.01/7.33 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)))))
% 7.01/7.33 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ 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) Q3)))) tptp.one_one_real)) Q3)) P2))))
% 7.01/7.33 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ 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) Q3)))) tptp.one_one_rat)) Q3)) P2))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N))) (=> (@ (@ tptp.ord_less_rat _let_1) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 7.01/7.33 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X2) (@ (@ tptp.plus_plus_int N) tptp.one_one_int)))))))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 7.01/7.33 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 7.01/7.33 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) Y4) (=> _let_1 (not (=> (and (=> _let_6 (= Y4 (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y4 (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X2) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 7.01/7.33 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 7.01/7.33 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 7.01/7.33 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 7.01/7.33 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 7.01/7.33 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 7.01/7.33 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 7.01/7.33 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 7.01/7.33 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 7.01/7.33 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 7.01/7.33 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 7.01/7.33 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 7.01/7.33 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ tptp.summable_real F))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N)) tptp.zero_zero_rat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N)) tptp.zero_zero_int))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N)) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N)) tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 7.01/7.33 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 7.01/7.33 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 7.01/7.33 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 7.01/7.33 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_nat)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_int)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (= (@ F N2) tptp.zero_zero_real)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ F N2)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_complex Z) N2)))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.power_power_real Z) N2)))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N) N)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N) N)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N) N)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N) N)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I4))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I4 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (I tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex X2) N2)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_int F)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_nat F)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N3))) X2)) (@ tptp.summable_real F)))))
% 7.01/7.33 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 7.01/7.33 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat)) (=> (@ tptp.summable_int F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) I5)) (@ tptp.suminf_int F)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (I5 tptp.set_nat)) (=> (@ tptp.summable_nat F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) I5)) (@ tptp.suminf_nat F)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (I5 tptp.set_nat)) (=> (@ tptp.summable_real F) (=> (@ tptp.finite_finite_nat I5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) (@ tptp.uminus5710092332889474511et_nat I5)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) I5)) (@ tptp.suminf_real F)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N2) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 7.01/7.33 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 7.01/7.33 (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)))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real Z) N2))))) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (E tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M5) N7)))) E)))))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (E tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N9 tptp.nat)) (not (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) M5) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M5) N7)))) E)))))))))))
% 7.01/7.33 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N7)))))) R2))))))))
% 7.01/7.33 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N9 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N7) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N7)))))) R2))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I3)) tptp.one_one_real)) (=> (forall ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I3))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ F I4)) (@ (@ tptp.power_power_real Z) I4))))))))))
% 7.01/7.33 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R0) N3))) M7)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N2))) (@ (@ tptp.power_power_real R2) N2)))))))))
% 7.01/7.33 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_rat (= M2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.33 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_int (= M2 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.33 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_complex (= M2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.33 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_real (= M2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.33 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M2) tptp.one_one_nat)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.01/7.33 (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))
% 7.01/7.33 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))))
% 7.01/7.33 (assert (forall ((C tptp.real) (N5 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N5) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_int F))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_nat F))))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (I tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M4)))) (=> (@ (@ tptp.ord_less_eq_nat N) I) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) (@ tptp.suminf_real F))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 7.01/7.33 (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))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y4))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y4))))
% 7.01/7.33 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K3 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K3) L4)) (=> (=> (not (and (@ (@ tptp.member_int K3) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K3) L4)))))) (@ (@ P A0) A1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 7.01/7.33 (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 ((B9 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M2)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B9) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M2)) (@ tptp.semiri2265585572941072030t_real M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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))))))))))))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 7.01/7.33 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X2))) (let ((_let_2 (@ tptp.cos_complex X2))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (let ((_let_2 (@ tptp.cos_real X2))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.01/7.33 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 7.01/7.33 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.cos_real X2))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) tptp.one_one_complex))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) tptp.one_one_complex))))
% 7.01/7.33 (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)))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 7.01/7.33 (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)))
% 7.01/7.33 (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)))
% 7.01/7.33 (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))
% 7.01/7.33 (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)))
% 7.01/7.33 (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))))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.cos_complex X2) tptp.one_one_complex) (= (@ tptp.sin_complex X2) tptp.zero_zero_complex))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.cos_real X2) tptp.one_one_real) (= (@ tptp.sin_real X2) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (exists ((R3 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X2 (@ _let_1 (@ tptp.cos_real A5))) (= Y4 (@ _let_1 (@ tptp.sin_real A5))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y4))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X2))) (@ tptp.cos_complex X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X2))) (@ tptp.cos_real X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y3) (@ (@ tptp.ord_less_eq_real Y3) tptp.pi) (= (@ tptp.sin_real Y3) (@ tptp.sin_real X2)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X2))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y4))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y4))))) tptp.one_one_real)))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_2)))))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y4)) (@ (@ tptp.ord_less_real Y4) X2)))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_real Y4) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.pi) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.pi) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) tptp.pi))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.pi) (= X2 (@ tptp.cos_real T4)) (= Y4 (@ tptp.sin_real T4)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.01/7.33 (assert (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X4) tptp.zero_zero_real) (forall ((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 X4))))))
% 7.01/7.33 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y4)) (@ tptp.cos_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X2 (@ tptp.cos_real T4)) (= Y4 (@ tptp.sin_real T4)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X2 (@ tptp.cos_real T4)) (= Y4 (@ tptp.sin_real T4))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X2 (@ tptp.cos_real T4)) (not (= Y4 (@ tptp.sin_real T4))))))))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X2))) tptp.one_one_real))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_1) (=> (= (@ tptp.sin_real X2) (@ tptp.sin_real Y4)) (= X2 Y4))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y4)) (@ _let_1 Y4)))))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y4)) (@ tptp.sin_real X2))))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (exists ((X tptp.int)) (= X2 (@ (@ 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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.cos_real X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y4)) (@ tptp.sin_real X2))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.sin_real X4) Y4) (forall ((Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y5) (@ (@ tptp.ord_less_eq_real Y5) _let_1) (= (@ tptp.sin_real Y5) Y4)) (= Y5 X4)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X2 (@ (@ 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)) (= X2 (@ 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))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((I4 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I4)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real T4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) 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) (= X2 (@ (@ 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) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) 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)) (= X2 (@ (@ 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)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 7.01/7.33 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J2) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)) (@ (@ P I3) J2)))) (@ (@ P A0) A1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 7.01/7.33 (assert (forall ((X2 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 X2) _let_1))))) (@ tptp.sin_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X2) (@ (@ tptp.ord_less_eq_real X2) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 7.01/7.33 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2))) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X2) tptp.zero_zero_real))) (let ((_let_2 (= X2 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X2) A)) (not (= X2 tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X2) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 7.01/7.33 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X2))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X2)) X2)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y4)) Y4)))))
% 7.01/7.33 (assert (forall ((A (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 7.01/7.33 (assert (forall ((A (-> tptp.nat tptp.real)) (X2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.sums_nat G) T) (@ (@ tptp.ord_less_eq_nat S2) T))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S2 tptp.int) (T tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S2) (=> (@ (@ tptp.sums_int G) T) (@ (@ tptp.ord_less_eq_int S2) T))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S2 tptp.real) (T tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S2) (=> (@ (@ tptp.sums_real G) T) (@ (@ tptp.ord_less_eq_real S2) T))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real A) C)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) A)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_real A) B))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N2)) (@ G N2)))) (@ (@ tptp.plus_plus_int A) B))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y4) A)) (@ (@ tptp.powr_real X2) A)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X2)) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A) B))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 7.01/7.33 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 7.01/7.33 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 7.01/7.33 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 7.01/7.33 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y4) A)) (@ (@ tptp.powr_real X2) A)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y4) A)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X2) (@ _let_1 Y4)) (= X2 Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (@ _let_1 (@ (@ tptp.powr_real X2) Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X2) Y4)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y4) A))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X2) Y4)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y4) A))))))))
% 7.01/7.33 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 7.01/7.33 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N2)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ F (@ tptp.suc N2)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ F tptp.zero_zero_nat))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F I3) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N) (= (@ F I3) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 7.01/7.33 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X2)) B)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (B tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X2 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X2) Y4)) (@ (@ tptp.times_times_real Y4) (@ _let_1 X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X2) Y4)) (@ (@ tptp.times_times_real Y4) (@ tptp.ln_ln_real X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N2 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N2)))) (@ (@ tptp.power_power_complex Z) M))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N2 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N2)))) (@ (@ tptp.power_power_real Z) M))))
% 7.01/7.33 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N2 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N2)))) (@ (@ tptp.power_power_int Z) M))))
% 7.01/7.33 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ A tptp.zero_zero_nat))))
% 7.01/7.33 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ A N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ A tptp.zero_zero_nat))))
% 7.01/7.33 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))
% 7.01/7.33 (assert (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X2) N)))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y4)) X2) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.log B) X2)))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y4)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y4))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y4) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y4)))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y4)) X2))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))) (@ (@ tptp.sums_real F) S2))))
% 7.01/7.33 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (@ (@ tptp.sums_real (lambda ((I4 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I4) N)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N)))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (S3 tptp.real) (A4 tptp.set_nat) (S5 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.sums_real G) S3) (=> (@ tptp.finite_finite_nat A4) (=> (= S5 (@ (@ tptp.plus_plus_real S3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) A4))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.member_nat N2) A4)) (@ F N2)) (@ G N2)))) S5))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real X2) (@ _let_1 Y4)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y4)))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y4)) X2))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y4) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y4)))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y4))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y4)) X2) (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.log B) X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) A))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X2)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X2))))))
% 7.01/7.33 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real (@ _let_1 X2)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) Y4)))))))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y4) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y4)) X2))))))))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y4) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y4)) X2))))))))))
% 7.01/7.33 (assert (= tptp.powr_real (lambda ((X tptp.real) (A3 tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ tptp.exp_real (@ (@ tptp.times_times_real A3) (@ tptp.ln_ln_real X)))))))
% 7.01/7.33 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 7.01/7.33 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 7.01/7.33 (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))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y4) (@ tptp.tan_real X4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y4)) (@ _let_1 Y4)))))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y4) (=> (@ _let_1 _let_2) (=> (@ _let_3 X2) (=> (@ (@ tptp.ord_less_real X2) _let_2) (= (@ _let_1 X2) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y4)) (@ tptp.tan_real X2))))))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y4) (=> (@ (@ tptp.ord_less_real Y4) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y4)) (@ tptp.tan_real X2))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.tan_real X4) Y4) (forall ((Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y5) (@ (@ tptp.ord_less_real Y5) _let_1) (= (@ tptp.tan_real Y5) Y4)) (= Y5 X4)))))))))
% 7.01/7.33 (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)))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y4)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y4)))))
% 7.01/7.33 (assert (forall ((B tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real (@ _let_1 X2)) Y4) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y4))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y4))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y4))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y4))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y4)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y4))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (@ (@ 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)))))) X2))))
% 7.01/7.33 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real) (F (-> tptp.nat tptp.real)) (Y4 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (=> (@ (@ tptp.sums_real F) Y4) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X2) Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (exists ((X4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X4) Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (@ _let_2 Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (=> (@ (@ tptp.ord_less_real Y4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y4))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X2))) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arctan Y4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X2)) X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (= (@ tptp.tan_real X2) Y4) (= (@ tptp.arctan Y4) X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y4))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y4))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y4))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.cos_real Y4))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y4))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y4))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y4))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X2) Y4))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y4))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_real X2) Y4))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y4))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X2) Y4))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex Y4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_3) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.tan_real Y4))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.plus_plus_real X2) Y4))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real Y4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_3) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_3) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) 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) X2)))))))
% 7.01/7.33 (assert (forall ((X2 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 X2) _let_1))))) (@ tptp.cos_real X2))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2)))) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ C N2))) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2))))))))
% 7.01/7.33 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2)))) (@ (@ tptp.sums_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ C N2))) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2))))))))
% 7.01/7.33 (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))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X2) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X8 M4)) (@ X8 N3)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 M4)) (@ X8 N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X8 M4)) (@ X8 N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 M4)) (@ X8 N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X8 M4)) (@ X8 N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X8 M4)) (@ X8 N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X2) tptp.one_one_complex) (= X2 tptp.one_one_real))))
% 7.01/7.33 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 7.01/7.33 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 7.01/7.33 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 7.01/7.33 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.times_times_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y4)))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X2) Y4)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (N tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X2)) N))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y4)) (@ _let_1 Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) X2)) (@ tptp.abs_abs_real X2))))
% 7.01/7.33 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 7.01/7.33 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 7.01/7.33 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X2)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X2) (@ tptp.numeral_numeral_real B))))))
% 7.01/7.33 (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))
% 7.01/7.33 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 7.01/7.33 (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))
% 7.01/7.33 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.times_times_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X2)) (@ tptp.real_V1803761363581548252l_real Y4))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (not (= Y4 tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X2)) (@ tptp.real_V4546457046886955230omplex Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real X2) _let_1) _let_1)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y4) Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X2))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 7.01/7.33 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 7.01/7.33 (assert (= tptp.diffs_rat (lambda ((C2 (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C2 _let_1))))))
% 7.01/7.33 (assert (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))
% 7.01/7.33 (assert (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))
% 7.01/7.33 (assert (= tptp.diffs_complex (lambda ((C2 (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C2 _let_1))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4) (@ (@ tptp.ord_less_real X2) (@ tptp.sqrt Y4)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y4) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt Y4)))))
% 7.01/7.33 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (forall ((X4 tptp.complex)) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X4) N2))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2)))))))
% 7.01/7.33 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X4) N2))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2)))))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y4)))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (= (@ tptp.sqrt X2) Y4)))))
% 7.01/7.33 (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))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) X2) (= Y4 tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) Y4) (= X2 tptp.zero_zero_real)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 7.01/7.33 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt Y4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y4))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.cos_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.cos_real (@ _let_1 X2)))))))
% 7.01/7.33 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 7.01/7.33 (assert (forall ((M tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)))) (= (@ tptp.sin_real (@ _let_1 (@ tptp.real_V1803761363581548252l_real X2))) (@ tptp.real_V1803761363581548252l_real (@ tptp.sin_real (@ _let_1 X2)))))))
% 7.01/7.33 (assert (forall ((M tptp.int) (X2 tptp.real)) (= (@ tptp.sin_complex (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex M)) (@ tptp.real_V4546457046886955230omplex X2))) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real M)) X2))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) Y4)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X2) (=> (@ _let_2 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))) (@ (@ tptp.plus_plus_real X2) Y4))))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y4))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.sqrt X2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (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)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) K5) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) K5) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ C N2)) (@ (@ tptp.power_power_real X4) N2)))))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N2)) (@ (@ tptp.power_power_real X2) N2))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) K5) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) K5) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N2)) (@ (@ tptp.power_power_complex X4) N2)))))) (@ tptp.summable_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N2)) (@ (@ tptp.power_power_complex X2) N2))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 7.01/7.33 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) N) (@ (@ tptp.power_power_real X2) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y4))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X2)))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X2)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))) tptp.one_one_real))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (U tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y4)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))) U))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.arcosh_real X2) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (U tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X2) _let_4) (=> (@ (@ tptp.ord_less_real Y4) _let_4) (=> (@ _let_3 X2) (=> (@ _let_3 Y4) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y4) _let_2)))) U)))))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 7.01/7.33 (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)))))))))))))
% 7.01/7.33 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X5 (-> tptp.nat tptp.set_nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 7.01/7.33 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X5 (-> tptp.nat tptp.rat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 7.01/7.33 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X5 (-> tptp.nat tptp.num))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 7.01/7.33 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X5 (-> tptp.nat tptp.nat))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 7.01/7.33 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X5 (-> tptp.nat tptp.int))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 7.01/7.33 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X5 (-> tptp.nat tptp.real))) (or (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 N2)) (@ X5 (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X5 (@ tptp.suc N2))) (@ X5 N2)))))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N3))) (@ X8 N3))) (@ tptp.topolo6980174941875973593q_real X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 (@ tptp.suc N3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 7.01/7.33 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X5 (-> tptp.nat tptp.set_nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X5 M2)) (@ X5 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ X5 N2)) (@ X5 M2))))))))
% 7.01/7.33 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X5 (-> tptp.nat tptp.rat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X5 M2)) (@ X5 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_rat (@ X5 N2)) (@ X5 M2))))))))
% 7.01/7.33 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X5 (-> tptp.nat tptp.num))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X5 M2)) (@ X5 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_num (@ X5 N2)) (@ X5 M2))))))))
% 7.01/7.33 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X5 (-> tptp.nat tptp.nat))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X5 M2)) (@ X5 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_nat (@ X5 N2)) (@ X5 M2))))))))
% 7.01/7.33 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X5 (-> tptp.nat tptp.int))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X5 M2)) (@ X5 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_int (@ X5 N2)) (@ X5 M2))))))))
% 7.01/7.33 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X5 (-> tptp.nat tptp.real))) (or (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X5 M2)) (@ X5 N2)))) (forall ((M2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M2) N2) (@ (@ tptp.ord_less_eq_real (@ X5 N2)) (@ X5 M2))))))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N3)) (@ X8 M4)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_rat (@ X8 N3)) (@ X8 M4)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_num (@ X8 N3)) (@ X8 M4)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_nat (@ X8 N3)) (@ X8 M4)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_int (@ X8 N3)) (@ X8 M4)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 7.01/7.33 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M4) N3) (@ (@ tptp.ord_less_eq_real (@ X8 N3)) (@ X8 M4)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 7.01/7.33 (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))))))))))
% 7.01/7.33 (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)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 7.01/7.33 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 7.01/7.33 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.01/7.33 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.01/7.33 (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))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y4)) (@ tptp.arccos X2)))))))
% 7.01/7.33 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X2)) (@ tptp.arccos Y4)) (@ (@ tptp.ord_less_real Y4) X2))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y4)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y4)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y4)) (@ (@ tptp.ord_less_real X2) Y4))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arccos Y4))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X2)) tptp.zero_zero_real))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X2)) tptp.zero_zero_real))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y4))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X2)) X2))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y4))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y4) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y4)) X2))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) Y4) (@ _let_1 (@ tptp.sin_real Y4)))))))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y4)))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.real)) (let ((_let_1 (@ tptp.arcsin Y4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y4) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y4))))))))
% 7.01/7.34 (assert (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 7.01/7.34 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N2) tptp.zero_zero_rat))))
% 7.01/7.34 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N2) tptp.zero_zero_int))))
% 7.01/7.34 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I4 tptp.real)) (@ (@ tptp.plus_plus_real I4) tptp.one_one_real))) N2) tptp.zero_zero_real))))
% 7.01/7.34 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N2) tptp.zero_zero_nat))))
% 7.01/7.34 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I4 tptp.complex)) (@ (@ tptp.plus_plus_complex I4) tptp.one_one_complex))) N2) tptp.zero_zero_complex))))
% 7.01/7.34 (assert (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R2) _let_1))))))
% 7.01/7.34 (assert (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_1) N) _let_1))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 7.01/7.34 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 7.01/7.34 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 7.01/7.34 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 7.01/7.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 7.01/7.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.01/7.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.01/7.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.01/7.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.01/7.34 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 7.01/7.34 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 7.01/7.34 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 7.01/7.34 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 7.01/7.34 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.01/7.34 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X2))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real V)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat V)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (N tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N))))
% 7.01/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X2))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X2))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 7.01/7.34 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 7.01/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X2))))
% 7.01/7.34 (assert (forall ((V tptp.num) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 7.01/7.34 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y4)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y4)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X2))) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X2))) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y4)) (@ (@ tptp.ord_less_rat X2) Y4))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X2) N))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X2) N))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X2) N))))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X2) N))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (= (@ _let_1 N) tptp.zero_zero_complex)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 7.01/7.34 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 7.01/7.34 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 7.01/7.34 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 7.01/7.34 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X2))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X2))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real Y4))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) Y4)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat Y4))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) Y4)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X2)))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) (@ tptp.ring_1_of_int_real Z))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) (@ tptp.ring_1_of_int_rat Z))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L))) (@ (@ tptp.divide_divide_int K) L))))
% 7.01/7.34 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L))) (@ (@ tptp.divide_divide_int K) L))))
% 7.01/7.34 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex A3)) K2))) (@ tptp.semiri5044797733671781792omplex K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat A3)) K2))) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real A3)) K2))) (@ tptp.semiri2265585572941072030t_real K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat K2))) tptp.one_one_rat)) K2)) (@ tptp.semiri773545260158071498ct_rat K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex K2))) tptp.one_one_complex)) K2)) (@ tptp.semiri5044797733671781792omplex K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real K2))) tptp.one_one_real)) K2)) (@ tptp.semiri2265585572941072030t_real K2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (=> (= X2 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (=> (= X2 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X2) N)) (@ (@ tptp.power_power_int _let_1) N))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X2) N)))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X2) N)))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X2) N)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X2) N)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X2)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X2)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N) tptp.zero_zero_rat) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K2))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N) tptp.zero_zero_real) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K2))))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N) tptp.zero_zero_complex) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K2))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) Z))))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X2) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X2) Z))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X2) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X2) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.int Bool)) (T tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I4))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T) (@ (@ tptp.ord_less_real T) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I4)))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.int Bool)) (T tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T) (@ (@ tptp.ord_less_rat T) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 7.01/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X2))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (X2 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X2)) Z) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X2)) Z) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X2))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X2))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((N tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)) P2))))
% 7.01/7.34 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)) P2))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat K2)) A3)) tptp.one_one_rat)) K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real K2)) A3)) tptp.one_one_real)) K2)))))
% 7.01/7.34 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex K2)) A3)) tptp.one_one_complex)) K2)))))
% 7.01/7.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.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))))))
% 7.01/7.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ 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) Q3)))) tptp.one_one_real)) Q3)))))
% 7.01/7.34 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ 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) Q3)))) tptp.one_one_rat)) Q3)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.real) (K tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real B) (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K)) (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real B)) K)))))
% 7.01/7.34 (assert (forall ((B tptp.complex) (K tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex B) (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex B)) K)))))
% 7.01/7.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 7.01/7.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 7.01/7.34 (assert (forall ((K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X2)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X2) (@ (@ tptp.ord_less_real X2) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 7.01/7.34 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial 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 K2)))))))))
% 7.01/7.34 (assert (= tptp.gbinomial_rat (lambda ((A3 tptp.rat) (K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.divide_divide_rat (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K2))))))
% 7.01/7.34 (assert (= tptp.gbinomial_complex (lambda ((A3 tptp.complex) (K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.divide1717551699836669952omplex (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K2))))))
% 7.01/7.34 (assert (= tptp.gbinomial_real (lambda ((A3 tptp.real) (K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.divide_divide_real (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K2))))))
% 7.01/7.34 (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 ((K2 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K2)) (@ 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))))))))
% 7.01/7.34 (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 ((K2 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K2)) (@ 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))))))))
% 7.01/7.34 (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 ((K2 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K2)) (@ 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))))))))
% 7.01/7.34 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 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 A3) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat)))))
% 7.01/7.34 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 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 A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int)))))
% 7.01/7.34 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 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 A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real)))))
% 7.01/7.34 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 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 A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex)))))
% 7.01/7.34 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 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 A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat)))))
% 7.01/7.34 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K2))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 7.01/7.34 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I) K))))
% 7.01/7.34 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I) K))))
% 7.01/7.34 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I) K))))
% 7.01/7.34 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I) K))))
% 7.01/7.34 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I) K))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I) K))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A4) tptp.one_one_nat)))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A4) tptp.one_one_int)))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A4) tptp.one_one_int)))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups6464643781859351333omplex G) A4) tptp.one_one_complex))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups7440179247065528705omplex G) A4) tptp.one_one_complex))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups3708469109370488835omplex G) A4) tptp.one_one_complex))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups129246275422532515t_real G) A4) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.real))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups2316167850115554303t_real G) A4) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups766887009212190081x_real G) A4) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A4)) (= (@ (@ tptp.groups73079841787564623at_rat G) A4) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups1072433553688619179nt_rat G) A4) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A4)) (= (@ (@ tptp.groups225925009352817453ex_rat G) A4) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A4)) (= (@ (@ tptp.groups1707563613775114915nt_nat G) A4) tptp.one_one_nat))))
% 7.01/7.34 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X2)) (@ tptp.set_or4236626031148496127et_nat Y4)) (@ (@ tptp.ord_less_eq_set_nat X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X2)) (@ tptp.set_ord_atMost_rat Y4)) (@ (@ tptp.ord_less_eq_rat X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X2)) (@ tptp.set_ord_atMost_num Y4)) (@ (@ tptp.ord_less_eq_num X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X2)) (@ tptp.set_ord_atMost_int Y4)) (@ (@ tptp.ord_less_eq_int X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real X2)) (@ tptp.set_ord_atMost_real Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X2)) (@ tptp.set_ord_atMost_nat Y4)) (@ (@ tptp.ord_less_eq_nat X2) Y4))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups713298508707869441omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7440179247065528705omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.complex))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3708469109370488835omplex (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.one_one_complex))) S3) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1681761925125756287l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.member_int A) S3))) (=> (@ tptp.finite_finite_int S3) (and (=> _let_1 (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2316167850115554303t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.member_complex A) S3))) (=> (@ tptp.finite3207457112153483333omplex S3) (and (=> _let_1 (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups766887009212190081x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.one_one_real))) S3) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S3))) (=> (@ tptp.finite_finite_real S3) (and (=> _let_1 (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4061424788464935467al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S3))) (=> (@ tptp.finite_finite_nat S3) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.one_one_rat))) S3) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A4)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A4)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A4)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A4)) (@ (@ tptp.times_times_real (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (=> (not (@ (@ tptp.member_VEBT_VEBT X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A4) (=> (not (@ (@ tptp.member_real X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_real X2) A4)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A4) (=> (not (@ (@ tptp.member_nat X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) A4)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (=> (not (@ (@ tptp.member_int X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_int X2) A4)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (=> (not (@ (@ tptp.member_complex X2) A4)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) A4)) (@ (@ tptp.times_times_rat (@ G X2)) (@ _let_1 A4))))))))
% 7.01/7.34 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 7.01/7.34 (assert (forall ((L tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))))
% 7.01/7.34 (assert (forall ((L tptp.num) (H2 tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H2)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H2)) (@ (@ tptp.ord_less_eq_num H2) H3)))))
% 7.01/7.34 (assert (forall ((L tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 7.01/7.34 (assert (forall ((L tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 7.01/7.34 (assert (forall ((L tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N))) (@ G _let_1)))))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.complex tptp.complex)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A4) tptp.one_one_complex)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A4) (= (@ G A5) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.complex)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A4) tptp.one_one_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A4) (= (@ G A5) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.complex)) (A4 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A4) tptp.one_one_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A4) (= (@ G A5) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.complex)) (A4 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A4) tptp.one_one_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A4) (= (@ G A5) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.complex tptp.real)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A4) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A4) (= (@ G A5) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A4) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A4) (= (@ G A5) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (A4 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A4) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A4) (= (@ G A5) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.real)) (A4 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A4) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A4) (= (@ G A5) tptp.one_one_real)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.complex tptp.rat)) (A4 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups225925009352817453ex_rat G) A4) tptp.one_one_rat)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A4) (= (@ G A5) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.rat)) (A4 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A4) tptp.one_one_rat)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A4) (= (@ G A5) tptp.one_one_rat)))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (= (@ G X4) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A4) tptp.one_one_nat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (= (@ G X4) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A4) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (= (@ G X4) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A4) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A4)) (@ (@ tptp.groups708209901874060359at_nat H2) A4)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A4 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A4)) (@ (@ tptp.groups705719431365010083at_int H2) A4)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A4 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A4) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A4)) (@ (@ tptp.groups1705073143266064639nt_int H2) A4)))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A4)) N) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N))) A4))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.int)) (A4 tptp.set_nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A4)) N) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N))) A4))))
% 7.01/7.34 (assert (forall ((F (-> tptp.int tptp.int)) (A4 tptp.set_int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A4)) N) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N))) A4))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N)))) (@ tptp.set_ord_lessThan_nat N)))))
% 7.01/7.34 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) U2))))))
% 7.01/7.34 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) U2))))))
% 7.01/7.34 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) U2))))))
% 7.01/7.34 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) U2))))))
% 7.01/7.34 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) U2))))))
% 7.01/7.34 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) U2))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A4)))))
% 7.01/7.34 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups225925009352817453ex_rat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups4061424788464935467al_rat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups73079841787564623at_rat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups1072433553688619179nt_rat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A4)) (@ (@ tptp.groups861055069439313189ex_nat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A4)) (@ (@ tptp.groups4696554848551431203al_nat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A4)) (@ (@ tptp.groups1707563613775114915nt_nat G) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I3 tptp.complex)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_complex I3) A4) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups858564598930262913ex_int F) A4)) (@ (@ tptp.groups858564598930262913ex_int G) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I3 tptp.real)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_real I3) A4) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A4)) (@ (@ tptp.groups4694064378042380927al_int G) A4)))))
% 7.01/7.34 (assert (forall ((A4 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) A4) (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) A4)) (@ (@ tptp.groups766887009212190081x_real G) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X4)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X4)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A4) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X4)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A4) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X4)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X4)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A4)))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6464643781859351333omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A3)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N))))))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups713298508707869441omplex G) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A4) (@ P X))))) (@ (@ tptp.groups713298508707869441omplex (lambda ((X tptp.real)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups6464643781859351333omplex G) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (@ P X))))) (@ (@ tptp.groups6464643781859351333omplex (lambda ((X tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups7440179247065528705omplex G) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A4) (@ P X))))) (@ (@ tptp.groups7440179247065528705omplex (lambda ((X tptp.int)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups3708469109370488835omplex G) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A4) (@ P X))))) (@ (@ tptp.groups3708469109370488835omplex (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_complex (@ P X)) (@ G X)) tptp.one_one_complex))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.real)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups1681761925125756287l_real G) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A4) (@ P X))))) (@ (@ tptp.groups1681761925125756287l_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.real)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (@ P X))))) (@ (@ tptp.groups129246275422532515t_real (lambda ((X tptp.nat)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.real)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A4) (= (@ (@ tptp.groups2316167850115554303t_real G) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A4) (@ P X))))) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X tptp.int)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.real)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ (@ tptp.groups766887009212190081x_real G) (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A4) (@ P X))))) (@ (@ tptp.groups766887009212190081x_real (lambda ((X tptp.complex)) (@ (@ (@ tptp.if_real (@ P X)) (@ G X)) tptp.one_one_real))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A4) (= (@ (@ tptp.groups4061424788464935467al_rat G) (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A4) (@ P X))))) (@ (@ tptp.groups4061424788464935467al_rat (lambda ((X tptp.real)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G X)) tptp.one_one_rat))) A4)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A4) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A4) (@ P X))))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X)) (@ G X)) tptp.one_one_rat))) A4)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.34 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.power_power_real C) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A3)))) A4))))
% 7.01/7.34 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.power_power_complex C) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A3)))) A4))))
% 7.01/7.34 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A3)))) A4))))
% 7.01/7.34 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A4 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A4)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A3 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A3)))) A4))))
% 7.01/7.34 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A4 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A4)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A3 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A3)))) A4))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_complex X4) A4) (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) A4)) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A4) (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) A4)) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X4 tptp.nat)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_nat X4) A4) (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) A4)) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A4) (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) A4)) tptp.one_one_rat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_complex X4) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A4)) tptp.one_one_nat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A4)) tptp.one_one_nat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X4 tptp.int)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_int X4) A4) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A4)) tptp.one_one_nat))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_complex X4) A4) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) tptp.one_one_int))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups858564598930262913ex_int F) A4)) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_real X4) A4) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) tptp.one_one_int))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4694064378042380927al_int F) A4)) tptp.one_one_int))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X4 tptp.complex)) (let ((_let_1 (@ F X4))) (=> (@ (@ tptp.member_complex X4) A4) (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) A4)) tptp.one_one_real))))
% 7.01/7.34 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_complex X16) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups6464643781859351333omplex H2) S3)) (@ (@ tptp.groups6464643781859351333omplex G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_complex X16) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups7440179247065528705omplex H2) S3)) (@ (@ tptp.groups7440179247065528705omplex G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.complex tptp.complex Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ (@ R tptp.one_one_complex) tptp.one_one_complex) (=> (forall ((X16 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_complex X16) Y15)) (@ (@ tptp.times_times_complex X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups3708469109370488835omplex H2) S3)) (@ (@ tptp.groups3708469109370488835omplex G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X16) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups129246275422532515t_real H2) S3)) (@ (@ tptp.groups129246275422532515t_real G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X16) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups2316167850115554303t_real H2) S3)) (@ (@ tptp.groups2316167850115554303t_real G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.real tptp.real Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R tptp.one_one_real) tptp.one_one_real) (=> (forall ((X16 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_real X16) Y15)) (@ (@ tptp.times_times_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups766887009212190081x_real H2) S3)) (@ (@ tptp.groups766887009212190081x_real G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X16) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups73079841787564623at_rat H2) S3)) (@ (@ tptp.groups73079841787564623at_rat G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X16) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups1072433553688619179nt_rat H2) S3)) (@ (@ tptp.groups1072433553688619179nt_rat G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X16 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_rat X16) Y15)) (@ (@ tptp.times_times_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups225925009352817453ex_rat H2) S3)) (@ (@ tptp.groups225925009352817453ex_rat G) S3))))))))
% 7.01/7.34 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S3 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X16 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R X16) X23) (@ (@ R Y15) Y23)) (@ (@ R (@ (@ tptp.times_times_nat X16) Y15)) (@ (@ tptp.times_times_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (@ (@ R (@ H2 X4)) (@ G X4)))) (@ (@ R (@ (@ tptp.groups1707563613775114915nt_nat H2) S3)) (@ (@ tptp.groups1707563613775114915nt_nat G) S3))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.real))) (let ((_let_1 (@ tptp.groups2703838992350267259T_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A4)))) (let ((_let_4 (@ (@ tptp.member_real X2) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A4)))) (let ((_let_4 (@ (@ tptp.member_int X2) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_real (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (G (-> tptp.vEBT_VEBT tptp.rat))) (let ((_let_1 (@ tptp.groups5726676334696518183BT_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) A4)))) (let ((_let_4 (@ (@ tptp.member_VEBT_VEBT X2) A4))) (=> (@ tptp.finite5795047828879050333T_VEBT A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (X2 tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X2) A4)))) (let ((_let_4 (@ (@ tptp.member_real X2) A4))) (=> (@ tptp.finite_finite_real A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (X2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_nat X2) A4)))) (let ((_let_4 (@ (@ tptp.member_nat X2) A4))) (=> (@ tptp.finite_finite_nat A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (X2 tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X2) A4)))) (let ((_let_4 (@ (@ tptp.member_int X2) A4))) (=> (@ tptp.finite_finite_int A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (X2 tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (let ((_let_2 (@ _let_1 A4))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X2) A4)))) (let ((_let_4 (@ (@ tptp.member_complex X2) A4))) (=> (@ tptp.finite3207457112153483333omplex A4) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ G X2)) _let_2)))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S3 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T6 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T6) T5)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_int) (S3 tptp.set_real) (I (-> tptp.int tptp.real)) (J (-> tptp.real tptp.int)) (T6 tptp.set_int) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T6) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T6) T5)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_complex) (S3 tptp.set_real) (I (-> tptp.complex tptp.real)) (J (-> tptp.real tptp.complex)) (T6 tptp.set_complex) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T6) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_real) (S3 tptp.set_int) (I (-> tptp.real tptp.int)) (J (-> tptp.int tptp.real)) (T6 tptp.set_real) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T6) T5)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_int) (S3 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T6 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T6) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T6) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_int) (T5 tptp.set_complex) (S3 tptp.set_int) (I (-> tptp.complex tptp.int)) (J (-> tptp.int tptp.complex)) (T6 tptp.set_complex) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite_finite_int S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S3) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T6) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S3) S5)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_real) (S3 tptp.set_complex) (I (-> tptp.real tptp.complex)) (J (-> tptp.complex tptp.real)) (T6 tptp.set_real) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T6) T5)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_int) (S3 tptp.set_complex) (I (-> tptp.int tptp.complex)) (J (-> tptp.complex tptp.int)) (T6 tptp.set_int) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite_finite_int T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T6) T5)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T6) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_complex) (T5 tptp.set_complex) (S3 tptp.set_complex) (I (-> tptp.complex tptp.complex)) (J (-> tptp.complex tptp.complex)) (T6 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (@ tptp.finite3207457112153483333omplex T5) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex S3) S5)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T6) T5)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T6) T5)) (@ (@ tptp.member_complex (@ I B5)) (@ (@ tptp.minus_811609699411566653omplex S3) S5)))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S5) (= (@ G A5) tptp.one_one_complex))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T5) (= (@ H2 B5) tptp.one_one_complex))) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((S5 tptp.set_real) (T5 tptp.set_real) (S3 tptp.set_real) (I (-> tptp.real tptp.real)) (J (-> tptp.real tptp.real)) (T6 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S5) (=> (@ tptp.finite_finite_real T5) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S3) S5)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T6) T5)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T6) T5)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S3) S5)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S5) (= (@ G A5) tptp.one_one_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T5) (= (@ H2 B5) tptp.one_one_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S3) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S3) (@ (@ tptp.groups1681761925125756287l_real H2) T6)))))))))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.complex))) (let ((_let_1 (@ tptp.groups713298508707869441omplex G))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups7440179247065528705omplex G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups3708469109370488835omplex G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.one_one_complex))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups1681761925125756287l_real G))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.one_one_real))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups4061424788464935467al_rat G))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.one_one_rat))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) (@ tptp.collect_int (lambda ((X tptp.int)) (= (@ G X) tptp.one_one_rat))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) (@ tptp.collect_complex (lambda ((X tptp.complex)) (= (@ G X) tptp.one_one_rat))))) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups4696554848551431203al_nat G))) (=> (@ tptp.finite_finite_real A4) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A4) (@ tptp.collect_real (lambda ((X tptp.real)) (= (@ G X) tptp.one_one_nat))))) (@ _let_1 A4))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 7.01/7.34 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 7.01/7.34 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I4)))) _let_1)))))
% 7.01/7.34 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_complex (= J3 K)) tptp.one_one_complex) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.01/7.34 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_real (= J3 K)) tptp.one_one_real) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.01/7.34 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H2 (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.one_one_rat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.01/7.34 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.one_one_nat) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.01/7.34 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P2) (=> (@ (@ tptp.ord_less_eq_nat K) P2) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.one_one_int) (@ H2 (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H2 J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4694064378042380927al_int F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups858564598930262913ex_int F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_real I5) (=> (@ (@ tptp.member_real I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups129246275422532515t_real F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (@ (@ tptp.member_complex I) I5) (=> (@ _let_1 (@ F I)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups766887009212190081x_real F) I5)))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial K2) M))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc N)) (@ tptp.suc M)))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ F I3)))) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_complex) (F (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex I5) (=> (not (= I5 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (@ (@ tptp.member_complex I3) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups858564598930262913ex_int F) I5)))))))
% 7.01/7.34 (assert (forall ((I5 tptp.set_real) (F (-> tptp.real tptp.int))) (=> (@ tptp.finite_finite_real I5) (=> (not (= I5 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (@ (@ tptp.member_real I3) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups4694064378042380927al_int F) I5)))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups2316167850115554303t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups766887009212190081x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups225925009352817453ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_int) (A4 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B4) A4) (=> (@ tptp.finite_finite_int A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups861055069439313189ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_complex) (A4 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups858564598930262913ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B4) A4) (=> (@ tptp.finite3207457112153483333omplex A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((B4 tptp.set_nat) (A4 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A4) (=> (@ tptp.finite_finite_nat A4) (= (@ _let_1 A4) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A4) B4))) (@ _let_1 B4))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups713298508707869441omplex G) T6) (@ (@ tptp.groups713298508707869441omplex H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups7440179247065528705omplex G) T6) (@ (@ tptp.groups7440179247065528705omplex H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups3708469109370488835omplex G) T6) (@ (@ tptp.groups3708469109370488835omplex H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1681761925125756287l_real G) T6) (@ (@ tptp.groups1681761925125756287l_real H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2316167850115554303t_real G) T6) (@ (@ tptp.groups2316167850115554303t_real H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups766887009212190081x_real G) T6) (@ (@ tptp.groups766887009212190081x_real H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) T6) (@ (@ tptp.groups4061424788464935467al_rat H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.rat)) (H2 (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) T6) (@ (@ tptp.groups1072433553688619179nt_rat H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ G X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups225925009352817453ex_rat G) T6) (@ (@ tptp.groups225925009352817453ex_rat H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (G (-> tptp.real tptp.nat)) (H2 (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ G X4) tptp.one_one_nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) T6) (@ (@ tptp.groups4696554848551431203al_nat H2) S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups713298508707869441omplex G) S3) (@ (@ tptp.groups713298508707869441omplex H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups7440179247065528705omplex G) S3) (@ (@ tptp.groups7440179247065528705omplex H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ H2 X4) tptp.one_one_complex))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups3708469109370488835omplex G) S3) (@ (@ tptp.groups3708469109370488835omplex H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1681761925125756287l_real G) S3) (@ (@ tptp.groups1681761925125756287l_real H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups2316167850115554303t_real G) S3) (@ (@ tptp.groups2316167850115554303t_real H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ H2 X4) tptp.one_one_real))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups766887009212190081x_real G) S3) (@ (@ tptp.groups766887009212190081x_real H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4061424788464935467al_rat G) S3) (@ (@ tptp.groups4061424788464935467al_rat H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) S3) (@ (@ tptp.groups1072433553688619179nt_rat H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_complex) (S3 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T6) (=> (@ (@ tptp.ord_le211207098394363844omplex S3) T6) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex T6) S3)) (= (@ H2 X4) tptp.one_one_rat))) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups225925009352817453ex_rat G) S3) (@ (@ tptp.groups225925009352817453ex_rat H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_real) (S3 tptp.set_real) (H2 (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real T6) (=> (@ (@ tptp.ord_less_eq_set_real S3) T6) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real T6) S3)) (= (@ H2 X4) tptp.one_one_nat))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S3) (= (@ G X4) (@ H2 X4)))) (= (@ (@ tptp.groups4696554848551431203al_nat G) S3) (@ (@ tptp.groups4696554848551431203al_nat H2) T6))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (=> (@ tptp.finite_finite_nat T6) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T6) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T6) S3)) (= (@ G X4) tptp.one_one_complex))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ tptp.finite_finite_nat T6) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T6) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T6) S3)) (= (@ G X4) tptp.one_one_real))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T6) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T6) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T6) S3)) (= (@ G X4) tptp.one_one_rat))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ tptp.finite_finite_nat T6) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T6) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T6) S3)) (= (@ G X4) tptp.one_one_nat))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_nat) (S3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ tptp.finite_finite_nat T6) (=> (@ (@ tptp.ord_less_eq_set_nat S3) T6) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat T6) S3)) (= (@ G X4) tptp.one_one_int))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 7.01/7.34 (assert (forall ((T6 tptp.set_int) (S3 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int G))) (=> (@ tptp.finite_finite_int T6) (=> (@ (@ tptp.ord_less_eq_set_int S3) T6) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int T6) S3)) (= (@ G X4) tptp.one_one_int))) (= (@ _let_1 T6) (@ _let_1 S3))))))))
% 7.01/7.34 (assert (forall ((R2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K2)) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N))) N))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M) K2)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K2)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R2) K2))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R2))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I3) (= (@ A I3) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ (@ tptp.power_power_nat X2) I4)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X2) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B (@ (@ tptp.minus_minus_nat R5) K2))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N) I4)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 7.01/7.34 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 7.01/7.34 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M2)) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X2)) N)))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (=> (@ (@ tptp.ord_less_real T4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T4)) (@ tptp.sin_real T4)))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X2)) tptp.zero_zero_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X2))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X2) Y4)) (@ (@ tptp.complex2 (@ _let_1 X2)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X2) Y4)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X2) R2)) (@ (@ tptp.times_times_real Y4) R2)))))
% 7.01/7.34 (assert (= tptp.divide_divide_real (lambda ((X tptp.real) (Y tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y)))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C))))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sqrt X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.divide_divide_real _let_1) X2) (@ tptp.inverse_inverse_real _let_1))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X2))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X2) Y4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y4) _let_1)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X2)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.cot_real X2))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.sinh_real Y4)) (@ (@ tptp.ord_less_real X2) Y4))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X2)) (@ _let_1 X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 7.01/7.34 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.times_times_complex X) (@ tptp.invers8013647133539491842omplex Y)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X2)) (@ tptp.cosh_real X2))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X2))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y4) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y4)) (@ (@ tptp.ord_less_real Y4) X2))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y4) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y4)) (@ (@ tptp.ord_less_real X2) Y4)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X2)) (@ tptp.cosh_real Y4))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 7.01/7.34 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))))))))
% 7.01/7.34 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 7.01/7.34 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 7.01/7.34 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((L tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 7.01/7.34 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 7.01/7.34 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 7.01/7.34 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (Y4 tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N) (@ tptp.nat2 Y4)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N) Y4))))
% 7.01/7.34 (assert (forall ((Y4 tptp.int) (X2 tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (= Y4 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))) A) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real A)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 7.01/7.34 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.34 (assert (forall ((A tptp.int) (X2 tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N)) A))))
% 7.01/7.34 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 7.01/7.34 (assert (= tptp.numeral_numeral_nat (lambda ((I4 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I4)))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y4) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y4)))))
% 7.01/7.34 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 7.01/7.34 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 7.01/7.34 (assert (forall ((K tptp.int) (L tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L)) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) N) (@ (@ tptp.ord_less_eq_int X2) (@ tptp.semiri1314217659103216013at_int N)))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 7.01/7.34 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 7.01/7.34 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 7.01/7.34 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 7.01/7.34 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B3))))))
% 7.01/7.34 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 7.01/7.34 (assert (forall ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 7.01/7.34 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y4) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y4))))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y4))))))
% 7.01/7.34 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N) M)))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) A) (@ (@ tptp.ord_less_eq_nat X2) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 7.01/7.34 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K2))))))))))))
% 7.01/7.34 (assert (= tptp.modulo_modulo_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K2))))) _let_2)))))))))))
% 7.01/7.34 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.34 (assert (forall ((K tptp.int)) (not (forall ((N3 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 N3) M5) (= (@ _let_1 M5) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N)))))
% 7.01/7.34 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) 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)))))))))))
% 7.01/7.34 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K2 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 K2) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 7.01/7.34 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R2)))))))
% 7.01/7.34 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K2 tptp.int)) (and (= A12 K2) (= A23 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A12 K2) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K2 (@ (@ tptp.times_times_int Q4) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K2 tptp.int) (Q4 tptp.int)) (and (= A12 K2) (= A23 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L2)) R5))))))))
% 7.01/7.34 (assert (forall ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A22) A33) (=> (=> (= A22 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q2) A22)))))) (not (forall ((R3 tptp.int) (Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A22)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A22)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) A22)) R3)))))))))))))
% 7.01/7.34 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L))) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K)))))))))
% 7.01/7.34 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z4)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 7.01/7.34 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.minus_minus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 7.01/7.34 (assert (forall ((L tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 7.01/7.34 (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))
% 7.01/7.34 (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))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X2))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X2)) (@ tptp.uminus1482373934393186551omplex X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X2))))
% 7.01/7.34 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.34 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.34 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 7.01/7.34 (assert (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real X) (@ tptp.abs_abs_real X)))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 7.01/7.34 (assert (= tptp.sgn_sgn_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex Z4) (@ tptp.real_V4546457046886955230omplex (@ tptp.real_V1022390504157884413omplex Z4))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 7.01/7.34 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 7.01/7.34 (assert (= tptp.complex2 (lambda ((A3 tptp.real) (B3 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (N tptp.nat) (X2 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X2) (=> (= X2 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 7.01/7.34 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 7.01/7.34 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M2) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 7.01/7.34 (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)))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z4 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z4)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z4) tptp.one_one_int)))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 7.01/7.34 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 7.01/7.34 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 7.01/7.34 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 7.01/7.34 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S) (forall ((T4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T4) (not (= R2 (@ (@ tptp.plus_plus_rat S) T4)))))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((S2 tptp.vEBT_VEBT) (M tptp.nat) (Listy tptp.list_VEBT_VEBT) (N tptp.nat)) (let ((_let_1 (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M))))) (=> (@ (@ tptp.vEBT_invar_vebt S2) M) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Listy)) (@ (@ tptp.vEBT_invar_vebt X4) N))) (=> (= M (@ tptp.suc N)) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Listy)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height X4)) (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N)))))) (=> (= (@ tptp.semiri1314217659103216013at_int (@ tptp.vEBT_VEBT_height S2)) _let_1) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT S2) (@ tptp.set_VEBT_VEBT2 Listy))))) _let_1)))))))))
% 7.01/7.34 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B3 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B3)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P2)))))
% 7.01/7.34 (assert (forall ((T tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 TreeList))) (=> (@ (@ tptp.member_VEBT_VEBT T) _let_1) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height T)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) _let_1))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X14 tptp.vEBT_VEBT) (M tptp.nat) (X13 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_VEBT_height X14))) (let ((_let_2 (@ tptp.times_times_nat N))) (@ (@ tptp.ord_less_eq_nat (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat M) (@ _let_2 (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.insert_nat _let_1) (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13)))))))))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (Foo tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I))) (@ (@ tptp.ord_max_nat Foo) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (X13 tptp.list_VEBT_VEBT) (N tptp.nat) (X14 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s6755466524823107622T_VEBT X13)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ tptp.vEBT_VEBT_height (@ (@ tptp.nth_VEBT_VEBT X13) I)))) (@ tptp.suc (@ tptp.suc (@ _let_1 (@ (@ tptp.ord_max_nat (@ tptp.vEBT_VEBT_height X14)) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ tptp.set_VEBT_VEBT2 X13))))))))))))
% 7.01/7.34 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 7.01/7.34 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 7.01/7.34 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((Uu2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (= (@ tptp.vEBT_VEBT_height (@ (@ (@ (@ tptp.vEBT_Node Uu2) Deg) TreeList) Summary)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary) (@ tptp.set_VEBT_VEBT2 TreeList))))))))
% 7.01/7.34 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P5 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P5)))))
% 7.01/7.34 (assert (forall ((R2 tptp.rat) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y4) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= Y4 tptp.zero_zero_nat))) (not (forall ((Uu tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu) Deg2) TreeList2) Summary2)) (not (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList2))))))))))))))
% 7.01/7.34 (assert (= tptp.divide_divide_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N2)) M2))))))))
% 7.01/7.34 (assert (= tptp.cis (lambda ((B3 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B3))))))
% 7.01/7.34 (assert (= tptp.ord_less_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B3 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C2) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 7.01/7.34 (assert (= tptp.ord_less_eq_rat (lambda ((P5 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 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 A3) D2)) (@ (@ tptp.times_times_int C2) B3)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P5)))))
% 7.01/7.34 (assert (forall ((Z tptp.complex) (X2 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X2)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.pi) (= (@ tptp.arg Z) X2))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))))))
% 7.01/7.34 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 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 A3) D2)) (@ (@ tptp.times_times_int B3) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 7.01/7.34 (assert (= tptp.arg (lambda ((Z4 tptp.complex)) (@ (@ (@ tptp.if_real (= Z4 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z4) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((Q3 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q3) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q3)))))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A4)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((R2 tptp.product_prod_int_int) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 7.01/7.34 (assert (forall ((Q3 tptp.int) (S2 tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q3 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P2) S2) (@ (@ tptp.times_times_int R2) Q3)))))))
% 7.01/7.34 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 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 A3) D2)) (@ (@ tptp.times_times_int C2) B3))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 7.01/7.34 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 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 A3) B3)) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 7.01/7.34 (assert (forall ((P2 tptp.rat) (Q3 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 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 A3) D2)) (@ (@ tptp.times_times_int B3) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q3)))) (@ tptp.quotient_of P2)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.nat)) (=> (= (@ tptp.vEBT_VEBT_height X2) Y4) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (= Y4 tptp.zero_zero_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1)))))) (not (forall ((Uu tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu) Deg2) TreeList2) Summary2))) (=> (= X2 _let_1) (=> (= Y4 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.lattic8265883725875713057ax_nat (@ (@ tptp.image_VEBT_VEBT_nat tptp.vEBT_VEBT_height) (@ (@ tptp.insert_VEBT_VEBT Summary2) (@ tptp.set_VEBT_VEBT2 TreeList2)))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_VEBT_height_rel) _let_1))))))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((M7 tptp.set_nat) (N5 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N5) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N5))))
% 7.01/7.34 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4)))))
% 7.01/7.34 (assert (forall ((Y4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y4)))))
% 7.01/7.34 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X2) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 7.01/7.34 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M2 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M2) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 7.01/7.34 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M2)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M2) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X2) Y4) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y4 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y4 (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X2) Y4) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X2 _let_1) (=> (and (=> A5 (= Y4 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y4 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y4 tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw))) (=> (= X2 _let_1) (=> (= Y4 tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X2 _let_1) (=> (= Y4 (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 7.01/7.34 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C))))))))
% 7.01/7.34 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X2) (@ _let_1 Y4)) (= X2 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_real X2) Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y4)) (@ (@ tptp.ord_less_eq_real X2) Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X2) tptp.one_one_real) (= X2 tptp.one_one_real)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y4)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y4)) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat) (X2 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X2) (@ (@ tptp.root M) (@ (@ tptp.root N) X2)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y4)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X2) Y4) (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y4)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (Y4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X2) Y4) (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y4)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ _let_1 X2)) K))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ _let_1 X2)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X2)) (@ tptp.sgn_sgn_real X2)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N) X2)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N5) X2)) (@ (@ tptp.root N) X2)))))))
% 7.01/7.34 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y4) N))) (@ tptp.abs_abs_real Y4)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X2))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N5) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N5) X2))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N5) X2)) (@ (@ tptp.root N) X2)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y4) (=> (= (@ (@ tptp.power_power_real Y4) N) X2) (= (@ (@ tptp.root N) X2) Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X2) N)) X2))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y4) N) X2) (= (@ (@ tptp.root N) X2) Y4)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X2)) N) X2))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (N5 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X2)) (@ (@ tptp.root N5) X2))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X2)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y4)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y4)) N))) Y4))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (B tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X2)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (N tptp.nat) (Y4 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y4) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y4)) _let_1)))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X2 tptp.real)) (= (@ P (@ (@ tptp.root N) X2)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N)) X2) (@ P Y))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N) X2) (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 7.01/7.34 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K2)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 7.01/7.34 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y4) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (=> Y4 (not (@ _let_2 _let_1)))) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux2) Uy2))) (=> (= X2 _let_1) (=> Y4 (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y4) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (@ _let_2 X2) (=> (=> (= X2 _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X2) (=> (forall ((Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) true))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K2))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K2) _let_1))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M2) tptp.one_one_nat)))))
% 7.01/7.34 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M2) tptp.one_one_nat)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q3)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N) M))))))
% 7.01/7.34 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.34 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.times_times_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X5 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M2) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X5 M2)) (@ X5 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X))))))
% 7.01/7.34 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (forall ((C tptp.nat) (Y4 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X2) Y4))) (let ((_let_2 (@ (@ tptp.ord_less_nat X2) Y4))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y4))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C)) (@ (@ tptp.minus_minus_nat Y4) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I3)) (@ A J2))))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I3))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I4)) (@ B I4)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 7.01/7.34 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 7.01/7.34 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 7.01/7.34 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 7.01/7.34 (assert (forall ((Uu2 Bool) (Uv2 Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D) (= D tptp.one_one_nat))))
% 7.01/7.34 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))) N)))
% 7.01/7.34 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N)))) (@ tptp.suc N))))
% 7.01/7.34 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= tptp.unique3479559517661332726nteger (lambda ((M2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 7.01/7.34 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.34 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.34 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (X2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X2)) (@ (@ tptp.times_times_real R2) (@ tptp.re X2)))))
% 7.01/7.34 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 7.01/7.34 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M7) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 7.01/7.34 (assert (forall ((M7 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M7) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 7.01/7.34 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A4))))) (=> (@ (@ tptp.ord_less_eq_set_nat A4) _let_1) (= A4 _let_1)))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S3)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S3))))))
% 7.01/7.34 (assert (forall ((N5 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N5) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N5)) N))))
% 7.01/7.34 (assert (forall ((S3 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 S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S3))))
% 7.01/7.34 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) C)))) N)))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z4 tptp.complex)) (= (@ (@ tptp.power_power_complex Z4) N) tptp.one_one_complex)))) N))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= tptp.csqrt (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z4))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z4))) (let ((_let_4 (@ tptp.im Z4))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (= tptp.code_integer_of_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X2) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.sgn_sgn_complex Z)) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.real_V1022390504157884413omplex Z)))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.im X2))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X2)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X2)))))))
% 7.01/7.34 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 7.01/7.34 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_int Xa2) X2))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa2) X2)))))
% 7.01/7.34 (assert (= tptp.abs_abs_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K2)) K2))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X2)))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (X2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X2)) (@ (@ tptp.times_times_real R2) (@ tptp.im X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X2) Y4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.im Y4))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.re Y4))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X2) Y4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.re Y4))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.im Y4))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))))
% 7.01/7.34 (assert (= tptp.exp_complex (lambda ((Z4 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z4)))) (@ tptp.cis (@ tptp.im Z4))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X2))) (@ tptp.im X2))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z4)) _let_1)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X2))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y4))) (let ((_let_3 (@ tptp.re Y4))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.complex) (X2 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X2) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y4) X2) (and (= X2 tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.complex) (X2 tptp.complex)) (=> (@ (@ tptp.member_complex Y4) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X2) tptp.real_V2521375963428798218omplex) (= (= X2 (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y4)) (and (= X2 tptp.zero_zero_complex) (= Y4 tptp.zero_zero_complex)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X2) Y4)) (@ (@ tptp.times_times_complex (@ tptp.cnj X2)) (@ tptp.cnj Y4)))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.divide1717551699836669952omplex X2) Y4)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cnj X2)) (@ tptp.cnj Y4)))))
% 7.01/7.34 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 7.01/7.34 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z4 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z4) (@ tptp.cnj Z4)))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B3))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (= tptp.code_int_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K2)))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 7.01/7.34 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K2) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K2)))))))
% 7.01/7.34 (assert (= tptp.code_num_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X2) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X2) Xa2)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K2)) (@ tptp.code_int_of_integer L2)))))
% 7.01/7.34 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K2) L2)) (@ (@ tptp.modulo364778990260209775nteger K2) L2)))))
% 7.01/7.34 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K2)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (= tptp.code_nat_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 7.01/7.34 (assert (= tptp.code_divmod_abs (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 7.01/7.34 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 7.01/7.34 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 7.01/7.34 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K2)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S6)))))) _let_1))))))))))))
% 7.01/7.34 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 7.01/7.34 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M6) N)))) M)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M6)))) M)))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N))))))
% 7.01/7.34 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 7.01/7.34 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M2 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M2) K2)) (@ (@ tptp.product_Pair_nat_nat M2) (@ (@ tptp.minus_minus_nat K2) M2))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M2) _let_1)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y4) (and (=> _let_2 (= Y4 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_2) (= Y4 (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 7.01/7.34 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.34 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_integer K) L)) (@ (@ tptp.divide6298287555418463151nteger K) L))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc8508995932063986495nteger (@ (@ tptp.code_divmod_abs K) L)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L)))))
% 7.01/7.34 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R2)))))
% 7.01/7.34 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ (@ tptp.divide_divide_nat M2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))))))))
% 7.01/7.34 (assert (forall ((Y4 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y4) (@ (@ tptp.modulo_modulo_nat X2) Y4)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y4) (= (@ (@ tptp.bezw X2) Y4) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Y4)))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y4) (and (=> _let_3 (= Y4 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y4 (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y4 tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) Y4) (=> _let_1 (not (=> (and (=> _let_4 (= Y4 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y4 (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X2) Xa2)))))))) (not _let_1)))))))))))
% 7.01/7.34 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X2)) (@ (@ tptp.times_times_int V2) Y4)) (@ (@ tptp.gcd_gcd_int X2) Y4)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 7.01/7.34 (assert (forall ((Y4 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y4) (= (@ (@ tptp.gcd_gcd_int X2) Y4) (@ (@ tptp.gcd_gcd_int Y4) (@ (@ tptp.modulo_modulo_int X2) Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I2) (@ P I2))) (@ P K3)))) (@ P M)))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ tptp.suc X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y4) (=> _let_1 (not (=> (and (=> _let_3 (= Y4 (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_3) (= Y4 (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 7.01/7.34 (assert (forall ((S3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S3) (exists ((R3 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R3) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S3))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N7)) S3))))))))
% 7.01/7.34 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L2) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K2) (@ tptp.sgn_sgn_Code_integer L2))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S6 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L2)) S6)))))) _let_1))))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 7.01/7.34 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 7.01/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 7.01/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X4))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X4))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 7.01/7.34 (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))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X2) Y4))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X2) Y4)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X2))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y4)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 X2)) (=> (not _let_2) (= Y4 (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2))))) (not _let_1)))))))))
% 7.01/7.34 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ 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 ((U2 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 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X2)))))
% 7.01/7.34 (assert (forall ((Z tptp.int)) (not (forall ((X4 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X4) Y3))))))))
% 7.01/7.34 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 7.01/7.34 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 7.01/7.34 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X))) X2)))))
% 7.01/7.34 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0))) Xa2) X2))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ 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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))) Xa2) X2)))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ 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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))) Xa2) X2)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((Q3 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q3)) Q3)))
% 7.01/7.34 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 7.01/7.34 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y tptp.nat) (Z4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y) V4)) (@ (@ tptp.plus_plus_nat U2) Z4)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 7.01/7.34 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X))))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit1 Y4)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y4))) X2)))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 7.01/7.34 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 7.01/7.34 (assert (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit0 Y4)) (@ tptp.sqr (@ _let_1 Y4))))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 7.01/7.34 (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 ((U2 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 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0))))))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0))))))
% 7.01/7.34 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 7.01/7.34 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.rat Bool)) (Q3 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ P (@ (@ tptp.fract A5) B5)))) (@ P Q3))))
% 7.01/7.34 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.gcd_gcd_int A) B))) (= (@ (@ tptp.fract (@ (@ tptp.divide_divide_int A) _let_1)) (@ (@ tptp.divide_divide_int B) _let_1)) (@ (@ tptp.fract A) B)))))
% 7.01/7.34 (assert (= tptp.fract (lambda ((K2 tptp.int) (L2 tptp.int)) (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K2)) (@ tptp.ring_1_of_int_rat L2)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 7.01/7.34 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 7.01/7.34 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 7.01/7.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 7.01/7.34 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (=> (@ tptp.positive X2) (=> (@ tptp.positive Y4) (@ tptp.positive (@ (@ tptp.times_times_rat X2) Y4))))))
% 7.01/7.34 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y) X)))))
% 7.01/7.34 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M2 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M2)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 7.01/7.34 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M2 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 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 ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X))) A3))) (@ (@ tptp.product_Pair_nat_num N2) M2)))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 tptp.none_num)))) (let ((_let_2 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y4) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) (not (= Y4 (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num _let_1))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N3)))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))))))))))))))))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y4) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y4 tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit1 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (=> (= Xa2 tptp.one) (not (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))))))))))))))))))))
% 7.01/7.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 7.01/7.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num (@ tptp.bit0 N)))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num (@ tptp.bit1 N)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (not (= Y4 (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y4 tptp.none_num)))) (let ((_let_5 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y4) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa2 (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M4 tptp.num)) (= X2 (@ tptp.bit0 M4))) (=> _let_2 _let_4)) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (=> (=> (exists ((M4 tptp.num)) (= X2 (@ tptp.bit1 M4))) _let_3) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 N3)) (not (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 N3)) (not (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3)))))))))))))))))))))))))
% 7.01/7.34 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N)) (@ tptp.some_num tptp.one))))
% 7.01/7.34 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N)) tptp.none_num)))
% 7.01/7.34 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 7.01/7.34 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q3) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 7.01/7.34 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q3) tptp.zero_z5237406670263579293d_enat)))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N)) Q3) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N) Q3)))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N) Q3)) (@ (@ tptp.ord_min_nat (@ _let_1 N)) (@ _let_1 Q3))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M6) N)))) M))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N) M6)))) M))))
% 7.01/7.34 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 7.01/7.34 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M2) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 7.01/7.34 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X2) Xa2))) (=> (= (@ (@ tptp.upto X2) Xa2) Y4) (=> _let_1 (not (=> (and (=> _let_2 (= Y4 (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y4 tptp.nil_int))) (not _let_1)))))))))
% 7.01/7.34 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 7.01/7.34 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 7.01/7.34 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 7.01/7.34 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 7.01/7.34 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I4) J3)) __flatten_var_0))))
% 7.01/7.34 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I4) J3) tptp.nil_int))))
% 7.01/7.34 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 7.01/7.34 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) J3)))))
% 7.01/7.34 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J3)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))) tptp.nil_int))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y4 tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X2) Xa2))) (=> (= (@ (@ tptp.upto X2) Xa2) Y4) (and (=> _let_1 (= Y4 (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y4 tptp.nil_int)))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))))))))
% 7.01/7.34 (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)))))))))))))
% 7.01/7.34 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((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 X2) H4))) (@ F X2)))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((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 X2)) (@ F (@ (@ tptp.minus_minus_real X2) H4))))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((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 X2)) (@ F (@ (@ tptp.plus_plus_real X2) H4))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((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 X2) H4))) (@ F X2)))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real L) 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 X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (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 X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (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 X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real L) 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 X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F3 Z2)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D) (= (@ F X2) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X2)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X2)))) (= L tptp.zero_zero_real))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (S2 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 X2) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X2) S2))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((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 X2)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 7.01/7.34 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z4 tptp.real)) (@ (@ tptp.powr_real Z4) 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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((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)))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) 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)))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (A4 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A4))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (A4 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A4)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (A4 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A4)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 7.01/7.34 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))
% 7.01/7.34 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 7.01/7.34 (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) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 7.01/7.34 (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) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 7.01/7.34 (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) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T4) (@ (@ tptp.ord_less_eq_real T4) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real H2) T4) (@ (@ tptp.ord_less_real T4) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real H2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 7.01/7.34 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T4))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N)))))))))))))
% 7.01/7.34 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T4)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real X2) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X2) N))))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (=> (not (= X2 C)) (exists ((T4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T4))) (let ((_let_2 (@ tptp.ord_less_real X2))) (let ((_let_3 (@ _let_2 C))) (and (=> _let_3 (and (@ _let_2 T4) (@ _let_1 C))) (=> (not _let_3) (and (@ (@ tptp.ord_less_real C) T4) (@ _let_1 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) N))))))))))))))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real C) T4) (@ (@ tptp.ord_less_real T4) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T4) (@ (@ tptp.ord_less_eq_real T4) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (exists ((T4 tptp.real)) (and (@ (@ tptp.ord_less_real A) T4) (@ (@ tptp.ord_less_real T4) C) (= (@ F A) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M2) C)) (@ tptp.semiri2265585572941072030t_real M2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M2)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T4)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 7.01/7.34 (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) (T4 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T4)) (@ (@ tptp.topolo2177554685111907308n_real T4) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M5 tptp.nat) (T7 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) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M5))) (@ (@ tptp.minus_minus_real (@ (@ Diff M5) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M5) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M5)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T7) P5)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B4) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real T7) _let_2)) (@ tptp.semiri2265585572941072030t_real _let_2)))))) (@ (@ tptp.topolo2177554685111907308n_real T7) tptp.top_top_set_real))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K2)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.times_times_nat K2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 7.01/7.34 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X4) 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)))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real) (Y4 tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X2) _let_1) (=> (@ (@ tptp.member_real Y4) _let_1) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (= (@ F X2) (@ F Y4)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F3 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F3 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ F X) N3))) (@ (@ F3 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X4)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X4 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X4) N3)) (@ (@ F Y3) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y3)))))))) (@ (@ (@ 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)))))))))))
% 7.01/7.34 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L)))))
% 7.01/7.34 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X3 tptp.real)) (=> (and (not (= X3 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X3))) R3)) (@ (@ tptp.ord_less_real (@ F X3)) tptp.zero_zero_real)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X3 tptp.real)) (=> (and (not (= X3 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X3))) R3)) (not (= (@ F X3) tptp.zero_zero_real))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (forall ((X3 tptp.real)) (=> (and (not (= X3 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X3))) R3)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X3))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (X2 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (= (@ G (@ F Z2)) Z2)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcosh_real))))
% 7.01/7.34 (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)))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X2)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X2) (=> (@ (@ tptp.ord_less_real X2) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arccos)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcsin)))))
% 7.01/7.34 (assert (forall ((B tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X2) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) (@ (@ tptp.set_or1633881224788618240n_real B) X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X2)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.artanh_real)))))
% 7.01/7.34 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 7.01/7.34 (assert (forall ((D tptp.real) (X2 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X2))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X2))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X2)) tptp.top_top_set_real)) G))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z2) (=> (@ (@ tptp.ord_less_eq_real Z2) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) G)))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z2) (=> (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 Z2)) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F3 C3))))))))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N7 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 7.01/7.34 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R3) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.01/7.34 (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))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))
% 7.01/7.34 (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)))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N7)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.01/7.34 (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)))
% 7.01/7.34 (assert (forall ((X2 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 X2) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_nat)))
% 7.01/7.34 (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)))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))))
% 7.01/7.34 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K3 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 7.01/7.34 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K3 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) 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 X2) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat)))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))))) tptp.at_top_nat))))))
% 7.01/7.34 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I4)) (@ A I4)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 7.01/7.34 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F4 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F4 (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C2)))))))
% 7.01/7.34 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 7.01/7.34 (assert (forall ((X2 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 X2) Y))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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))
% 7.01/7.34 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) B) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 B))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))
% 7.01/7.34 (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)))
% 7.01/7.34 (assert (forall ((X2 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 X2) Y))) Y))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_real)))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X4) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 B))))))
% 7.01/7.34 (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))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 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 (@ F3 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))))))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I4) K)))) tptp.at_top_nat))))
% 7.01/7.34 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F5)))))
% 7.01/7.34 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P N2)))))))
% 7.01/7.34 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X4) (@ P X4))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 7.01/7.34 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((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) (@ F3 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 (@ F3 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))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((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) (@ F3 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 (@ F3 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))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5984915006950818249n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ (@ (@ 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) (@ F3 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 (@ F3 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))))))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (X2 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X2))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (not (= (@ G2 X) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 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 (@ F3 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))))))))))
% 7.01/7.34 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (X2 tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((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) (@ F3 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 (@ F3 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))))))))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (A tptp.real) (G (-> tptp.real tptp.real)) (F3 (-> 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) (@ F3 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 (@ F3 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)))))))))
% 7.01/7.34 (assert (forall ((G (-> tptp.real tptp.real)) (X2 tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real)) (Y4 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) (@ tptp.set_or5849166863359141190n_real X2)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y4))) (=> (@ (@ (@ 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) (@ F3 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 (@ F3 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))))))))))
% 7.01/7.34 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 7.01/7.34 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 7.01/7.34 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y4) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= Y4 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y4 (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ 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 TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _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) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _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) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))
% 7.01/7.34 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ 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 TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) 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)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima2)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (=> (exists ((Uu Bool) (Uv Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _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) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X4) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _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) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _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) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y4 Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y4) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu Bool) (Uv Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu) Uv))) (=> (= X2 _let_1) (=> (= Y4 (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X2 _let_1) (=> (= Y4 (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ 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 TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X5))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X5)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I4))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X5 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X5)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _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) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) 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) Xa2)))))))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) G))) (=> (forall ((X4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X4) (@ (@ tptp.ord_less_real X4) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F3 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (= (@ F3 Z2) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F3 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F3 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y5) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (exists ((Y5 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y5) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (= (@ F X2) (@ F A)))))))))
% 7.01/7.34 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))))))))
% 7.01/7.34 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 7.01/7.34 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M2)) M2))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 7.01/7.34 (assert (forall ((N5 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N5)))
% 7.01/7.34 (assert (forall ((N5 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N5) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) K))) N5))))
% 7.01/7.34 (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))))))))))))
% 7.01/7.34 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 7.01/7.34 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I) J)) I))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))))
% 7.01/7.34 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 7.01/7.34 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M2)))))
% 7.01/7.34 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I4) J3)))))
% 7.01/7.34 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M2))))))
% 7.01/7.34 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 7.01/7.34 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M2))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q3)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q3))))))
% 7.01/7.34 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((I tptp.nat) (J tptp.nat) (X2 tptp.nat) (Xs2 tptp.list_nat)) (= (= (@ (@ tptp.upt I) J) (@ (@ tptp.cons_nat X2) Xs2)) (and (@ (@ tptp.ord_less_nat I) J) (= I X2) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat)) J) Xs2)))))
% 7.01/7.34 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) N))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N5))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N5)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N5))))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N5 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N5))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N5) M)) tptp.one_one_nat)) N5))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N))))
% 7.01/7.34 (assert (forall ((I tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I) J))))
% 7.01/7.34 (assert (forall ((M tptp.int) (N tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (or (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N)) (= (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.power_int_real X2) N))))))
% 7.01/7.34 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M2 tptp.nat) (N2 tptp.nat)) (= N2 (@ tptp.suc M2)))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (N2 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.semiri5074537144036343181t_real N2))) (not (= N2 tptp.zero_zero_nat))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X2) X4) (@ (@ tptp.ord_less_real X4) Y4))))))
% 7.01/7.34 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I4 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I4)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 7.01/7.34 (assert (forall ((F (-> tptp.real tptp.real)) (F3 (-> tptp.real tptp.real))) (=> (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F3 X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F3 X4))) (@ tptp.order_7092887310737990675l_real F)))))
% 7.01/7.34 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N) (@ F N)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat tptp.zero_zero_nat) A4)) (@ _let_1 A4)))))
% 7.01/7.34 (assert (forall ((F5 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.vimage_nat_nat tptp.suc) F5)) (@ tptp.finite_finite_nat F5))))
% 7.01/7.34 (assert (forall ((N tptp.nat) (A4 tptp.set_nat)) (let ((_let_1 (@ tptp.vimage_nat_nat tptp.suc))) (= (@ _let_1 (@ (@ tptp.insert_nat (@ tptp.suc N)) A4)) (@ (@ tptp.insert_nat N) (@ _let_1 A4))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat)) (= (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.vimage_nat_nat tptp.suc) (@ tptp.nat_set_decode X2)))))
% 7.01/7.34 (assert (forall ((A4 tptp.set_nat)) (= (@ tptp.nat_set_encode (@ (@ tptp.vimage_nat_nat tptp.suc) A4)) (@ (@ tptp.divide_divide_nat (@ tptp.nat_set_encode A4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ tptp.field_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y)))))) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 7.01/7.34 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 7.01/7.34 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))) (lambda ((Uu3 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.01/7.34 (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))))
% 7.01/7.34 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 7.01/7.34 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 7.01/7.34 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M2 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M2) N2))) M2)))))
% 7.01/7.34 (assert (forall ((X2 tptp.list_nat) (Y4 tptp.nat)) (=> (= (@ tptp.nat_list_encode X2) Y4) (=> (=> (= X2 tptp.nil_nat) (not (= Y4 tptp.zero_zero_nat))) (not (forall ((X4 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X2 (@ (@ tptp.cons_nat X4) Xs3)) (not (= Y4 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs3)))))))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)) (lambda ((Uu3 tptp.nat)) (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X tptp.nat) (Y tptp.nat)) (and (@ (@ tptp.ord_less_nat X) N) (@ (@ tptp.ord_less_nat Y) N) (@ (@ tptp.ord_less_eq_nat X) Y))))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) N))))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Xs2 tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X2) Xs2)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X2) (@ tptp.nat_list_encode Xs2)))))))
% 7.01/7.34 (assert (forall ((X2 tptp.list_nat) (Y4 tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X2) Y4) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.nil_nat) (=> (= Y4 tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X4 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X4) Xs3))) (=> (= X2 _let_1) (=> (= Y4 (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 7.01/7.34 (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)))))))))
% 7.01/7.34 (assert (forall ((Q3 tptp.int) (P2 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P2) Q3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3) (=> (@ (@ tptp.algebr932160517623751201me_int P2) Q3) (= (@ tptp.normalize _let_1) _let_1))))))
% 7.01/7.34 (assert (forall ((Q3 tptp.rat)) (not (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= Q3 (@ (@ tptp.fract A5) B5)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (not (@ (@ tptp.algebr932160517623751201me_int A5) B5))))))))
% 7.01/7.34 (assert (forall ((P (-> tptp.rat Bool)) (Q3 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 Q3))))
% 7.01/7.34 (assert (forall ((A tptp.int) (D tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int D))) (let ((_let_2 (@ tptp.abs_abs_int C))) (let ((_let_3 (@ tptp.abs_abs_int B))) (let ((_let_4 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.algebr932160517623751201me_int A) D) (=> (@ (@ tptp.algebr932160517623751201me_int B) C) (= (= (@ (@ tptp.times_times_int _let_4) _let_2) (@ (@ tptp.times_times_int _let_3) _let_1)) (and (= _let_4 _let_3) (= _let_2 _let_1)))))))))))
% 7.01/7.34 (assert (forall ((Q3 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= Q3 (@ (@ 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)))))) (= Q3 tptp.zero_zero_rat))))
% 7.01/7.34 (assert (forall ((R2 tptp.rat)) (exists ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X4))) (let ((_let_2 (@ tptp.product_fst_int_int X4))) (and (= R2 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((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 X4)))))))))))
% 7.01/7.34 (assert (forall ((A tptp.nat) (B tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X2))) (=> (@ (@ tptp.algebr934650988132801477me_nat A) B) (=> (@ _let_1 A) (=> (@ _let_1 B) (= X2 tptp.one_one_nat)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc tptp.zero_zero_nat))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc tptp.zero_zero_nat)) N)))
% 7.01/7.34 (assert (forall ((A tptp.nat) (D tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.algebr934650988132801477me_nat A) D) (=> (@ (@ tptp.algebr934650988132801477me_nat B) C) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) D)) (and (= A B) (= C D)))))))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat (@ tptp.suc N)) N)))
% 7.01/7.34 (assert (forall ((N tptp.nat)) (@ (@ tptp.algebr934650988132801477me_nat N) (@ tptp.suc N))))
% 7.01/7.34 (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))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real) (not (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (=> (= (@ tptp.abs_abs_real X2) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M4)) (@ tptp.semiri5074537144036343181t_real N3))) (not (@ (@ tptp.algebr934650988132801477me_nat M4) N3)))))))))
% 7.01/7.34 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X tptp.nat)) X)) _let_1) _let_1))))
% 7.01/7.34 (assert (forall ((I tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X tptp.int)) X)) _let_1) _let_1))))
% 7.01/7.34 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (Y7 (-> tptp.nat tptp.rat))) (=> (exists ((A8 tptp.rat)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A8) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N3))) A8)))) (=> (@ tptp.vanishes Y7) (@ tptp.vanishes (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_rat (@ X8 N2)) (@ Y7 N2))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y4) (exists ((Q2 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q2))) (and (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real _let_1) Y4)))))))
% 7.01/7.34 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.vanishes X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K3 tptp.nat)) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N7))) R2))))))))
% 7.01/7.34 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (exists ((K4 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X8 N3))) R3)))))) (@ tptp.vanishes X8))))
% 7.01/7.34 (assert (= tptp.vanishes (lambda ((X5 (-> tptp.nat tptp.rat))) (forall ((R5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R5) (exists ((K2 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ X5 N2))) R5)))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_int_int) (X2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X2))) (let ((_let_2 (@ tptp.product_snd_int_int Xa2))) (=> (@ (@ tptp.ratrel Xa2) Xa2) (=> (@ (@ tptp.ratrel X2) X2) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa2)) (@ tptp.abs_Rat X2)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa2)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X2) X2) (= (@ tptp.positive (@ tptp.abs_Rat X2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X2)) (@ tptp.product_snd_int_int X2)))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (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))))))))
% 7.01/7.34 (assert (forall ((Xa2 tptp.product_prod_int_int) (X2 tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa2) Xa2) (=> (@ (@ tptp.ratrel X2) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa2)) (@ tptp.abs_Rat X2)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa2)) (@ tptp.product_fst_int_int X2))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa2)) (@ tptp.product_snd_int_int X2)))))))))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (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))))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num (@ tptp.bit1 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit1 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit0 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) _let_1))))))))) (=> (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.some_num (@ tptp.bit0 M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))) (not (forall ((M4 tptp.num)) (=> (= X2 (@ tptp.bit1 M4)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa2 _let_1) (=> (= Y4 (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M4) N3))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) _let_1))))))))))))))))))))))))
% 7.01/7.34 (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)))))))
% 7.01/7.34 (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))))))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_int) tptp.ord_less_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)))) tptp.divide_divide_nat) tptp.divide_divide_nat))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)))) tptp.divide_divide_int) tptp.divide_divide_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re711492959462206631nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3))) (lambda ((Y6 tptp.int) (Z3 tptp.int)) (= Y6 Z3)))) tptp.times_times_int) tptp.times_times_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)))) tptp.times_times_nat) tptp.times_times_nat))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) tptp.suc) tptp.suc))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re1345281282404953727at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re5653821019739307937at_nat (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3)))) tptp.plus_plus_nat) tptp.plus_plus_nat))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y4 tptp.num)) (let ((_let_1 (= X2 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y4) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X2) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y4 tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y4 _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (=> (= Y4 tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X2 (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y4 (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 7.01/7.34 (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))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3))) (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))
% 7.01/7.34 (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))
% 7.01/7.34 (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 ((U2 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 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 7.01/7.34 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y6 tptp.nat) (Z3 tptp.nat)) (= Y6 Z3))) tptp.pcr_int) (lambda ((N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re7400052026677387805at_int tptp.pcr_int) tptp.pcr_int) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X)))) tptp.uminus_uminus_int))
% 7.01/7.34 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_int))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))) tptp.plus_plus_int))
% 7.01/7.34 (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 ((U2 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 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __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 ((U2 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 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0)))))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X2) Y4)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X2) V) (@ (@ tptp.plus_plus_nat U) Y4)))))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re2241393799969408733at_nat tptp.intrel) tptp.intrel) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X)))) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y) X)))))
% 7.01/7.34 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 7.01/7.34 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X) V4) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) 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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 7.01/7.34 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y6 Bool) (Z3 Bool)) (= Y6 Z3)))) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) 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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y)))) __flatten_var_0)))))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ 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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y) V4)))) __flatten_var_0)))))
% 7.01/7.34 (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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __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 ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y) U2)))) __flatten_var_0)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.re (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.cos_real A)))))
% 7.01/7.34 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.im (@ (@ tptp.rcis R2) A)) (@ (@ tptp.times_times_real R2) (@ tptp.sin_real A)))))
% 7.01/7.34 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.times_times_real R1) R22)) (@ (@ tptp.plus_plus_real A) B)))))
% 7.01/7.34 (assert (forall ((R1 tptp.real) (A tptp.real) (R22 tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.rcis R1) A)) (@ (@ tptp.rcis R22) B)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real R1) R22)) (@ (@ tptp.minus_minus_real A) B)))))
% 7.01/7.34 (assert (= tptp.rcis (lambda ((R5 tptp.real) (A3 tptp.real)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R5)) (@ tptp.cis A3)))))
% 7.01/7.34 (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)))))
% 7.01/7.34 (assert (forall ((X8 (-> tptp.nat tptp.rat)) (R2 tptp.rat)) (=> (@ tptp.cauchy X8) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (exists ((K3 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) M5) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N7) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M5)) (@ X8 N7)))) R2))))))))))
% 7.01/7.34 (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 ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K4) N3) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ X8 M4)) (@ X8 N3)))) R3)))))))) (@ tptp.cauchy X8))))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.int) (Y4 tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.nat) (Y4 tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.num) (Y4 tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.rat) (Y4 tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.real) (Y4 tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X5 tptp.real)) (@ P X5)))))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.complex) (Y4 tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.extended_enat) (Y4 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.extended_enat) (Y4 tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.code_integer) (Y4 tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.vEBT_VEBT) (Y4 tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.list_int) (Y4 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.list_int) (Y4 tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.list_nat) (Y4 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.list_nat) (Y4 tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y4 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y4 (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.option_nat) (Y4 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.option_nat) (Y4 tptp.option_nat)) (= (@ (@ (@ tptp.if_option_nat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.option_num) (Y4 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.option_num) (Y4 tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.product_prod_int_int) (Y4 tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y4 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y4 tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X2) Y4) X2)))
% 7.01/7.34 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 7.01/7.34 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y4 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X2) Y4) Y4)))
% 7.01/7.34 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y4 tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X2) Y/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 11744 Alarm clock ( read result; case "$result" in
% 299.59/300.11 unsat)
% 299.59/300.11 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.59/300.11 ;;
% 299.59/300.11 sat)
% 299.59/300.11 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.59/300.11 ;;
% 299.59/300.11 esac; exit 1 )
% 299.59/300.11 Alarm clock
% 299.59/300.11 % cvc5---1.0.5 exiting
% 299.59/300.12 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------